การประมวลผลสัญญาณสำหรับการจัดเก็บข้อมูลดิจิทัล เล่ม 2: การออกแบบวงจรภาครับ

128 ÈÙ¹Âàì ·¤â¹âÅÂÕÍÔàÅç¡·Ã͹¡Ô Êàì àÅФÍÁ¾ÇÔ àµÍÃìààËè§ªÒµÔ -1 0 -1 -1 0 -1.5061 2 2 -2 1 -1 0.4939 -1 1 -0.4939 10 -2 1.5061 (a) 11 0 ak = -1 ak = 1 (b)ÃÙ»·Õ‹ 6.7: á¼¹ÀÒ¾à·ÃÅÅÔʢͧ (a) ·ÒÃìà¡çµ H (D) = 1 − D áÅÐ (b) ·ÒÃìà¡çµ»ÃÐÊ·Ô ¸¼Ô Å Heff (D)= 1 − 0.247D − 0.753D2 ·‹ãÕ ªé㹡ÒöʹÃËÑÊ¢Íé ÁÙŢͧÃкº PRML áÅÐ NPML µÒÁÅӴѺ 0 0.29 0.29 0.64 0.93 1.04 1.97 0.35 2.32 2.24-1 0.96 0 0 0.29 0.29 0.64 0.93 1.89 0.35 2.24 3.92 6.161 ÃÙ»·‹Õ 6.8: á¼¹ÀÒ¾ÊÃØ»¢Œ¹Ñ µÍ¹¡Ò÷ӧҹ¢Í§Ç§¨ÃµÃǨËÒÇÕà·Íúì ÔÊÓËÃºÑ Ãкº PRML¨Ò¡¹Ñ¹Œ ÅÓ´ºÑ ¢éÍÁÙÅ {zk} ¨Ð¶¡Ù ¶Í´ÃËÑÊ¢Íé ÁÙÅ´éÇÂǧ¨ÃµÃǨËÒÇàÕ ·ÍÃìºÔ··‹Õ Ó§Ò¹â´Âãªéá¼¹ÀÒ¾à·ÃÅÅÊÔ ·ÊՋ ÃéÒ§¨Ò¡·ÒÃàì ¡çµ»ÃÐÊ·Ô ¸Ô¼Å Heff (D) = H(D)[1 − P (D)] = 1 − 0.247D − 0.753D2µÒÁ·Õ‹áÊ´§ã¹ÃÙ»·‹Õ 6.6(b) â´Â·‹Õ ¢¹ŒÑ µÍ¹¡ÒöʹÃËÊÑ ¢éÍÁÙÅ {zk} ÊÒÁÒöÊÃ»Ø ä´éµÒÁÃÙ»·Õ‹ 6.9

6.5. ¼Å¡Ò÷´Åͧ 129 0 0.29 0.29 0.15 0.45 2.63 3.08 0.03 3.11 1.88 0.24-1 -1 0.14 0.84 0 1.07 0.01 0.59 4.59 9.56 0 4.181 -1 0 0.79 0.45 8.52 3.94 4.48 6.19 0 1.07 0 0.01 1.86 4.49 0.10 0.24-1 1 0.01 0.18 0.26 1.04 0 0.29 0.29 0.15 0.45 0.03 0.03 0.06 5.88 5.93 2.22 8.1611ÃÙ»·‹Õ 6.9: á¼¹ÀÒ¾ÊÃØ»¢Ñ¹Œ µÍ¹¡Ò÷ӧҹ¢Í§Ç§¨ÃµÃǨËÒÇÕà·Íúì ÔÊÓËÃºÑ Ãкº NPMLà¹×͋ §¨Ò¡ ¤Òè àÁµÃÔ¡àÊ¹é ·Ò§·‹Õ¹éÍÂ·Õ‹Ê´Ø ¤×Í ¤Òè 0.24 à¾ÃÒЩйь¹ ǧ¨ÃµÃǨËÒÇàÕ ·ÍÃìºÔ¨Ð¶Í´ÃËÑÊ¢éÍÁÙÅâ´Â¡ÒÃÁͧÂÍé ¹¡ÅѺ仵ÒÁàÊé¹·Ò§·‹ÕÂѧÁÕªÇÕ µÔ ÍÂÙ跋ÕÁÒ¶Ö§ ³ ¨´Ø µèÍ·‹ÕÁÕ¤Òè àÁµÃ¡Ô àÊ¹é ·Ò§à·Òè ¡ºÑ0.24 «§‹Ö ¨Ð¾ºÇÒè ¤Òè »ÃÐÁÒ³¢Í§ÅÓ´ºÑ ¢éÍÁÙÅÍÔ¹¾µØ {aˆk} ·Ê‹Õ Í´¤Åéͧ¡ÑºàÊé¹·Ò§·‹Õ处 ÁªÕ ÕÇµÔ ÍÂÙè¹ÕŒ ¤Í× {aˆk} = {aˆ0, aˆ1, aˆ2, aˆ3} = {−1, 1, 1, 1}«§‹Ö ÁÕ¤Òè µÃ§¡ºÑ ÅÓ´ºÑ ¢Íé ÁÙÅÍ¹Ô ¾Øµ {ak} = {−1, 1, 1, 1} ·Õ‹Êè§ÁÒ¨Ò¡µé¹·Ò§ ´Ñ§¹ÑŒ¹ ¡ÒöʹÃËÑÊ´Çé Âǧ¨ÃµÃǨËÒ NPML ã¹µÑÇÍÂèÒ§¢é͹Ռ ¨Ö§äÁÁè Õ¢éͼ´Ô ¾ÅÒ´à¡´Ô ¢¹ŒÖ6.5 ¼Å¡Ò÷´Åͧã¹ÊÇè ¹¹ŒÕ¨Ð·Ó¡ÒÃà»ÃÂÕ ºà·ÂÕ º»ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ç§¨ÃµÃǨËÒ PRML áÅÐ NPML â´Âãªáé ºº¨ÓÅͧªÍè §Ê­Ñ ­Ò³¢Í§Ãкº¡Òúѹ·Ö¡áººá¹Ç¹Í¹ (longitudinal recording) µÒÁû٠·Õ‹ 6.10 â´Â·‹Õ

130 ȹ٠Âàì ·¤â¹âÅÂÍÕ àÔ Å¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÇÔ àµÍÃìààË§è ªÒµÔ n(t)ak 1− D bk g(t) p(t) s(t) sk equalizer yk detector aˆk{±1} 2 LPF tk = kT ÃÙ»·‹Õ 6.10: Ẻ¨ÓÅͧªÍè §Ê­Ñ ­Ò³¢Í§Ãкº¡Òúѹ·Ö¡áÁàè ËÅ¡çÊÑ­­Ò³ readback ÊÒÁÒöà¢Õ¹ãËÍé ÂãÙè ¹Ã»Ù ¢Í§ÊÁ¡Òä³µÔ ÈÒʵÃìä´é ¤Í× (6.25) S−1 p(t) = bkg(t − kT ) + n(t) k=0àÁÍ‹× bk = (ak − ak−1)/2 ¤×Í ºµÔ à»ÅÕ‹ ¹Ê¶Ò¹Ð (bk = ±1 ÊÍ´¤Åéͧ¡ºÑ ¡ÒÃà»ÅÂՋ ¹á»Å§Ê¶Ò¹ÐºÇ¡ËÃÍ× Åº áÅÐ bk = 0 ËÁÒ¶§Ö äÁèÁÕ¡ÒÃà»ÅÂՋ ¹á»Å§Ê¶Ò¹Ð), ak ∈ ±1 ¤Í× ºµÔ ÍÔ¹¾µØ ·Õ‹Áըӹǹ·ÑŒ§ËÁ´ S = 4096 ºµÔ ËÃÍ× 1 à«¡àµÍÃì (sector), g(t) ¤Í× Ê­Ñ ­Ò³¾ÅÑ Êìà»ÅÂՋ ¹Ê¶Ò¹Ð µÒÁÊÁ¡ÒÃ(1.1), áÅÐ n(t) ¤Í× Ê­Ñ ­Ò³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇẺºÇ¡·Õ‹ÁÕ¤ÇÒÁ˹Òá¹¹è Ê໡µÃÑÁ¡ÓÅ§Ñ áººÊͧ´éÒ¹à·Òè ¡ºÑ N0/2 ÊÑ­­Ò³ readback p(t) ¨Ð¶Ù¡Ê觼èÒ¹ä»Â§Ñ ǧ¨Ã¡Ãͧ¼èÒ¹µ‹ÓºµÑ à·ÍÃìàÇÃÔ ìµÍ¹Ñ ´ºÑ ·Õ‹ 7 áÅж¡Ù ·Ó¡Òê¡Ñ µÇÑ ÍÂèÒ§´Çé ¤ÇÒÁ¶‹Õ¡ÒêѡµÇÑ ÍÂÒè §à·Òè ¡Ñº 1/T â´ÂÊÁÁصÔÇÒè ¡Ãкǹ¡ÒÃ㹡ÒêѡµÇÑ ÍÂèÒ§ÁÕ¡ÒÃà¢éÒ¨§Ñ ËÇÐÃÐËÇÒè §ÊÑ­­Ò³ readback áÅÐǧ¨Ãª¡Ñ µÇÑ ÍÂèҧẺÊÁºÃÙ ³ì (perfect synchronization) ¨Ò¡¹Œ¹Ñ ÅӴѺ¢éÍÁÅÙ àÍÒµì¾Øµ {sk}¨Ð¶¡Ù »Í‡ ¹ä»ÂѧÍÕ¤ÇÍäÅà«ÍÃì (equalizer) à¾×‹Í»ÃºÑ û٠ÃèÒ§¢Í§Ê­Ñ ­Ò³ãËé໚¹ä»µÒÁ·ÒÃìà¡çµ·‹ÕµÍé §¡Òà áÅéÇ¡çʧè ÅÓ´ºÑ ¢éÍÁÙÅàÍÒµì¾Øµ {yk} ·Õ‹ä´é ä»·Ó¡ÒöʹÃËÊÑ¢éÍÁÅÙ ´Çé Âǧ¨ÃµÃǨËÒ (detector) ྋ×ÍËÒ¤Òè »ÃÐÁÒ³¢Í§ÅÓ´ºÑ ¢éÍÁÅÙ ÍÔ¹¾µØ {ak} ·‹Õ໚¹ä»ä´éÁÒ¡·Õʋ ´Ø ã¹·Õ¹‹ Ռ ¤Òè SNR ·ã‹Õ ªé¨Ð¹ÂÔ ÒÁâ´Â SNR = 10 log10 Vp2 (dB) (6.26) σ2àÁ‹×Í Vp = 1 ¤×Í ¢¹Ò´ÊÙ§ÊØ´¢Í§Ê­Ñ ­Ò³¾ÑÅÊìà»Å‹ÂÕ ¹Ê¶Ò¹ÐàÍ¡à·È (isolated transition pulse)áÅÐ σ2 = N0/(2T ) ¤Í× ¡ÓÅ§Ñ ¢Í§ÊÑ­­Ò³Ãº¡Ç¹ n(t) ¹Í¡¨Ò¡¹ÕŒ áµÅè Шش¢Í§ÍѵÃÒ¢éͼԴ¾ÅÒ´

6.5. ¼Å¡Ò÷´Åͧ 131 10−1 10−2BER 10−3 10−4 PRML: 22 states NPML (2−tap predictor): 24 states NPML (4−tap predictor): 26 states 10−5 10 11 12 13 14 15 16 SNR (dB) û٠·Õ‹ 6.11: »ÃÐÊÔ·¸ÀÔ Ò¾¢Í§ÃкºµÒè §æ ·Õ‹ ND = 2ºÔµ (BER) ¨Ð¶Ù¡¤Ó¹Ç³â´Âãªé¢Íé ÁÙÅËÅÒÂæ à«¡àµÍÃì ¨¹¡ÇèÒ¨Ðä´é¢Íé ¼Ô´¾ÅÒ´ºµÔ ÁÒ¡¡ÇèÒËÃÍ× à·èÒ¡ºÑ 1000 ºÔµ ÃÙ»·‹Õ 6.11 à»ÃÂÕ ºà·ÂÕ º»ÃÐÊÔ·¸ÀÔ Ò¾¢Í§Ç§¨ÃµÃǨËÒ PRML áÅÐ NPML ·‹Õ ND = 2 àÁ׋͡Ó˹´ãËé·Ø¡Ãкºãªé·ÒÃàì ¡µç Ẻ PR4, H (D) = 1 − D2 à¾ÃÒЩйѹŒ ¨Ó¹Ç¹Ê¶Ò¹Ð·§ŒÑ ËÁ´·Õ‹ãªéã¹á¼¹ÀÒ¾à·ÃÅÅÔʢͧǧ¨ÃµÃǨËÒ PRML ¤×Í 22 = 4 ʶҹР㹢³Ð·Õ‹ ¨Ó¹Ç¹Ê¶Ò¹Ð·ÑŒ§ËÁ´·Õ‹ãªãé ¹á¼¹ÀÒ¾à·ÃÅÅÊÔ ¢Í§Ç§¨ÃµÃǨËÒ NPML ¤Í× 22+2 = 16 ʶҹР(ÊÓËÃºÑ Ç§¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·ç») áÅÐ 22+4 = 64 ʶҹР(ÊÓËÃºÑ Ç§¨Ã¡Ãͧ·Ó¹ÒÂẺ 4 á·»ç ) ´§Ñ ¹Ñ¹Œ ¨ÐàËç¹ä´éÇèÒǧ¨ÃµÃǨËÒ NPML ÁÕ¤ÇÒÁ«ºÑ «Íé ¹ÁÒ¡¡ÇÒè ǧ¨ÃµÃǨËÒ PRML áµè¨Ò¡¼Å¡Ò÷´ÅͧµÒÁÃÙ»·Õ‹6.11 ¾ºÇèÒ Ç§¨ÃµÃǨËÒ NPML ÁÕ»ÃÐÊÔ·¸ÀÔ Ò¾ÁÒ¡¡ÇÒè ǧ¨ÃµÃǨËÒ PRML ÍÂÒè §à˹ç ä´éªÑ´ ËÃ×ÍÍÒ¨¨Ð¡ÅèÒÇä´éèÇèÒ ³ ÃдѺ BER = 10−4 ǧ¨ÃµÃǨËÒ NPML ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒǧ¨ÃµÃǨËÒPRML »ÃÐÁÒ³ 2 dB ¹Í¡¨Ò¡¹ÕŒ ¨Ò¡¼Å¡Ò÷´ÅͧÂѧ¾ºÇèÒ Ç§¨ÃµÃǨËÒ NPML ·‹Õãªéǧ¨Ã¡Ãͧ·Ó¹Ò 2 á·»ç Á»Õ ÃÐÊÔ·¸ÔÀÒ¾ã¡Åéà¤Õ§¡ÑºÇ§¨Ã¡Ãͧ·Ó¹Ò 4 á·ç» ´Ñ§¹ŒÑ¹ ÊÓËÃºÑ Ãкº·¾Õ‹ ¨Ô ÒóҹŒÕ

132 ȹ٠Âìà·¤â¹âÅÂÍÕ ÔàÅ¡ç ·Ã͹ԡÊìààÅФÍÁ¾ÔÇàµÍÃàì àËè§ªÒµÔ Predictor MMSE 0.078 0.076 0.074 0.072 0.07 0.068 0.066 0.064 0.062 1 2 3 4 5 6 7 8 9 10 Number of predictor taps ÃÙ»·‹Õ 6.12: »ÃÐÊ·Ô ¸ÀÔ Ò¾¢Í§Ç§¨Ã¡Ãͧ·Ó¹Ò·Ջ㪨é ӹǹá·ç»µèÒ§¡Ñ¹ ·‹Õ SNR = 17 dBǧ¨ÃµÃǨËÒ NPML ÊÒÁÒöãªéǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·»ç ¡àç ¾ÂÕ §¾ÍµèÍ¡ÒÃãªé§Ò¹áÅéÇ à¹×‹Í§¨Ò¡ãË»é ÃÐÊÔ·¸ÀÔ Ò¾·ãՋ ¡Åéà¤Õ§¡ºÑ ¡ÒÃãªÇé §¨Ã¡Ãͧ·Ó¹ÒÂẺ 4 á·»ç ᵤè ÇÒÁ«ºÑ «é͹¨Ð¹Íé ¡ÇèÒÁÒ¡ ÃÙ»·Õ‹ 6.12 à»ÃÂÕ ºà·ÂÕ º»ÃÐÊ·Ô ¸ÔÀÒ¾¢Í§Ç§¨Ã¡Ãͧ·Ó¹Ò·Ջãªé¨Ó¹Ç¹á·»ç µèÒ§¡¹Ñ ·‹Õ SNR = 17dB ¨ÐàËç¹ä´Çé èÒ Ç§¨Ã¡Ãͧ·Ó¹Ò 2 á·ç» ¡çÁÕ»ÃÐÊ·Ô ¸ÀÔ Ò¾à¾Õ§¾ÍÊÓËÃºÑ ¡ÒÃãªé§Ò¹áÅéÇ à¹×‹Í§¨Ò¡¶§Ö áÁÇé èÒ¨ÐྋÔÁ¨Ó¹Ç¹á·ç»ÁÒ¡¢¹ŒÖ »ÃÐÊÔ·¸ÔÀÒ¾·Õ‹ä´é¡çྋÔÁ¢¹ÖŒ ¹éÍÂÁÒ¡ «§Ö‹ äÁè¤ØÁé ¤Òè ¡Ñº¤ÇÒÁ«Ñº«Íé ¹·‹Õä´éÃѺ 㹷ӹͧà´ÕÂÇ¡¹Ñ û٠·‹Õ 6.13 à»ÃÕºà·ÂÕ º»ÃÐÊ·Ô ¸ÀÔ Ò¾¢Í§Ç§¨ÃµÃǨËÒ PRML áÅÐ NPML ·Õ‹ ND = 2.5 â´Âãªé·ÒÃàì ¡µç Ẻ PR4 àËÁÍ× ¹à´ÔÁ áµè¤ÃÒǹŒÕ¨Ð¾ºÇèÒ Ç§¨ÃµÃǨËÒ NPML ãËé»ÃÐÊÔ·¸ÀÔ Ò¾·´‹Õ ¡Õ ÇèÒǧ¨ÃµÃǨËÒ PRML ¤è͹¢Òé §ÁÒ¡ àÁ×͋ à·Õº¡Ñº¡Ò÷ӧҹ·Õ‹ ND = 2 â´ÂÍÒ¨¨Ð¡ÅèÒÇä´éèÇèÒ ³ ÃдºÑ BER = 10−4 ǧ¨ÃµÃǨËÒ NPML ÁÕ»ÃÐÊ·Ô ¸ÔÀÒ¾´Õ¡ÇÒè ǧ¨ÃµÃǨËÒ PRML»ÃÐÁÒ³ 3 dB ·§ÑŒ ¹ŒàÕ »š¹à¾ÃÒÐÇèÒ ·Õ¤‹ ÇÒÁ¨Ø¢éÍÁÅÙ ¢Í§ÎÒÃì´´ÊÔ ¡äì ´Ã¿ìʧ٠(ËÃÍ× ND ÊÙ§) ͧ¤ì»ÃСͺ¢Í§ÊÑ­­Ò³Ãº¡Ç¹·Õ‹á½§ÍÂÙèã¹¢Íé ÁÅÙ ·Õ‹¨Ð·Ó¡ÒöʹÃËÊÑ ´Çé Âǧ¨ÃµÃǨËÒÇÕà·Íúì Ô ¨ÐÁÕÅ¡Ñ É³Ð໹šç Ê­Ñ ­Ò³Ãº¡Ç¹áººÊÕÁÒ¡¢ŒÖ¹ ¨Ö§·ÓãË¡é ÒÃãªé§Ò¹Ç§¨ÃµÃǨËÒ NPML ä´é»ÃÐÊ·Ô ¸ÀÔ Ò¾·‹Õ´Õ¡ÇÒè

6.5. ¼Å¡Ò÷´Åͧ 133 10−1 10−2BER 10−3 10−4 PRML: 22 states 16 17 10−5 NPML (2−tap predictor): 24 states 12 13 14 15 SNR (dB) û٠·Õ‹ 6.13: »ÃÐÊ·Ô ¸ÀÔ Ò¾¢Í§ÃкºµÒè §æ ·‹Õ ND = 2.5¡ÒÃ㪧é ҹǧ¨ÃµÃǨËÒ PRML ÁÒ¡ ྋÍ× ãËé¡ÒÃà»ÃÕºà·ÂÕ ºà»š¹ä»ÍÂÒè §Âص¸Ô ÃÃÁã¹àÃÍ׋ §¢Í§¤ÇÒÁ«Ñº«é͹¢Í§Ãкº ¨Ð·Ó¡Ò÷´Åͧà»ÃÂÕ ºà·ÂÕ º»ÃÐÊ·Ô ¸ÀÔ Ò¾¢Í§Ãкº 3 Ãкº ·‹Õ ND = 2.5 ´§Ñ µèÍ仹ŒÕ 1) ǧ¨ÃµÃǨËÒ NPML ·Õ‹ãªé·ÒÃàì ¡çµáºº PR4 H (D) = 1 − D2 áÅÐǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·»ç 2) ǧ¨ÃµÃǨËÒ PRML ·Õ‹ãª·é ÒÃìà¡çµáºº PR H (D) = 1 + 2D − 2D3 − D4 3) ǧ¨ÃµÃǨËÒ GPRML2 ·Õ‹ãªé·ÒÃàì ¡çµáºº GPR «Ö§‹ Í͡Ẻâ´Âà§Í׋ ¹ä¢ºÑ§¤ºÑ ẺâÁ¹Ô¡ (´Ù ÃÒÂÅÐàÍÕ´ã¹ËÑÇ¢Íé ·‹Õ 3.2.1) â´Â·‹Õ ·ÒÃàì ¡µç Ẻ GPR ¹Œ¨Õ ж١Í͡ẺÊÓËÃѺáµèÅÐ SNRµÒÁû٠·‹Õ 6.14 àÁ×͋ á¼¹ÀÒ¾à·ÃÅÅÔÊ·‹Õãªé㹡ÒöʹÃËÑÊ¢éÍÁÅÙ ´éÇÂÍÅÑ ¡ÍÃ·Ô ÖÁÇàÕ ·ÍÃìºÔ¢Í§·¡Ø Ãкº 2ǧ¨ÃµÃǨËÒ GPRML ¤Í× Ç§¨ÃµÃǨËÒÇàÕ ·Íúì Ô·‹Õãªé·ÒÃàì ¡µç Ẻ GPR ã¹¢³Ð·‹Õ ǧ¨ÃµÃǨËÒ PRML ¤Í× Ç§¨ÃµÃǨËÒÇÕà·ÍÃìº·Ô Õ㋠ª·é ÒÃàì ¡çµáºº PR

134 ÈÙ¹Âàì ·¤â¹âÅÂÕÍÔàÅç¡·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃàì àËè§ªÒµÔ 10−1 NPML: 22+2 = 16 states 10−2 PRML: [1 2 0 −2 −1] GPRML: (5−tap GPR) BER 10−3 10−4 10−5 12 13 14 15 16 17 SNR (dB) û٠·‹Õ 6.14: ¼Å¡ÒÃà»ÃÕºà·Õº»ÃÐÊ·Ô ¸ÔÀÒ¾¢Í§ÃкºµèÒ§æ ·‹Õ ND = 2.5¨ÐÁըӹǹʶҹÐà·Òè ¡Ñ¹ ¤Í× 16 ʶҹРáÅÐÍ¤Õ ÇÍäÅà«ÍÃì·Õ‹ãªé¢Í§áµÅè ÐÃкº¨Ð¶Ù¡Í͡ẺãËéàËÁÒÐÊÁ¡ºÑ ·ÒÃàì ¡çµ H (D) ·‹Õ¡Ó˹´ ¨Ò¡Ã»Ù ¨Ðà˹ç ä´éÇÒè ǧ¨ÃµÃǨËÒ NPML ÁÕ»ÃÐÊÔ·¸ÀÔ Ò¾ÁÒ¡¡ÇèÒǧ¨ÃµÃǨËÒ PRML ·‹Õãªé·ÒÃàì ¡µç Ẻ PR áµèÁÕ»ÃÐÊÔ·¸Ôã¡Åéà¤ÂÕ §¡ºÑ ǧ¨ÃµÃǨËÒ GPRML·Ñ§Œ ¹ŒÕ໚¹à¾ÃÒÐÇÒè ·ÒÃàì ¡µç »ÃÐÊÔ·¸Ô¼Å Heff (D) = H (D)[1 − P (D)] ·‹Õãªé㹡ÒÃÊÃéҧἹÀÒ¾à·ÃÅÅÊÔ ¢Í§Ç§¨ÃµÃǨËÒ NPML ÊÒÁÒö·‹Õ¨Ð¶¡Ù ¾Ô¨ÒóÒä´éÇèÒ໚¹·ÒÃàì ¡çµáºº GPR Ẻ˹§‹Ö ä´éà¹×͋ §¨Ò¡ ¤Òè ÊÑÁ»ÃÐÊ·Ô ¸Ô¢Í§·ÒÃìà¡çµ»ÃÐÊ·Ô ¸¼Ô Å໹š àÅ¢¨Ó¹Ç¹¨ÃÔ§6.6 ÊÃ»Ø ·éÒº·àÁ‹Í× Ãкº·Ó§Ò¹·‹Õ¤ÇÒÁ¨Ø¢éÍÁÅÙ ¢Í§ÎÒÃ´ì ´ÊÔ ¡ìä´Ã¿ìʧ٠ͧ¤ì»ÃСͺ¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹·‹Õ´éÒ¹¢Òà¢éҢͧǧ¨ÃµÃǨËÒÇÕà·ÍÃºì ¨Ô ÐÁÕÅ¡Ñ É³Ð໚¹Ê­Ñ ­Ò³Ãº¡Ç¹áººÊÕ (colored noise) ÁÒ¡¢ŒÖ¹ 㹡óչŒÇÕ §¨ÃµÃǨËÒ PRML äÁèÊÒÁÒö·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ´§Ñ ¹Œ¹Ñ ǧ¨ÃµÃǨËÒ NPML ¨§Ö

6.7. à຺½ƒ¡Ë´Ñ ·éÒº· 135ä´é¶Ù¡¹ÓÁÒãªéà¾×‹Íà¾Á‹Ô »ÃÐÊÔ·¸ÔÀÒ¾¢Í§Ãкº ·ÑŒ§¹ŒÕ๋Í× §ÁÒ¨Ò¡ÇèÒǧ¨ÃµÃǨËÒ NPML ¨ÐÁÕ¡ÒÃãªéǧ¨Ã¡Ãͧ·Ó¹Ò (㹡Ò÷Ջ¨Ð·ÓãËéÊ­Ñ ­Ò³Ãº¡Ç¹áººÊÕ¡ÅÒÂ໹š Ê­Ñ ­Ò³Ãº¡Ç¹ÊÕ¢ÒÇ) ÃèÇÁ¡ºÑǧ¨ÃµÃǨËÒÇàÕ ·Íúì Ô㹡ÒöʹÃËÑÊ¢éÍÁÙÅ ¹Í¡¨Ò¡¹ŒÕÂѧ¾ºÇèÒ·ÒÃàì ¡çµ»ÃÐÊ·Ô ¸¼Ô Å·‹Õãªé㹡ÒÃÊÃÒé §á¼¹ÀÒ¾à·ÃÅÅÔʢͧǧ¨ÃµÃǨËÒ NPML ÊÒÁÒö·‹Õ¨Ð¶¡Ù ¾¨Ô ÒóÒä´éÇÒè ໚¹·ÒÃìà¡çµáºº GPR ¨§Ö໹š à˵ؼŢéÍ˹§Ö‹ ÇÒè ·ÓäÁǧ¨ÃµÃǨËÒ NPML ¨Ö§Á»Õ ÃÐÊ·Ô ¸ÀÔ Ò¾´¡Õ ÇèÒǧ¨ÃµÃǨËÒ PRML à¾ÃÒÐÇèÒ·ÒÃàì ¡µç Ẻ GPR Á»Õ ÃÐÊ·Ô ¸ÔÀÒ¾´¡Õ ÇèÒ·ÒÃìà¡çµáºº PR µÒÁ·Í‹Õ ¸ºÔ ÒÂ㹺··‹Õ 3 ¶Ö§áÁÇé èÒǧ¨ÃµÃǨËÒ NPML Á»Õ ÃÐÊ·Ô ¸ÔÀÒ¾´¡Õ ÇèÒǧ¨ÃµÃǨËÒ PRML áµèǧ¨ÃµÃǨËÒ NPML¨ÐÁÕ¤ÇÒÁ«Ñº«Íé ¹ÁÒ¡¡ÇÒè à¾ÃÒЩйŒ¹Ñ 㹡Òõ´Ñ Ê¹Ô ã¨ÇèҨйÓǧ¨ÃµÃǨËÒ NPML ÁÒãªé§Ò¹ËÃÍ×äÁè ã˾é Ô¨ÒóÒÇèÒ »ÃÐÊ·Ô ¸ÀÔ Ò¾·Õ‹¨Ðä´Ãé ºÑ à¾Áԋ ¢Ö¹Œ ¨Ð¤ØéÁ¤Òè ¡ºÑ ¤ÇÒÁ«ºÑ «Íé ¹·Õµ‹ ÒÁÁÒËÃ×ÍäÁè6.7 à຺½¡ƒ Ë´Ñ ·éÒº· 1. ¨§Í¸ÔºÒ·‹ÁÕ Ò¢Í§á¹Ç¤Ô´¢Í§Ç§¨ÃµÃǨËÒ NPML 2. ¨§Í¸ºÔ Ò¤ÇÒÁᵡµèÒ§¢Í§Ç§¨ÃµÃǨËÒ PRML áÅÐǧ¨ÃµÃǨËÒ NPML 3. ¨Ò¡¡ÒÃÍ͡Ẻ·ÒÃìࡵç áÅÐÍÕ¤ÇÍäÅà«ÍÃì µÒÁẺ¨ÓÅͧã¹ÃÙ»·Õ‹ 3.2 ÊÓËÃºÑ Ãкº¡Òú¹Ñ ·¡Ö Ẻá¹Çµ§ŒÑ (perpendicular recording) ·Õ‹ ND = 2.5 áÅÐ SNR = 20 dB â´Â¡Ó˹´ ãËé·ÒÃàì ¡çµ·Õ‹µÍé §¡Òà ¤Í× H (D) = 1 + D »ÃÒ¡®ÇÒè ÅӴѺ¢éͼԴ¾ÅÒ´ {wk} ·‹Õä´é ¤×Í {1.56, 0.35, −0.66, −0.69, 0.81, 0.20} â´Â·Õ‹ ak ∈ {−1, 1} ¨§¤Ó¹Ç³ËÒ Ç§¨Ã¡Ãͧ ·Ó¹Ò P (D), ·ÒÃàì ¡çµ»ÃÐÊÔ·¸Ô¼Å Heff (D), áÅÐáÊ´§á¼¹ÀÒ¾à·ÃÅÅÊÔ ·ã‹Õ ªãé ¹¡ÒöʹÃËÊÑ ¢éÍÁÙÅ ¢Í§Ç§¨ÃµÃǨËÒ NPML ·‹Õãªé 3.1) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 1 á·ç» 3.2) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·»ç 3.3) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 3 á·»ç 3.4) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 4 á·»ç

136 ȹ٠Âàì ·¤â¹âÅÂÕÍÔàÅç¡·Ã͹ԡÊìààÅФÍÁ¾ÔÇàµÍÃìààË觪ҵÔ4. ·ÓàËÁ×͹㹢Íé 3 áµè¡Ó˹´ãËé·ÒÃàì ¡µç ·‹Õµéͧ¡Òà ¤×Í H (D) = 1 + 2D + D2 áÅÐÅÓ´ºÑ ¢éͼ´Ô ¾ÅÒ´ {wk} = {−0.56, −1.65, −0.21, 0.49, −0.98, −0.09}5. Ẻ¨ÓÅͧ¡ÒÃÍ͡Ẻ·ÒÃìࡵç áÅÐÍÕ¤ÇÍäÅà«ÍÃì ã¹Ã»Ù ·Õ‹ 3.2 ÊÓËÃºÑ Ãкº¡Òúѹ·Ö¡áºº á¹Çµ§ŒÑ ·‹Õ ND = 2.5 áÅÐ SNR = 20 dB ÊÒÁÒö·‹Õ¨ÐÅ´ÃÙ»ä´é໹š Ẻ¨ÓÅͧªèͧÊÑ­­Ò³ ẺÊÁÁÙÅ µÒÁÃÙ»·‹Õ 6.6 àÁ×‹Í ·ÒÃìà¡çµ·Õ‹µéͧ¡Òà ¤×Í H (D) = 1+D ¶éÒ¡Ó˹´ãËé ÅÓ´ºÑ ¢éÍÁÅÙ Í¹Ô ¾Øµ {ak} = {1, −1, −1, 1} áÅÐÊÑ­­Ò³Ãº¡Ç¹ {wk} = {−0.41, −0.33, 0.41, −0.59, −1.29} ¨§¶Í´ÃËÑÊ¢Íé ÁÅÙ yk ´Çé Âǧ¨ÃµÃǨËÒ NPML àÁ‹×Íãªé 5.1) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 1 á·ç» ¤×Í P (D) = −0.2613D 5.2) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·ç» ¤Í× P (D) = −0.3929D − 0.5035D2 5.3) ǧ¨Ã¡Ãͧ·Ó¹ÒÂẺ 2 á·ç» ¤×Í P (D) = −0.3443D − 0.4656D2 + 0.0964D36. ·ÓàËÁ×͹㹢éÍ 5 áµè¡Ó˹´ãËé·ÒÃìà¡çµ·‹Õµéͧ¡Òà ¤×Í H (D) = 1 + 2D + D2, ÅӴѺ¢éÍÁÅÙ ÍÔ¹¾Øµ {ak} = {−1, 1, 1, −1} áÅÐÅÓ´ºÑ ¢Íé ¼Ô´¾ÅÒ´ {wk} = {0.47, 0.25, −0.38, −0.09, −1.12, −3.18}

º··Õ‹ 7ǧ¨ÃµÃǨËÒ PDNP㹺·¹¨ÕŒ СÅèÒǶ§Ö ·ÕÁ‹ Ò, ËÅ¡Ñ ¡Ò÷ӧҹ, áÅлÃÐ⪹ì¢Í§ ǧ¨ÃµÃǨËÒ PDNP (patterndependentnoisepredictive) [54] «Ö§‹ ໚¹Ç§¨ÃµÃǨËҷՋ¶Ù¡Í͡ẺÁÒྋ×ͨѴ¡ÒáºÑ Ê­Ñ ­Ò³Ãº¡Ç¹¨ÔµàµÍÃì¢Í§ÊÍ‹× ºÑ¹·Ö¡ (media jitter noise) «‹Ö§¾ººÍè Âã¹Ãкº¡Òúѹ·¡Ö áÁàè ËÅç¡·‹Õ¤ÇÒÁ¨Ø¢Íé ÁÙÅÊ§Ù æ ´§Ñ ·Õ‹¨Ð͸ԺÒµèÍä»ã¹º·¹ÕŒ ¾ÃéÍÁ·§ÑŒ áÊ´§¼Å¡ÒÃà»ÃÂÕ ºà·ÂÕ º»ÃÐÊ·Ô ¸ÀÔ Ò¾ÃÐËÇÒè §Ç§¨ÃµÃǨËÒ PDNPáÅÐǧ¨ÃµÃǨËÒ PRML7.1 º·¹Ó¨Ò¡·Õ‹ä´é͸ºÔ ÒÂä»ã¹º··Õ‹ 4 à·¤¹¤Ô PRML ¤Í× à·¤¹¤Ô ¡ÒÃãªé§Ò¹ÃèÇÁ¡Ñ¹ÃÐËÇèÒ§Í¤Õ ÇÍäÅà«ÍÃìẺPR (partialresponse equalizer) áÅÐǧ¨ÃµÃǨËÒÇàÕ ·Íúì Ô (Viterbi detector) «‹Ö§à»š¹·‹Õ¹ÂÔ Áãªé§Ò¹¡Ñ¹ÁÒ¡ã¹Ãкº¡ÒûÃÐÁÇżÅÊÑ­­Ò³¢Í§ÎÒÃ´ì ´ÔÊ¡ìä´Ã¿ì [27] à·¤¹Ô¤ PRML ¨Ð·Ó§Ò¹à»¹š 2¢ÑŒ¹µÍ¹ ¤×Í ¢¹ÑŒ µÍ¹áá¨Ð·Ó¡ÒÃ»ÃºÑ Ã»Ù ÃèÒ§¢Í§Ê­Ñ ­Ò³·‹Õä´éÃѺãËé໹š 仵ÒÁÃÙ»ÃèÒ§¢Í§·ÒÃìà¡çµ(target) ·‹ÕµÍé §¡Òà áÅТ¹ŒÑ µÍ¹·‹ÕÊͧ¨Ð·Ó¡ÒöʹÃËÑÊ¢Íé ÁÅÙ â´Âǧ¨ÃµÃǨËÒÇÕà·Íúì Ô·‹ÕÊÃÒé §¢Œ¹Ö ¨Ò¡·ÒÃìà¡µç ·¡‹Õ Ó˹´äÇé ǧ¨ÃµÃǨËÒÇÕà·ÍÃìºÔ¶Í× ÇèÒ໚¹ “ǧ¨ÃµÃǨËÒÅÓ´ºÑ àËÁÒзÕʋ ´Ø (optimal sequence detector)”¡çµèÍàÁÍ׋ ͧ¤ì»ÃСͺ¢Í§ÊÑ­­Ò³Ãº¡Ç¹·‹ÕὧÍÂÙèã¹ÊÑ­­Ò³·‹Õ¨Ð·Ó¡ÒöʹÃËÊÑ ¢éÍÁÙÅÁÕÅѡɳР137

138 ÈÙ¹Âàì ·¤â¹âÅÂÍÕ àÔ Åç¡·Ã͹ԡÊàì àÅФÍÁ¾ÔÇàµÍÃàì àË§è ªÒµÔ໚¹ÊÑ­­Ò³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇẺºÇ¡ [15] ÍÂÒè §äáçµÒÁã¹·Ò§»¯ºÔ ÑµÔ ¡ÒÃãªé§Ò¹ÍÕ¤ÇÍäÅà«ÍÃìẺ PR ¨ÐÊ§è ¼Å·ÓãËéͧ¤ì»ÃСͺ¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹·Õ‹´Òé ¹¢Òà¢Òé ¢Í§Ç§¨ÃµÃǨËÒÇÕà·Íúì ÔÁÕ¤Ø³Å¡Ñ É³Ð໚¹ÊÑ­­Ò³Ãº¡Ç¹áººÊÕ (colored noise) â´Â੾ÒÐÍÂÒè §Â§Ô‹ àÁÍ׋ ¤ÇÒÁ¨Ø¢Íé ÁÅÙ ¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿ìÊÙ§ (ND ʧ٠) «Ö§‹ 㹡óչՌ ǧ¨ÃµÃǨËÒÇÕà·ÍÃìºÔ¨ÐäÁè¶×ÍÇÒè ໹š ǧ¨ÃµÃǨËÒÅӴѺàËÁÒз‹ÕÊ´Ø ÍÕ¡µèÍä» ´§Ñ ¹¹ŒÑ ǧ¨ÃµÃǨËÒ NPML (noisepredictive maximumlikelihood) [51, 52] ¨§Öä´é¶¡Ù ¹ÓÁÒãªéà¾Í׋ à¾Áԋ »ÃÐÊ·Ô ¸ÀÔ Ò¾¢Í§Ãкº â´Â·Õ‹ ǧ¨ÃµÃǨËÒ NPML ¨ÐÁÕ¡Ãкǹ¡ÒÃ㹡Ò÷ÓãËÊé ­Ñ ­Ò³Ãº¡Ç¹à»š¹Ê¢Õ ÒÇ ¡è͹·¨Õ‹ ÐÊ§è ¼ÅÅѾ¸·ì Ջä´éä»·Ó¡ÒöʹÃËÑÊ´éÇÂǧ¨ÃµÃǨËÒÇÕà·ÍÃìºÔ 㹺··Õ‹ 6 áÊ´§ãËéàËç¹ÇèÒ Ç§¨ÃµÃǨËÒ NPML ÁÕ»ÃÐÊ·Ô ¸ÔÀÒ¾´Õ¡ÇÒè ǧ¨ÃµÃǨËÒ PRML â´Â੾ÒÐÍÂÒè §ÂÔ§‹ ·¤‹Õ ÇÒÁ¨Ø¢éÍÁÙŢͧÎÒÃì´´ÔÊ¡äì ´Ã¿ìÊÙ§ ¹Í¡¨Ò¡¹ŒÕ ·Õ‹ ND ʧ٠æ ͧ¤»ì ÃСͺ¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹·‹Õ´éÒ¹¢Òà¢éҢͧǧ¨ÃµÃǨËÒÇàÕ ·ÍÃìºÔ处 ¨ÐÁÕÅѡɳТ֌¹ÍÂèÙ¡ºÑ “Ẻ¢Íé ÁÙÅ (data pattern)” µÇÑ ÍÂÒè §àª¹è ÊÑ­­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê׋ͺѹ·Ö¡ ¶Í× ä´éÇÒè ໚¹ “Ê­Ñ ­Ò³Ãº¡Ç¹·‹Õ¢¹ÖŒ ÍÂÙè¡Ñºáºº¢éÍÁÅÙ (patterndependent noise)” ¡ÅèÒǤÍ×ÃдѺ¤ÇÒÁÃعáç¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê‹×ͺѹ·¡Ö ¨Ð¢ÖŒ¹ÍÂÙè¡Ñºáºº¢Íé ÁÅÙ ·‹Õà¢ÂÕ ¹Å§ä»ã¹ÊÍ‹× ºÑ¹·Ö¡ à·¤¹Ô¤µèÒ§æ ä´¶é Ù¡¹ÓàʹÍà¾×‹Í·ÓãËÊé ­Ñ ­Ò³Ãº¡Ç¹»ÃÐàÀ·¹ŒÕ [54, 55] ÁÅÕ Ñ¡É³Ð¡ÅÒÂ໚¹ÊÑ­­Ò³Ãº¡Ç¹ÊÕ¢ÒÇ (white noise) ¡Íè ¹·Õ‹¨Ð·‹·Õ Ó¡ÒöʹÃËÑÊ¢éÍÁÙÅ´éÇÂǧ¨ÃµÃǨËÒÇàÕ ·Íúì Ôã¹ÊèǹµèÍ仹ŒÕ¨Ð͸ԺÒ¶§Ö ËÅÑ¡¡Ò÷ӧҹ¢Í§Ç§¨ÃµÃǨËÒ PDNP [54] áÅÐà·¤¹Ô¤¡ÒÃÅ´¤ÇÒÁ«ºÑ «é͹¢Í§Ç§¨ÃµÃǨËÒ PDNP7.2 ¡ÒâֹŒ Í¡è٠Ѻà຺¢éÍÁÙÅ¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹¾¨Ô ÒóÒẺ¨ÓÅͧªÍè §ÊÑ­­Ò³ã¹ÃÙ»·Õ‹ 7.1 ¡Ó˹´ãËé C(D) = (1 − D)G(D) ¤×Í ¼ÅµÍºÊ¹Í§¢Í§ªÍè §ÊÑ­­Ò³ã¹â´àÁ¹ D, H (D) ¤Í× ¼ÅµÍºÊ¹Í§·ÒÃàì ¡çµã¹â´àÁ¹ D, Q(D) ¤×Í ¼ÅµÍºÊ¹Í§ÃÇÁã¹â´àÁ¹ D ¢Í§Ç§¨Ã¡Ãͧ¼èÒ¹µ‹ÓáÅÐÍ¤Õ ÇÍäÅà«ÍÃ,ì áÅÐྋÍ× ãËé§Òè µèÍ¡ÒÃ͸ºÔ ÒÂÍ¤Õ ÇÍäÅà«ÍÃáì ºº zeroforcing [2, 16] ¨Ð¶¡Ù ¹ÓÁÒãªãé ¹ÊÇè ¹¹ŒÕ ¹‹Ñ¹¤Í× Q(D) = H (D)/C(D) ã¹·Ò§»¯ÔºÑµÔ ·ÒÃàì ¡µç áÅÐÍ¤Õ ÇÍäÅà«ÍÃ쫋֧¶Ù¡ÊÃÒé §â´Âǧ¨Ã¡ÃͧàªÔ§àʹé Ẻ¼ÅµÍºÊ¹Í§ÍÔÁ¾ÅÑ Êì¨Ó¡Ñ´(FIR: nite impulse response) ¨ÐÁ¿Õ §˜ ¡ìª¹Ñ ¶èÒÂâ͹·á‹Õ µ¡µÒè §ä»¨Ò¡ H (D) áÅÐ Q(D) ·‹Õµéͧ¡ÒÃã¹·Ò§·ÄÉ®Õ à¾ÃÒЩйŒÑ¹ ¶Òé ¡Ó˹´ãËé H (D) áÅÐ Q (D) = H (D)/C(D) ¤×Í ¿§˜ ¡ªì ¹Ñ ¶èÒÂ

7.2. ¡ÒâŒ¹Ö ÍÂè¡Ù Ѻà຺¢Íé ÁÙŢͧÊÑ­­Ò³Ãº¡Ç¹ 139 n(t)ak 1 – D bk g(t) ∆tk p(t) s(t) sk yk aˆk LPF equalizer detector{0,1} tk = kT C(D) Q(D) H(D) ÃÙ»·‹Õ 7.1: Ẻ¨ÓÅͧªèͧÊÑ­­Ò³â͹¨ÃÔ§¢Í§·ÒÃàì ¡çµáÅÐ¢Í§Í¤Õ ÇÍäÅà«ÍÃì µÒÁÅÓ´ºÑ â´Â·‹Õ H (D) = H (D) áÅÐ Q (D) = Q(D)´§Ñ ¹ÑŒ¹ ¢éÍÁÙÅàÍÒµì¾µØ ¢Í§Í¤Õ ÇÍäÅà«ÍÃÊì ÒÁÒöà¢Õ¹໚¹ÊÁ¡Ò÷ҧ¤³ÔµÈÒʵÃìä´é ¤Í×Y (D) = A(D)C(D)Q (D) + N (D)Q (D) (7.1) = A(D)H (D) + N (D)Q (D) = A(D)H (D) + N (D)Q (D) + [A(D)H(D) − A(D)H(D)] = A(D)H(D) + A(D)[H (D) − H(D)] + N (D)Q (D) W (D)àÁÍ׋ N (D) ¤Í× ÊÑ­­Ò³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇẺºÇ¡ (AWGN) áÅÐ W (D) ¤×Í Ê­Ñ ­Ò³Ãº¡Ç¹ÃÇÁ·‹äÕ ´é ³ ´éÒ¹¢Òà¢Òé ¢Í§Ç§¨ÃµÃǨËÒÅÓ´ºÑ µÒÁÊÁ¡Òà (7.1) ¨ÐàËç¹ä´éÇÒè Ê­Ñ ­Ò³Ãº¡Ç¹ W (D)ÁÕÅѡɳТŒ¹Ö ÍÂè¡Ù ºÑ Ẻ¢Íé ÁÙÅ (datadependent) ๋×ͧ¨Ò¡ Á¾Õ ¨¹ì A(D) ÍÂèÙ Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê׋ͺѹ·¡Ö ໚¹¼ÅÁÒ¨Ò¡ “¡ÒÃàÅ×͋ ¹µÓá˹§è ¢Í§¡ÒÃà»ÅՋ¹ʶҹÐẺÊèÁØ (random transition shift)” ÃÐËÇÒè §¡Ãкǹ¡Ò÷ÓãËéʋ×ͺѹ·Ö¡ÁÕÊÀÒ¾¤ÇÒÁ໚¹áÁàè ËÅ¡ç(magnetization) µÒÁ·‹Õµéͧ¡Òà â´Â¨ÐÁÕ¿§˜ ¡ìª¹Ñ ¤ÇÒÁ˹Òá¹è¹¤ÇÒÁ¹Òè ¨Ð໹š Ẻà¡ÒÊìà«ÂÕ ¹·‹ÕÁÕ¤èÒà©ÅÂՋ à·èÒ¡ºÑ ¤èÒÈÙ¹ÂìáÅФèÒ¤ÇÒÁá»Ã»Ãǹà·èÒ¡ºÑ |bk|σj2 (¹¹Ñ‹ ¤Í× ∆tk ∼ N (0, |bk|σj2)) áÅж¡Ù¨Ó¡´Ñ ãËéÁÕ¤Òè äÁàè ¡¹Ô T /2) â´Â·Õ‹ σj ¨Ð¶Ù¡¡Ó˹´à»¹š ¨Ó¹Ç¹à»ÍÃìà«ç¹µì¢Í§ºÔµà«ÅÅì T áÅÐ |bk| ¤ÍפèÒÊÁÑ ºÙóì¢Í§ bk à¹Í‹× §¨Ò¡ µÓá˹§è ¡ÒÃà»Å‹Õ¹ʶҹж¡Ù ¡Ó˹´â´Â¢éÍÁÅÙ ºÔµÍÔ¹¾Øµ {ak} ´§Ñ ¹ÑŒ¹¤ÇÒÁÃ¹Ø áç¢Í§ÊÑ­­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê׋ͺѹ·¡Ö ¨§Ö ¢¹ÖŒ ÍÂÙè¡Ñºáºº¢Íé ÁÅÙ ¢Í§ {ak} û٠·Õ‹ 7.2

140 ȹ٠Âìà·¤â¹âÅÂÕÍÔàÅç¡·Ã͹ԡÊàì àÅФÍÁ¾ÇÔ àµÍÃàì àËè§ªÒµÔ Noise power (dB) 5 4.5 4 3.5 3 2.5 2 1.5 1 001 100 010 110 001 101 011 111 Data patternÃÙ»·‹Õ 7.2: ¡ÓÅ§Ñ Ê­Ñ ­Ò³Ãº¡Ç¹·‹Õ¢¹ÖŒ ¡ºÑ Ẻ¢éÍÁÙÅ ³ ´Òé ¹¢ÒÍÍ¡¢Í§Í¤Õ ÇÍäÅà«ÍÃ췋ն¡Ù Í͡ẺÊÓËÃºÑ ·ÒÃàì ¡çµ EEPR2 [1 4 6 4 1] ¢Í§Ãкº¡Òúѹ·Ö¡áººá¹ÇµÑŒ§ ·‹Õ ND = 2.5, SNR = 30dB, áÅÐ σj /T = 10%áÊ´§¡ÓÅѧÊÑ­­Ò³Ãº¡Ç¹ (noise power) ·‹¢Õ ֌¹¡ºÑ Ẻ¢Íé ÁÙÅ ³ ´Òé ¹¢ÒÍÍ¡¢Í§ÍÕ¤ÇÍäÅà«ÍÃáì ºº21 á·»ç (tap) ·‹¶Õ ¡Ù Í͡ẺãËéÊÍ´¤Åéͧ¡Ñº·ÒÃàì ¡çµ EEPR2, H (D) = 1 + 4D + 6D2 + 4D3 +D4, ¢Í§Ãкº¡Òú¹Ñ ·Ö¡áººá¹ÇµŒÑ§ (perpendicular recording) ·Õ‹ ND = 2.5, SNR = 30 dB,áÅÐ σj /T = 10% ¨Ðà˹ç ä´éª´Ñ ਹÇÒè ¡ÓÅÑ§Ê­Ñ ­Ò³Ãº¡Ç¹¨ÐÁÕ¤Òè ʧ٠àÁ‹Í× ÅӴѺ¢Íé ÁÙÅÁÕ¡ÒÃà»ÅÂՋ ¹Ê¶Ò¹ÐËÅÒ¤çь હè Ẻ¢éÍÁÅÙ “010” áÅÐ “101” ໹š µé¹7.3 ÍÑÅ¡ÍÃ·Ô ÁÖ PDNP (7.2)¾Ô¨ÒóÒǧ¨ÃµÃǨËÒÇÕà·ÍÃìºÔ [15] â´Â·Õ‹ àÁµÃÔ¡ÊÒ¢Ò (branch metric) ¤Ó¹Ç³ä´é¨Ò¡ ν λk(u, v) = |yk − hiak−1 |2 i=0 rˆk (u,v)

7.3. ÍÅÑ ¡ÍÃÔ·ÁÖ PDNP 141àÁ‹Í× (u, v) á·¹¡ÒÃà»Å‹ÂÕ ¹Ê¶Ò¹Ð¨Ò¡Ê¶Ò¹Ð u ä»ÂѧʶҹРv ã¹á¼¹ÀÒ¾à·ÃÅÅÔÊ (trellis diagram), yk ¤Í× ¢Íé ÁÙŷՋ¨Ð·Ó¡ÒöʹÃËÊÑ ´Çé Âǧ¨ÃµÃǨËÒÇàÕ ·Íúì Ô, rˆk(u, v) ¤Í× ¢Íé ÁÅÙ àÍÒµ¾ì صªÍè §ÊÑ­­Ò³·‹ÕäÁèÁÕÊ­Ñ ­Ò³Ãº¡Ç¹·Õ‹ÊÍ´¤Åéͧ¡ºÑ (u, v) (¹¹‹Ñ ¤×Í ¤Òè ·‹ÕáÊ´§ÍÂèÙã¹áµÅè Ðàʹé ÊҢҢͧἹÀÒ¾à·ÃÅÅÊÔ àª¹è µÒÁ·Õዠʴ§ã¹ÃÙ»·‹Õ 4.6) «‹§Ö ËÒä´é¨Ò¡ (7.3) ν rk = ak ∗ hk = ak−ihi i=0àÁ×͋ ∗ ¤Í× µÑÇ´Óà¹Ô¹¡Òä͹âÇÅ٪ѹ (convolution operator), H (D) = ν hk Dk ¤×Í ·ÒÃìà¡µç ·Õ‹ k=0µÍé §¡ÒÃ, hk ¤Í× ¤Òè ÊÁÑ »ÃÐÊ·Ô ¸ÔµÇÑ ·‹Õ k ¢Í§·ÒÃìà¡çµ, áÅÐ ν ¤Í× Ë¹èǤÇÒÁ¨Ó¢Í§·ÒÃàì ¡µçà¹Í׋ §¨Ò¡ ͧ¤»ì ÃСͺ¢Í§ÊÑ­­Ò³Ãº¡Ç¹·‹ÕὧÍÂÙèã¹¢Íé ÁÙÅ yk «Ö‹§ËÒä´é¨Ò¡ (´ÙẺ¨ÓÅͧ¡ÒÃÍ͡Ẻ·ÒÃìࡵç ã¹ÃÙ»·‹Õ 3.2) wk = yk − rk (7.4)â´Â¼Å¡ÒÃá»Å§ D ¤×Í W (D) µÒÁÊÁ¡Òà (7.1) ¨ÐÁÕÅѡɳÐ໹š Ê­Ñ ­Ò³Ãº¡Ç¹·Õ‹¢¹ŒÖ ÍÂÙè¡ºÑ áºº¢éÍÁÙÅ ¶éÒÊ觢Íé ÁÙÅ yk à¢Òé ä»·Ó¡ÒöʹÃËÑÊ´éÇÂǧ¨ÃµÃǨËÒÇàÕ ·Íúì Ô »ÃÐÊ·Ô ¸ÀÔ Ò¾ã¹Ã»Ù ¢Í§ÍѵÃÒ¢Íé ¼Ô´¾ÅÒ´ºÔµ (BER) ·‹Õä´éÃºÑ ¨ÐäÁè´Õ à¾ÃÒЩйŒ¹Ñ 㹡Ò÷‹Õ¨Ðà¾Á‹Ô »ÃÐÊ·Ô ¸ÀÔ Ò¾ÃÇÁ¢Í§Ãкº ¨ÐµéͧÁÕ¡ÒùӡÃкǹ¡ÒÃ㹡Ò÷ÓãËéÊÑ­­Ò³Ãº¡Ç¹à»š¹ÊÕ¢ÒÇ (noise whitening process) à¾Í‹×·ÓãËé¢Íé ÁÙÅ wk ÁÕÅ¡Ñ É³Ð໹š Ê­Ñ ­Ò³Ãº¡Ç¹ÊÕ¢ÒÇ ¡è͹·Õ‹¨ÐÊ觼ÅÅѾ¸ì·‹Õä´éä»·Ó¡ÒöʹÃËÊÑ ´éÇÂǧ¨ÃµÃǨËÒÇàÕ ·ÍÃìºÔ ´§Ñ ¹ŒÑ¹ 㹡ÒÃãªéà·¤¹Ô¤¡Ò÷ӹÒÂÊÑ­­Ò³Ãº¡Ç¹ (noise prediction) ÃÇè Á¡ºÑ ǧ¨ÃµÃǨËÒÇÕà·Íúì Ô ¨Ð·ÓãËéàÁµÃÔ¡ÊÒ¢Òã¹ÊÁ¡Òà (7.2) µÍé §¶Ù¡´Ñ´á»Å§à»¹š λk(u, v) = |yk − rˆk(u, v) − wˆk|2 (7.5)àÁ‹×Í wˆk ¤Í× Ê­Ñ ­Ò³Ãº¡Ç¹·‹¶Õ ¡Ù ·Ó¹Ò «Ö§‹ ËÒä´¨é Ò¡ L (7.6) wˆk = piwk−i i=1â´Â·‹Õ P (D) = L piDi ¤Í× Ç§¨Ã ¡Ãͧ ·Ó¹Ò (prediction lter) ÊÑ­­Ò³ ú¡Ç¹ Ẻ L i=1á·»ç , pi ¤×Í ¤èÒÊÑÁ»ÃÐÊÔ·¸µÔ ÇÑ ·Õ‹ i ¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊÑ­­Ò³Ãº¡Ç¹, áÅТéͼ´Ô ¾ÅÒ´·‹àÕ ¡Ô´¨Ò¡

142 ȹ٠Âìà·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹ԡÊàì àÅФÍÁ¾ÇÔ àµÍÃàì àË觪ҵԡÒ÷ӹÒ ek ¤Í× ek = wk − wˆk (7.7)ËÃ×Í L wk = piwk−i + ek (7.8) i=1â´Âǧ¨Ã¡Ãͧ·Ó¹ÒÂÊÑ­­Ò³Ãº¡Ç¹ P (D) ·Õ‹´Õ¨ÐµÍé §·ÓãËé¢éͼ´Ô ¾ÅÒ´·‹Õà¡´Ô ¨Ò¡¡Ò÷ӹÒ ek ÁÕÅѡɳÐ໹š ÊÑ­­Ò³Ãº¡Ç¹à¡ÒÊÊì ¢Õ ÒÇãËÁé Ò¡·ÊՋ Ø´ àÁ‹×ÍÃкº·Ó§Ò¹·‹Õ¤ÇÒÁ¨Ø¢Í§ÎÒÃì´´ÔÊ¡ìä´Ã¿Êì Ù§æ ¨Ð·ÓãËéÃдѺ¤ÇÒÁÃ¹Ø áç¢Í§ÊÑ­­Ò³Ãº¡Ç¹¨Ð¢ŒÖ¹ÍÂèÙ¡ºÑ Ẻ¢éÍÁÅÙ ´Ñ§¹¹ÑŒ ǧ¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹·‹ÕàËÁÒÐÊ´Ø P (D) ¡ç¤Ç÷‹Õ¨Ð¢¹ÖŒÍÂè١ѺẺ¢éÍÁÅÙ ´éÇÂàª¹è ¡¹Ñ à¾ÃÒЩйь¹ 㹡ÒÃËÒ¤Òè ÊÑÁ»ÃÐÊÔ·¸Ô¢Í§ P (D) ¨ÐµÍé §¨Ñ´ÃÙ»ÊÁ¡ÒÃ(7.8) ãËÁè ´§Ñ ¹ŒÕ L (7.9) wk(a) = pi(a)wk−i(a) + ek(a) i=1àÁ×‹Í a ãªé᷹Ẻ¢éÍÁÅÙ µèÒ§æ ·à‹Õ »¹š ä»ä´é ÊÁ¡Òà (7.9) ÊÒÁÒöà¢ÂÕ ¹ãËéÍÂÙèã¹Ã»Ù ¢Í§àÁ·Ã¡Ô «äì ´é ¤Í× wk(a) = p(a)Tw(a) + ek(a) (7.10)â´Â·‹Õ p(a) = [p1(a), p2(a), . . . , pL(a)]T ¤Í× àÇ¡àµÍÃìá¹ÇµŒ§Ñ ¢Í§¤èÒÊÑÁ»ÃÐÊÔ·¸Ô¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂ, áÅÐ w(a) = [wk−1(a), wk−2(a), . . . , wk−L(a)]T ¤Òè ÊÁÑ »ÃÐÊÔ·¸Ô¢Í§ P (D) ÊÒÁÒö¤Ó¹Ç³ËÒä´éâ´Â¡Òä³Ù ·Œ§Ñ Êͧ¢Òé §¢Í§ÊÁ¡Òà (7.10) ´éÇÂàÇ¡àµÍÃì w(a)T áÅÇé ãÊèµÑÇ´Óà¹¹Ô ¡ÒäèÒ¤Ò´ËÁÒ (expectation operator) «‹Ö§¨Ðä´é¼ÅÅ¾Ñ ¸àì »š¹ E wk(a)w(a)T = p(a)TE w(a)w(a)T = p(a)TR(a) (7.11)àÁ×͋ R(a) = E w(a)w(a)T ¤×Í àÁ·ÃÔ¡«ìÍѵÊËÊÁÑ ¾¹Ñ ¸ì (autocorrelation matrix) ¢Í§ÊÑ­­Ò³Ãº¡Ç¹ wk(a), áÅÐ E ek(a)w(a)T = 0 µÒÁËÅÑ¡¡ÒÃàªÔ§µ§ŒÑ ©Ò¡ (orthogonality principle)[25] á¡Êé Á¡Òà (7.11) ¨Ðä´¼é ÅÅ¾Ñ ¸ì໹š p(a)T = E[wk(a)w(a)T] R−1(a) (7.12)

7.3. ÍÅÑ ¡ÍÃ·Ô ÁÖ PDNP 143áÅФÒè ¤ÇÒÁá»Ã»Ãǹ¢Íé ¼Ô´¾ÅÒ´¡Ò÷ӹÒ (predictor error variance) ¤×Í [54] (7.13) σp2(a) = E wk(a)2 − E wk(a)w(a)T R−1(a)E wk(a)w(a)T TÊÁ¡Òà (7.12) áÅÐ (7.13) áÊ´§ãËàé ˹ç ÇÒè ¤èÒÊÁÑ »ÃÐÊÔ·¸Ô¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂáÅФÒè ¤ÇÒÁá»Ã»Ãǹ¢Íé ¼Ô´¾ÅÒ´¡Ò÷ӹÒ¨ТŒÖ¹ÍÂè¡Ù ºÑ ªÇè §àÇÅÒ k ·Õ‹¾Ô¨ÒÃ³Ò (³ ªèǧàÇÅÒ k ˹§Ö‹ æ ¡çÍÒ¨¨ÐÁáÕ ºº¢éÍÁÙÅa ·‹ÕµÒè §¡Ñ¹ä´é) ÍÂèÒ§äáçµÒÁ ¤èÒ·§ŒÑ 2 ¤èҹՌÊÒÁÒö·Õ‹¨Ð·ÓãËéäÁ袹ŒÖ ¡ÑºªèǧàÇÅÒ k ¡çä´é ¶éÒÊÁÁµØ ÔãËéÃкºà»š¹áººÊ൪¹Ñ à¹ÃÕ (stationary) [10, 26] ËÃÍ× ¶éÒ໚¹Ãкº·ä‹Õ Áàè »¹š ẺÊ൪¹Ñ à¹ÃÕ ÍÅÑ ¡ÍÃ·Ô ÖÁẺ»ÃºÑ µÇÑ (adaptive algorithm) [4, 10, 16] ÊÒÁÒö·¨Õ‹ ж١¹ÓÁÒãªé㹡ÒÃ»ÃºÑ ¤Òè ÊÁÑ »ÃÐÊ·Ô ¸¢Ô ͧǧ¨Ã¡Ãͧ·Ó¹Ò áÅФèÒ¤ÇÒÁá»Ã»Ãǹ¢éͼԴ¾ÅÒ´¡Ò÷ӹÒÂä´éà¹Í‹× §¨Ò¡ ¤Òè ¤ÇÒÁá»Ã»Ãǹ¢Íé ¼´Ô ¾ÅÒ´¡Ò÷ӹÒ («Ö§‹ ໹š ¼ÅÁÒ¨Ò¡¡Ãкǹ¡ÒÃ㹡Ò÷ÓãËéÊÑ­­Ò³Ãº¡Ç¹à»¹š ÊÕ¢ÒÇ) ¢Œ¹Ö ÍÂÙè¡ºÑ áºº¢éÍÁÙÅ µÒÁ·‹ÕáÊ´§ã¹ÊÁ¡Òà (7.13) ¤èÒàÁµÃ¡Ô ÊҢҢͧǧ¨ÃµÃǨËÒ PDNP ¨ÐµÍé §¤Ó¹§Ö ¶§Ö ¡Òâ¹ÖŒ ÍÂÙè¡Ñºáºº¢Íé ÁÅÙ ´éÇ à¾ÃÒЩйŒÑ¹ àÁµÃ¡Ô ÊҢҢͧǧ¨ÃµÃǨËÒ PDNP ÊÒÁÒöà¢Õ¹ä´àé »¹šλk(u, v) = log (σp(u, v)) + |yk − rˆk(u, v) − wˆk(u, v)|2 (7.14) 2σp2(u, v)àÁÍ‹× σp2(u, v) ¤×Í ¤èÒ¤ÇÒÁá»Ã»Ãǹ¢Íé ¼´Ô ¾ÅÒ´¡Ò÷ӹÒ·ՋÊÍ´¤ÅÍé §¡Ñº (u, v) áÅÐẺ¢éÍÁÅÙ ·Õ‹à¡ÂՋ Ç¢éͧ¡ºÑ (u, v), áÅÐ wˆk(u, v) ¤Í× ÊÑ­­Ò³Ãº¡Ç¹·‹Õ¶Ù¡·Ó¹Ò·‹ÕÊÍ´¤ÅÍé §¡ºÑ (u, v) áÅÐẺ¢Íé ÁÅÙ ·àՋ ¡Õ‹ÂÇ¢Íé §¡Ñº (u, v) «Ö‹§ËÒä´é¨Ò¡ L (7.15) wˆk(u, v) = pi(u, v){yk−i − rˆk−i(u, v)} i=1¨Ò¡ÊÁ¡Òà (7.12) áÅÐ (7.13) ¨Ð¾ºÇèÒ Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³ P (D) = L piDi áÅФèÒ¤ÇÒÁ iá»Ã»Ãǹ¢éͼ´Ô ¾ÅÒ´¡Ò÷ӹÒ σp2 ¨Ð¢ÖŒ¹ÍÂÙè¡ºÑ áºº¢éÍÁÙÅã¹áµÅè ÐàÊé¹ÊÒ¢Ò ´Ñ§¹¹ŒÑ ¤èÒ¾ÒÃÒÁàÔ µÍÃìP (D) áÅÐ σp2 ·Õ‹ãªé㹡ÒäӹdzàÁµÃ¡Ô ÊÒ¢Òã¹áµÅè Ðàʹé ÊҢҢͧἹÀÒ¾à·ÃÅÅÊÔ ¨ÐÁÕ¤Òè µèÒ§¡Ñ¹µÒÁẺ¢Íé ÁÅÙ ·Õʋ Í´¤Åéͧ¡ºÑ ¡ÒÃà»ÅՋ¹ʶҹР(u, v) ¹ŒÑ¹æ ã¹·Ò§»¯ºÔ ѵÔáÅÇé ¤èÒÊÁÑ »ÃÐÊÔ·¸Ô¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹ p(a) ¨Ð¢Ö¹Œ ÍÂè١Ѻ¢Íé ÁÙźԵÀÒÂã¹Ë¹éÒµÒè §àÅ׋͹Ẻ¨Ó¡Ñ´ (nite sliding window) [56] «‹Ö§à¢Õ¹᷹´Çé ÂÊÑ­Åѡɳì aWk−M

144 ÈÙ¹Âàì ·¤â¹âÅÂÕÍÔàÅç¡·Ã͹ԡÊàì àÅФÍÁ¾ÇÔ àµÍÃìààË§è ªÒµÔÊÓËÃѺ¤èҨӹǹàµçÁºÇ¡ M áÅÐ W ´§Ñ ¹¹ŒÑ ǧ¨ÃµÃǨËÒ PDNP ¨Ðãªáé ¼¹ÀÒ¾à·ÃÅÅÊÔ ·‹ÕÁըӹǹʶҹÐà·Òè ¡Ñº 2max(ν+L, M )+W ʶҹРÍÂèÒ§äáµç ÒÁ à¾×‹ÍãËé§èÒµèÍ¡ÒÃ͸ԺÒÂËÅ¡Ñ ¡Ò÷ӧҹ¢Í§ÍÑÅ¡ÍÃÔ·ÖÁ PDNP ã¹ÊÇè ¹¹¨ŒÕ о¨Ô ÒóÒ੾ÒСóշՋ W = 0 áÅÐ M < ν + L à¾ÃÒЩй¹ŒÑ ¨Ó¹Ç¹Ê¶Ò¹Ð·§ÑŒ ËÁ´·‹ãÕ ªãé ¹á¼¹ÀÒ¾à·ÃÅÅÔÊÁըӹǹà·èҡѺ 2ν+L7.4 ÍÑÅ¡ÍÃ·Ô ÖÁ PSPDNPÍÑÅ¡ÍÃ·Ô ÖÁ PDNP ·Õ‹Í¸ºÔ ÒÂä»ã¹ËÇÑ ¢Íé ·Õ‹ 7.3 µÍé §¡ÒÃá¼¹ÀÒ¾à·ÃÅÅÔʷՋÁըӹǹʶҹзѧŒ ËÁ´2ν+L ÍÂèÒ§äáµç ÒÁ ¤ÇÒÁ«ºÑ «é͹¢Í§Ç§¨ÃµÃǨËÒ PDNP ÊÒÁÒö·ÓãËÅé ´Å§ä´éâ´Âãªáé ¹Ç¤´Ô “¡Òû‡Í¹¡ÅѺ¤èҵѴÊԹ㨠(decisionfeedback)” [53] áÅÐྋÍ× ãËÃé кºÁ»Õ ÃÐÊÔ·¸ÔÀÒ¾·ÂՋ ÍÁÃºÑ ä´é á¹Ç¤Ô´¹ÕŒµéͧ¡ÒäÇÒÁÅ¡Ö (depth) ¡Òû‡Í¹¡ÅºÑ ¤èÒµÑ´Ê¹Ô ã¨·Õ‹¤è͹¢Òé §¹éÍ àÁÍ׋ à·Õº¡Ñº¤ÇÒÁÂÒÇ (ËÃÍרӹǹá·ç») ¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹ «§Ö‹ ËÁÒ¤ÇÒÁÇèÒ á¼¹ÀÒ¾à·ÃÅÅÔÊ·‹ãÕ ªÂé ѧ¨Ó໚¹µéͧ¶¡Ù ¢ÂÒÂãËéãË­è¢ÖŒ¹ (trellis expansion) ¹‹¹Ñ ¤Í× Á¨Õ ӹǹʶҹÐÁÒ¡¢ÖŒ¹¡ÇèÒÃкº·‹ÕäÁèãªéǧ¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹ ã¹ÊÇè ¹¹ŒÕ¨Ð͸ºÔ ÒÂ Ç¸Ô ¡Õ Ò÷‹ÕàʹÍã¹ [53] «‹§Ö ¤ÅÒé ¡ºÑ á¹Ç¤´Ô “¡ÒûÃÐÁÇżÅẺà¾Íà«ÍÃìäÇàÇÍÃì (PSP: persurvivor processing)” [57] ÊÓËÃѺŴ¤ÇÒÁ«ºÑ «é͹¢Í§ÍÅÑ ¡ÍÃ·Ô ÖÁ PDNP â´ÂÍÑÅ¡ÍÃ·Ô ÖÁãËÁ跋Õä´é ã¹Ë¹§Ñ ÊÍ× ¹ÕŒ¨ÐàÃÕ¡ÇèÒ “ÍÑÅ¡ÍÃ·Ô ÁÖ PSPDNP (persurvivor PDNP algorithm)” ǧ¨ÃµÃǨËÒ PSPDNP ¨Ð·Ó§Ò¹µÒÁÍÅÑ ¡ÍÃ·Ô ÁÖ PDNP º¹¾¹Œ× °Ò¹¢Í§á¹Ç¤Ô´ PSP «§‹Ö ¨Ð·ÓãËéá¼¹ÀÒ¾à·ÃÅÅÔʷՋãªéã¹Ç§¨ÃµÃǨËÒ PSPDNP ÁըӹǹʶҹÐà·èÒà´ÔÁ (ËÃ×Íà·èҡѺÃкº·Õ‹äÁèãªèǧ¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹) ¡ÅÒè Ǥ×Í á·¹·Õ‹¨Ð·Ó¡ÒâÂÒÂá¼¹ÀÒ¾à·ÃÅÅÔÊãËéã˭袹֌ǧ¨ÃµÃǨËÒ PSPDNP ¨Ð·Ó¡ÒÃÁͧÂÍé ¹¡ÅºÑ 仵ÒÁàÊé¹·Ò§·‹Õ处 ÁÕªÕÇµÔ ÍÂÙèµÒÁá¼¹ÀÒ¾à·ÃÅÅÊÔ·ÕÁ‹ Ò¶Ö§ ³ ¨Ø´µèÍ (node) ·Õ‹¡ÓÅѧ¾Ô¨ÒÃ³Ò áÅéÇãªé¢Íé ÁÅÙ µÒè §æ ·‹ÕÊÍ´¤Åéͧ¡ÑºàÊ¹é ·Ò§·‹Õ处 ÁÕªÇÕ µÔ ÍÂÙè¹¹ŒÑ 㹡ÒäӹdzËÒ¤èÒÊ­Ñ ­Ò³Ãº¡Ç¹·Õ‹¶¡Ù ·Ó¹Ò ËÃ×ÍÍÒ¨¨Ð¡ÅÒè Çä´éÇÒè ǧ¨ÃµÃǨËÒ PSPDNPÂѧ¤§ãªéÊÁ¡Òà (7.14) 㹡ÒäӹdzËÒ¤Òè àÁµÃÔ¡ÊÒ¢Ò Â¡àǹé áµè ÊÑ­­Ò³Ãº¡Ç¹·‹Õ¶Ù¡·Ó¹Ò¨ж¡Ù¤Ó¹Ç³¨Ò¡ L (7.16) wˆk(u, v) = pi(u, v)zˆk−i(u, v) i=1

7.4. ÍÑÅ¡ÍÃÔ·ÁÖ PSPDNP 145 time k 0 k+1 zˆk−2 (A) zˆk−1 (A) time k k+1(0) -1 -1 2 zˆk−2 (B) zˆk (0,1) A(1) 1 -1 0 (1) 2 ak = 1 B ak = -1 -2 zˆk (2,1)(2) -1 1 0 -2(3) 1 1 0 zˆk−1 (B) yk yk−2 = 0.5 yk−1 = 1 yk = 0.15(a) Trellis diagram: PR4 (b) Decoding procedureû٠·‹Õ 7.3: (a) á¼¹ÀÒ¾à·ÃÅÅÔÊÊÓËÃѺ·ÒÃàì ¡çµáºº PR4 áÅÐ (b) ¢¹ÑŒ µÍ¹¡ÒöʹÃËÊÑ ¢Íé ÁÙÅ´Çé Âá¼¹ÀÒ¾à·ÃÅÅÔÊàÁ×‹Í zˆk−i(u, v) ¤×Í ÊÑ­­Ò³Ãº¡Ç¹·‹ÕὧÍÂÙèã¹¢éÍÁÙÅ yk ·Õ‹à»š¹¼Å·ÓãËéà¡´Ô ¡ÒÃà»Å‹Õ¹ʶҹÐÊÍ´¤Åéͧ¡ÑºàÊ¹é ·Ò§·Â‹Õ ѧÁªÕ ÇÕ µÔ Í·Ùè ‹àÕ »š¹¼Å·ÓãËéà¡Ô´¡ÒÃà»ÅÂՋ ¹Ê¶Ò¹Ð (u, v) «‹§Ö ¹ÂÔ ÒÁâ´Â zˆk(u, v) = yk(u, v) − rˆk(u, v) (7.17)´Ñ§¹ÑŒ¹¨ÐàËç¹ä´Çé èÒ Ç§¨ÃµÃǨËÒ PSPDNP ¨Ðãªáé ¼¹ÀÒ¾à·ÃÅÅÔÊ·‹ÁÕ ¨Õ ӹǹʶҹÐà·èҡѺ 2ν ʶҹÐáµè¨ÐµéͧÁբь¹µÍ¹à¾Ô‹ÁàµÁÔ ã¹¡ÒÃà¡ºç ¤èҢͧ {zˆk−1, zˆk−2, . . . , zˆk−L} ÊÓËÃѺ·¡Ø àÊ¹é ·Ò§·Â‹Õ §Ñ ÁªÕ ÕÇÔµÍÂèÙµÑÇÍÂèÒ§·Õ‹ 7.1 û٠·‹Õ 7.3 áÊ´§µÑÇÍÂÒè §¡ÒÃËÒ¤Òè Ê­Ñ ­Ò³Ãº¡Ç¹·Õ‹á½§ÍÂÙèã¹¢éÍÁÅÙ yk ·Õ‹à»š¹¼Å·ÓãËéà¡Ô´¡ÒÃà»ÅÕ‹ ¹Ê¶Ò¹ÐÊÍ´¤Åéͧ¡ºÑ (u, v) µÒÁÊÁ¡Òà (7.17) ¢Í§Ãкº·Õ‹ãªé·ÒÃàì ¡çµáºº PR4,H (D) = 1 − D2, «§Ö‹ ÁáÕ ¼¹ÀÒ¾à·ÃÅÅÔʵÒÁÃÙ»·‹Õ 7.3(a) àÁÍ‹× Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊ­Ñ ­Ò³Ãº¡Ç¹·ã‹Õ ªéÁ¨Õ ӹǹ L = 2 á·ç»

146 ȹ٠Âàì ·¤â¹âÅÂÕÍàÔ Å¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃàì àË觪ҵÔÇ¸Ô Õ·Ó ãËé¾¨Ô ÒóÒʶҹР(1) ³ àÇÅÒ k + 1 µÒÁ·‹ÕáÊ´§ã¹ÃÙ»·‹Õ 7.3(b) ¨ÐàËç¹ä´Çé èÒÁÕàÊ¹é ·Ò§·Õ‹Ç§Ô‹à¢Òé ÁÒËÒʶҹР(1) ໚¹¨Ó¹Ç¹ 2 àÊé¹·Ò§ ¤×Í àÊé¹·Ò§ A áÅÐ B à¾ÃÒЩй¹ÑŒ ¤Òè zˆk−i(u, v) ã¹ÊÁ¡Òà (7.16) ÊÓËÃºÑ i = 1 áÅÐ 2 ËÒä´´é ѧµÍè 仹Ռ ÊÓËÃºÑ àÊ¹é ·Ò§ A ¨Ðä´éÇèÒ zˆk(0, 1) = yk − rˆk(0, 1) = 0.15 − 2 = −1.85 zˆk−1(A) = zˆk−1(0, 1) = yk−1 − rˆk−1(0, 0) = 1 − 0 = 1 zˆk−2(A) = zˆk−2(0, 1) = yk−2 − rˆk−2(0, 0) = 0.5 − 0 = 0.5áÅÐÊÓËÃºÑ àÊ¹é ·Ò§ B ¨Ðä´Çé Òè zˆk(2, 1) = yk − rˆk(2, 1) = 0.15 − 0 = 0.15 zˆk−1(B) = zˆk−1(2, 1) = yk−1 − rˆk−1(3, 2) = 1 − (−2) = 3 zˆk−2(B) = zˆk−2(2, 1) = yk−2 − rˆk−2(1, 3) = 0.5 − 2 = −1.57.5 ¤ÇÒÁ«Ñº«Íé ¹¢Í§Ç§¨ÃµÃǨËÒ PDNP㹡ÒÃà»ÃÕºà·Õº¤ÇÒÁ«ºÑ «é͹ (complexity) ¢Í§Ç§¨ÃµÃǨËÒ ¨Ð¾Ô¨ÒóҨҡ¨Ó¹Ç¹µÇÑ ´Óà¹¹Ô ¡ÒÃ(operator) ÊÓËÃºÑ ¡Òúǡ (addition) áÅСÒäٳ (multiplication) ·‹ÕµÍé §ãªé㹡Ò÷ӧҹ¢Í§áµÅè Ðǧ¨ÃµÃǨËÒ µÒÃÒ§·‹Õ 7.1 à»ÃÕºà·ÂÕ º¤ÇÒÁ«Ñº«Íé ¹¢Í§Ç§¨ÃµÃǨËÒ PDNP áÅÐ PSPDNP àÁ‹Í×Np ¤×Í ¨Ó¹Ç¹áºº¢éÍÁÅÙ ·Õ‹ãªéã¹Ç§¨ÃµÃǨËÒ PDNP áÅÐ PSPDNP ¨Ò¡µÒÃÒ§¨Ðà˹ç ä´Çé èÒ Ç§¨ÃµÃǨËÒ PSPDNP ÁÕ¤ÇÒÁ«Ñº«Íé ¹áÅеéͧ¡ÒÃãªé˹èǤÇÒÁ¨Ó (memory requirement) ¹Íé ¡ÇèÒǧ¨ÃµÃǨËÒ PDNP ÁÒ¡7.6 ¼Å¡Ò÷´Åͧã¹Êèǹ¹ŒÕ¨Ð·Ó¡ÒÃà»ÃÕºà·Õº»ÃÐÊ·Ô ¸ÔÀÒ¾¢Í§Ç§¨ÃµÃǨËÒ PRML áÅÐ PDNP â´ÂãªéẺ¨ÓÅͧªèÍ§Ê­Ñ ­Ò³ µÒÁû٠·Õ‹ 7.1 àÁ‹Í× ÊÑ­­Ò³ readback ÊÒÁÒöà¢ÂÕ ¹ãËéÍÂèãÙ ¹Ã»Ù ¢Í§ÊÁ¡Òä³µÔ ÈÒʵÃì

7.6. ¼Å¡Ò÷´Åͧ 147µÒÃÒ§·‹Õ 7.1: ¨Ó¹Ç¹¢Í§µÇÑ ´Óà¹¹Ô ¡Ò÷ãՋ ªµé èÍ¢éÍÁÙÅ 1 ºµÔ ¢Í§Ç§¨ÃµÃǨËÒ PDNP áÅÐ PSPDNP ǧ¨ÃµÃǨËÒ ¨Ó¹Ç¹¢Í§µÑÇ´Óà¹Ô¹¡Ò÷ՋãªéµÍè ¢Íé ÁÙÅ 1 ºÔµ ˹èǤÇÒÁ¨Ó·‹µÕ éͧ¡Òà (detector) ¡Òúǡ ¡Òä³Ù (memory requirement)ǧ¨ÃµÃǨËÒ PDNPǧ¨ÃµÃǨËÒ PSPDNP (4L + 7)2ν+L (2L + 8)2ν+L (2L + 4)2ν+L + NpL + 2 (2L + 8)2ν (2L + 8)2ν (2L + 8)2ν + NpLä´é¤Í× S−1 (7.18) p(t) = bkg(t − kT + ∆tk) + n(t) k=0àÁÍ׋ ak ∈ {0, 1} ¤×Í ¢Íé ÁÅÙ ºµÔ ÍÔ¹¾µØ ·Õ‹Áըӹǹ·ŒÑ§ËÁ´ S = 4096 ºÔµ, bk = (ak − ak−1) ¤Í׺µÔ à»ÅՋ¹ʶҹР(bk = ±1 ÊÍ´¤Åéͧ¡Ñº¡ÒÃà»ÅÂ‹Õ ¹á»Å§Ê¶Ò¹ÐºÇ¡ËÃ×Íź áÅÐ bk = 0 ¤Í× äÁèÁ¡Õ ÒÃà»Å‹ÂÕ ¹á»Å§Ê¶Ò¹Ð), g(t) ¤Í× Ê­Ñ ­Ò³¾ÑÅÊàì »ÅՋ¹ʶҹеÒÁÊÁ¡Òà (1.1) ÊÓËÃѺÃкº¡Òúѹ·Ö¡áººá¹Ç¹Í¹ áÅеÒÁÊÁ¡Òà (1.2) ÊÓËÃºÑ Ãкº¡Òúѹ·¡Ö Ẻá¹Çµ§ŒÑ , n(t) ¤Í× ÊÑ­­Ò³Ãº¡Ç¹à¡ÒÊìÊÕ¢ÒÇẺºÇ¡ (AWGN) ·Õ‹ÁÕ¤ÇÒÁ˹Òá¹¹è Ê໡µÃÁÑ ¡ÓÅѧẺÊͧ´Òé ¹à·èҡѺ N0/2,áÅÐ ∆tk ¤×Í ÊÑ­­Ò³Ãº¡Ç¹¨ÔµàµÍâì ͧÊ׋ͺѹ·¡Ö (media jitter noise) ·ÕÁ‹ Õ¿§˜ ¡ìª¹Ñ ¤ÇÒÁ˹Òá¹è¹¤ÇÒÁ¹èÒ¨Ð໚¹áººà¡ÒÊìà«Õ¹ (Gaussian probability density function) â´ÂÁÕ¤èÒà©ÅՋÂà·èҡѺ¤ÒèÈÙ¹Âì áÅФÒè ¤ÇÒÁá»Ã»Ãǹà·èÒ¡ºÑ |bk|σj2 (¹Ñ‹¹¤Í× ∆tk ∼ N (0, |bk|σj2)) áÅж١¨Ó¡Ñ´ãËéÁÕ¤èÒäÁèà¡Ô¹ T /2) àÁ‹Í× σj ¨Ð¶Ù¡¡Ó˹´à»¹š ¨Ó¹Ç¹à»ÍÃìà«ç¹µì¢Í§ºµÔ à«ÅÅì T áÅÐ |bk| ¤Í× ¤èÒÊÑÁºÙóì(absolute value) ¢Í§ bk ÊÑ­­Ò³ readback p(t) ¨Ð¶¡Ù Ê觼èÒ¹ä»Â§Ñ ǧ¨Ã¡Ãͧ¼èÒ¹µ‹Ó (LPF: lowpass lter) ºµÑ à·ÍÃìàÇÃÔ µì Í¹Ñ ´Ñº·‹Õ 7 áÅж١·Ó¡ÒêѡµÇÑ ÍÂÒè §´éǤÇÒÁ¶‹Õ¡Òê¡Ñ µÇÑ ÍÂÒè §à·èÒ¡ºÑ 1/T â´ÂÊÁÁµØ ÇÔ Òè ¡Ãкǹ¡ÒÃ㹡ÒêѡµÇÑ ÍÂÒè §ÁÕ¡ÒÃà¢Òé ¨§Ñ ËÇÐÃÐËÇÒè §ÊÑ­­Ò³ readback áÅÐǧ¨ÃªÑ¡µÑÇÍÂÒè §áººÊÁºÙóì(perfect synchronization) ¨Ò¡¹ÑŒ¹ ÅӴѺ¢Íé ÁÙÅàÍÒµì¾µØ {sk} ¨Ð¶Ù¡»Í‡ ¹ä»ÂÑ§Í¤Õ ÇÍäÅà«ÍÃì à¾×‹Í»ÃѺ¤³Ø Å¡Ñ É³Ð¢Í§ÊÑ­­Ò³ãËé໚¹ä»µÒÁ·ÒÃìà¡çµ·‹ÕµÍé §¡Òà áÅéÇ¡çʧè ÅÓ´ºÑ ¢Íé ÁÅÙ àÍÒµì¾Øµ {yk} ·‹Õä´éä»·Ó¡ÒöʹÃËÑÊ¢éÍÁÙÅ´éÇÂǧ¨ÃµÃǨËÒ (detector) à¾Í‹× ËÒ¤Òè »ÃÐÁÒ³¢Í§ÅӴѺ¢éÍÁÅÙ Í¹Ô ¾µØ {ak} ·‹Õ

148 ȹ٠Âàì ·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹ԡÊàì àÅФÍÁ¾ÔÇàµÍÃàì àË§è ªÒµÔ໹š ä»ä´éÁÒ¡·‹ÕÊ´Ø ã¹º·¹ŒÕ ¤èÒ SNR ¨Ð¹ÂÔ ÒÁâ´Â SNR = 10 log10 Ei (7.19) N0àÁ‹Í× Ei ¤×Í ¾Å§Ñ §Ò¹¢Í§¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¢Í§ªèͧÊÑ­­Ò³1 ¹Í¡¨Ò¡¹ÕŒ áµÅè Ш´Ø ¢Í§ BER¨Ð¶Ù¡¤Ó¹Ç³â´Âãªé¢Íé ÁÅÙ ËÅÒÂæ à«¡àµÍÃì (sector) ¨¹¡ÇèÒ¨Ðä´é¢Íé ¼´Ô ¾ÅÒ´ºÔµÁÒ¡¡ÇèÒËÃÍ× à·èÒ¡ºÑ1000 ºµÔ ǧ¨ÃµÃǨËÒ 3 Ẻ ¤Í× Ç§¨ÃµÃǨËÒ PRML, ǧ¨ÃµÃǨËÒ PDNP, áÅÐǧ¨ÃµÃǨËÒ PSPDNP ¨Ð¶Ù¡·Ó¡ÒÃà»ÃÕºà·ÂÕ º»ÃÐÊ·Ô ¸ÀÔ Ò¾ ÊÓËÃºÑ Ãкº·Õ‹ãªé·ÒÃàì ¡µç Ẻ GPR3 (·ÒÃàì ¡çµáºº 3á·»ç ·‹¶Õ Ù¡Í͡ẺµÒÁোÍ× ¹ä¢ºÑ§¤ºÑ ẺâÁ¹Ô¡ [19]) áÅÐÍ¤Õ ÇÍäÅà«ÍÃáì ºº 21 á·ç» â´Â·Õ‹ ·ÒÃìà¡çµáºº GPR3 ÊÓËÃѺÃкº¡Òúѹ·Ö¡áººá¹Ç¹Í¹ ¤×Í H (D) = 1 + 0.05D − 0.65D2 áÅÐÊÓËÃѺÃкº¡Òú¹Ñ ·¡Ö Ẻá¹Çµ§ŒÑ ¤Í× H (D) = 1 + 1.25D + 0.62D2 û٠·‹Õ 7.4 à»ÃÂÕ ºà·ÂÕ º»ÃÐÊ·Ô ¸ÀÔ Ò¾ã¹ÃÙ»¢Í§ BER ¢Í§Ç§¨ÃµÃǨËҷѧŒ 3 Ẻ ÊÓËÃºÑ Ãкº¡Òú¹Ñ ·¡Ö Ẻá¹Ç¹Í¹áÅÐẺá¹Çµ§ŒÑ·Õ‹ N D = 2.5 áÅÐÊÑ­­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê׋ͺ¹Ñ ·Ö¡ σj /T = 10% ¨Ò¡ÃÙ»·‹Õ 7.4(a) ÊÓËÃѺÃкº¡Òú¹Ñ ·Ö¡áººá¹Ç¹Í¹ ǧ¨ÃµÃǨËÒ PSPDNP ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ã¡Åàé ¤ÂÕ §¡ºÑ ǧ¨ÃµÃǨËÒ PDNP áµèǧ¨ÃµÃǨËÒ·§ÑŒ Êͧ¹ŒÕÁÕ»ÃÐÊÔ·¸ÀÔ Ò¾´Õ¡ÇèÒǧ¨ÃµÃǨËÒ PRML â´Â੾ÒÐÍÂèҧ‹§Ô ·‹Õ SNR ʧ٠(¹¹‹Ñ ¤Í× àÁÍ‹× Ê­Ñ ­Ò³Ãº¡Ç¹ËÅ¡Ñ ã¹Ãкº ¤Í× Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê‹×ͺѹ·Ö¡) ã¹¢³Ð·Õ‹ ÊÓËÃѺÃкº¡Òúѹ·Ö¡áººá¹ÇµŒÑ§ (´ÙÃÙ»·Õ‹ 7.4(b)) ǧ¨ÃµÃǨËÒPRML ´ÙàËÁ×͹¨ÐÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇèÒǧ¨ÃµÃǨËÒ PSPDNP áÅÐǧ¨ÃµÃǨËÒ PDNP àÅ¡ç ¹Íé ·‹Õ SNR µ‹Ó ·ÑŒ§¹ÍŒÕ Ò¨¨Ð໚¹à¾ÃÒÐÇèÒ ·Õ‹ SNR µÓ‹ ÊÑ­­Ò³Ãº¡Ç¹ËÅ¡Ñ ã¹ÃкºäÁèãªÊè ­Ñ ­Ò³Ãº¡Ç¹¨ÔµàµÍâì ͧʋÍ× º¹Ñ ·Ö¡ ´Ñ§¹Ñ¹Œ ǧ¨ÃµÃǨËÒ PSPDNP áÅÐǧ¨ÃµÃǨËÒ PDNP «§‹Ö ¶Ù¡Í͡ẺÁÒãËé¨Ñ´¡ÒáºÑ Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê×͋ ºÑ¹·¡Ö ¨§Ö äÁèÊÒÁÒö·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ÍÂèÒ§äáµç ÒÁ ·‹Õ SNR ʧ٠ǧ¨ÃµÃǨËÒ PSPDNP áÅÐǧ¨ÃµÃǨËÒ PDNP ¨ÐÁÕ»ÃÐÊÔ·¸ÔÀÒ¾´Õ¡ÇÒè ǧ¨ÃµÃǨËÒ PRML ÁÒ¡ ¨Ò¡¡Òüŷ´ÅͧáÊ´§ãËéà˹ç ä´éÇÒè ǧ¨ÃµÃǨËÒ PSPDNP ÁÕ»ÃÐÊ·Ô ¸ÔÀÒ¾ã¡Åàé ¤ÂÕ §¡ºÑ ǧ¨ÃµÃǨËÒ PDNP à¾ÃÒЩйŒÑ¹ ã¹·Ò§»¯ºÔ ÑµÔ Ç§¨ÃµÃǨËÒ PSPDNP ÍÒ¨¨Ð¶¡Ù¹ÓÁÒãªáé ·¹Ç§¨ÃµÃǨËÒ PDNP à¹Í׋ §¨Ò¡ Á¤Õ ÇÒÁ«ºÑ «Íé ¹¹Íé ¡ÇèÒÁÒ¡ 1¼ÅµÍºÊ¹Í§ÍÔÁ¾ÑÅÊì¢Í§ªèͧÊÑ­­Ò³ ÁÕ¤èÒà·Òè ¡Ñº ͹¾Ø ¹Ñ ¸ì¢Í§¼ÅµÍºÊ¹Í§¡ÒÃà»ÅÂՋ ¹Ê¶Ò¹Ð g (t) ÊÓËÃºÑ Ãкº¡Òúѹ·¡Ö Ẻá¹Ç¹Í¹ áÅÐÁÕ¤èÒà·èҡѺ g (t)/2 ÊÓËÃºÑ Ãкº¡Òúѹ·Ö¡áººá¹ÇµÑ§Œ

7.7. ÊÃ»Ø ·éÒº· 149 10−1 10−2 PRML (4 states) PS − PDNP (4 states) PDNP (32 states)BER BER 10−3 10−4 10−5 18 20 22 24 26 28 30 32 (a) SNR (dB) 100 PRML (4 states) 10−1 PS − PDNP (4 states) PDNP (32 states) 10−2 10−3 10−4 18 20 22 24 26 28 30 32 34 36 (b) SNR (dB)û٠·‹Õ 7.4: »ÃÐÊÔ·¸ÔÀÒ¾ã¹ÃÙ»¢Í§ BER ¢Í§Ç§¨ÃµÃǨËÒµèÒ§æ ÊÓËÃѺÃкº¡Òú¹Ñ ·Ö¡ (a) Ẻá¹Ç¹Í¹ áÅÐ (b) Ẻá¹ÇµÑŒ§ ·Õ‹ ND = 2.5 áÅÐ σj /T = 10%7.7 ÊÃØ»·Òé º·àÁ׋ͤÇÒÁ¨Ø¢éÍÁÅÙ ¢Í§ÎÒÃ´ì ´ÔÊ¡ìä´Ã¿ìʧ٠¢ŒÖ¹ Ê­Ñ ­Ò³Ãº¡Ç¹·Õ‹´éÒ¹¢Òà¢Òé ¢Í§Ç§¨ÃµÃǨËÒÊ­Ñ Å¡Ñ É³ì¹Í¡¨Ò¡¨ÐÁÅÕ Ñ¡É³Ð໚¹ÊÑ­­Ò³Ãº¡Ç¹áººÊÕ (colored noise) áÅéÇ Âѧ¨ÐÁÅÕ Ñ¡É³Ð¢Ö¹Œ Í¡Ùè ѺẺ

150 ÈÙ¹Âàì ·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹¡Ô ÊìààÅФÍÁ¾ÇÔ àµÍÃìààË觪ҵԢéÍÁÅÙ (data pattern) ´éÇ હè Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§Ê׋ͺ¹Ñ ·Ö¡ (media jitter noise) â´Â·Õ‹ ÃдѺ¤ÇÒÁÃ¹Ø áç¢Í§Ê­Ñ ­Ò³Ãº¡Ç¹¨µÔ àµÍÃì¢Í§ÊÍ‹× ºÑ¹·¡Ö ¨Ð¢¹ÖŒ ÍÂèÙ¡ºÑ Ẻ¢éÍÁÅÙ ·Õ‹à¢ÂÕ ¹Å§ä»ã¹Ê׋ͺѹ·¡Ö ǧ¨ÃµÃǨËÒ PDNP ¨Ö§ä´é¶¡Ù Í͡Ẻ¢Ö¹Œ ÁÒ à¾×͋ ¨´Ñ ¡ÒáºÑ Ê­Ñ ­Ò³Ãº¡Ç¹àËÅÒè ¹ÕŒ â´Â¨Ð໚¹¡Ò÷ӧҹÃèÇÁ¡Ñ¹ÃÐËÇÒè §Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊÑ­­Ò³Ãº¡Ç¹¡ÑºÍÑÅ¡ÍÃ·Ô ÁÖ ÇÕà·ÍÃìºÔ ¶Ö§áÁÇé Òè ǧ¨ÃµÃǨËÒ PDNP ¨ÐãËé»ÃÐÊÔ·¸ÀÔ Ò¾·Õ‹´Õ¡ÇÒè ǧ¨ÃµÃǨËÒ PRML ÁÒ¡ áµèǧ¨ÃµÃǨËÒ PDNP ÁÕ¤ÇÒÁ«Ñº«Íé ¹ÁÒ¡¡ÇÒè ǧ¨ÃµÃǨËÒ PRML à¾ÃÒÐÇèÒ á¼¹ÀÒ¾à·ÃÅÅÊÔ ·Õ‹ãªéã¹Ç§¨ÃµÃǨËÒ PDNP ¨ÐÁըӹǹʶҹÐà¾Áԋ ÁÒ¡¢¹ŒÖ ๋Í× §ÁÒ¨Ò¡¨Ó¹Ç¹á·»ç ¢Í§Ç§¨Ã¡Ãͧ·Ó¹ÒÂÊÑ­­Ò³Ãº¡Ç¹ »­˜ ËÒ¹ŒÕÊÒÁÒö·‹Õ¨Ðá¡éä¢ä´éâ´Â ¡ÒûÃÐÂ¡Ø µìãªéÍÅÑ ¡ÍÃ·Ô ÖÁ PDNP µÒÁá¹Ç¤´Ô¢Í§ PSP «‹§Ö ¨Ðä´é¼ÅÅѾ¸ì໚¹ ǧ¨ÃµÃǨËÒ PSPDNP «Ö‹§ÁÕ»ÃÐÊ·Ô ¸ÔÀÒ¾ã¡Åàé ¤Õ§¡ºÑ ǧ¨ÃµÃǨËÒPDNP áµèÁÕ¤ÇÒÁ«Ñº«é͹¹éÍ¡ÇÒè ÁÒ¡7.8 à຺½¡ƒ ËÑ´·Òé º· 1. ¨§Í¸ºÔ Ò·ՋÁҢͧá¹Ç¤Ô´¢Í§ÍÅÑ ¡ÍÃÔ·ÁÖ PDNP 2. ¨§¾Ôʨ٠¹¤ì èÒ¤ÇÒÁá»Ã»Ãǹ¢éͼԴ¾ÅÒ´¡Ò÷ӹÒ µÒÁÊÁ¡Òà (7.13) 3. ¨§¾ÊÔ ¨Ù ¹ì¤Òè àÁµÃÔ¡ÊÒ¢Ò·ã‹Õ ªãé ¹Ç§¨ÃµÃǨËÒ PDNP µÒÁÊÁ¡Òà (7.14) 4. ¨§Í¸ºÔ Ò¤ÇÒÁᵡµèÒ§¢Í§Ç§¨ÃµÃǨËÒ PRML, ǧ¨ÃµÃǨËÒ NPML, áÅÐǧ¨ÃµÃǨËÒ PDNP 5. ¨§Í¸ÔºÒÂËÅ¡Ñ ¡Ò÷ӧҹ¢Í§Ç§¨ÃµÃǨËÒ PSPDNP 6. ¨§¾Ôʨ٠¹ì¨Ó¹Ç¹¢Í§µÑÇ´Óà¹¹Ô ¡Òà (¡ÒúǡáÅСÒä³Ù ) ·‹ÕãªéµÍè ¢Íé ÁÅÙ 1 ºµÔ µÒÁ·‹ÕáÊ´§ã¹ µÒÃÒ§·‹Õ 7.1 7. ¨§¾ÔÊÙ¨¹¨ì ӹǹ˹èǤÇÒÁ¨Ó·Õ‹µéͧ¡Òà µÒÁ·á‹Õ Ê´§ã¹µÒÃÒ§·‹Õ 7.1

º··‹Õ 8¡ÒÃÍÍ¡à຺ÃËÊÑ RLL㹺·¹¨ÕŒ Ð͸ԺÒ¶֧˹Òé ·‹ÕáÅÐËÅÑ¡¡Ò÷ӧҹ¢Í§ÃËÊÑ RLL (runlength limited) [9] «‹Ö§à»š¹·¹Õ‹ ÔÂÁãªé§Ò¹ÁÒ¡ã¹Ãкº¡ÒûÃÐÁÇżÅÊÑ­­Ò³¢Í§ÎÒÃì´´ÊÔ ¡ìä´Ã¿ì ¾ÃÍé Á·Ñ§Œ áÊ´§¢¹ŒÑ µÍ¹¡ÒÃÍ͡ẺÃËÑÊ RLL ÍÂÒè §§Òè  à¾Í‹× ãªé㹡ÒÃà¢Òé áÅжʹÃËÑÊ¢Íé ÁÙÅ8.1 º·¹ÓÃËÑÊ RLL ¤Í× ÃËÊÑ ÁÍ´ÙàŪѹ (modulation code) »ÃÐàÀ·Ë¹‹Ö§·‹Õ¹ÂÔ ÁãªéÁÒ¡ã¹Í»Ø ¡Ã³ìÎÒÃì´´ÊÔ ¡ìä´Ã¿ì â´Â¨Ð·Ó˹éÒ·ãՋ ¹¡ÒáÓ˹´¨Ó¹Ç¹¢Í§ºµÔ “0” áÅкµÔ “1” (µÒÁÃٻẺ¢Í§ NRZI) ·àՋ ÃÂÕ §µÔ´¡Ñ¹ã¹ÅÓ´ºÑ ¢Íé ÁÅÙ ·‹ÕµÍé §¡ÒèÐà¢Õ¹ŧä»ã¹ÊÍ‹× º¹Ñ ·Ö¡ â´Â·‹ÇÑ ä» ÃËÊÑ RLL ¨Ð¶¡Ù ¡Ó˹´´Çé ¾ÒÃÒÁàÔ µÍÃì 4 µÑÇ ¤Í× m, n, d, áÅÐ k â´Â¨ÐÍÂãèÙ ¹ÃÙ»¢Í§ÃËÑÊ m/n (d, k) àÁ‹Í× 1) m ¤×Í ¨Ó¹Ç¹¢Íé ÁÙźԵÍÔ¹¾Øµ (µÍè ¡ÒÃà¢Òé ÃËÑÊ˹֋§¤ÃŒ§Ñ ) ·¨Õ‹ зӡÒÃà¢éÒÃËÑÊ RLL 2) n ¤Í× ¨Ó¹Ç¹¢Íé ÁÙźµÔ àÍÒµì¾µØ (µÍè ¡ÒÃà¢Òé ÃËÊÑ Ë¹Ö‹§¤ÃŒ§Ñ ) ·Õä‹ ´¨é Ò¡¡ÒÃà¢éÒÃËÑÊ RLL â´Â·‹ÑÇä» n ≥ m àÊÁÍ 3) d ¤Í× àÅ¢¨Ó¹Ç¹àµçÁ·¡‹Õ Ó˹´¨Ó¹Ç¹·¹‹Õ Íé Â·Ê‹Õ Ø´¢Í§ºÔµ 0 ·‹ÕÍÂèÙÃÐËÇÒè §ºµÔ 1 4) k ¤Í× àÅ¢¨Ó¹Ç¹àµÁç ·‹Õ¡Ó˹´¨Ó¹Ç¹·ÁՋ Ò¡·Ê‹Õ Ø´¢Í§ºµÔ 0 ·‹ÍÕ ÂèÙÃÐËÇÒè §ºµÔ 1 151

152 ÈÙ¹Âàì ·¤â¹âÅÂÕÍàÔ Å¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÇÔ àµÍÃàì àË§è ªÒµÔ # input bits RLL # output bits (m bits) code (n bits) ÃÙ»·Õ‹ 8.1: Ẻ¨ÓÅͧ¡ÒÃà¢éÒÃËÊÑ RLLàÁ×‹Í ¢éÍÁÅÙ ºµÔ 1 ¨ÐÊÍ´¤ÅÍé §¡Ñº¡ÒÃà»ÅÂ‹Õ ¹Ê¶Ò¹Ð (transition) ¢Í§¡ÃÐáÊ俿҇ à¢Õ¹ (write current) ·Õ‹¨Ð»Í‡ ¹à¢éÒä»ã¹ËÇÑ à¢Õ¹ (write head) ྋ×Í·ÓãËéÊ×͋ º¹Ñ ·Ö¡ ³ ºÃàÔ Ç³·‹µÕ Íé §¡ÒèÐà¢Õ¹¢Íé ÁÙÅŧä»ÁÕÊÀÒ¾¤ÇÒÁ໚¹áÁàè ËÅ¡ç (magnetization) µÒÁ·‹ÕµÍé §¡Òà Êèǹ¢éÍÁÅÙ ºÔµ 0 ËÁÒ¶§Ö äÁèÁÕ¡ÒÃà»ÅՋ¹ʶҹТͧ¡ÃÐáÊä¿¿‡Òà¢Õ¹ à¾ÃÒЩйŒÑ¹ ¾ÒÃÒÁÔàµÍÃì d ¨ÐªÇè ·ÓãËéºÔµ 1 ÊͧºµÔ ÍÂèÙËèÒ§¡Ñ¹ «‹Ö§¨ÐªèÇÂÅ´¼Å¡Ãзº¢Í§¡ÒÃá·Ã¡ÊÍ´ÃÐËÇÒè §ÊÑ­Å¡Ñ É³ì (ISI: intersymbol interference)ÊÇè ¹¾ÒÃÒÁÔàµÍÃì k ¨ÐªÇè ÂÃѺ»ÃС¹Ñ ÇÒè ÅӴѺ¢éÍÁÙŷՋ¨Ðà¢ÂÕ ¹Å§ä»ã¹Ê׋ͺѹ·Ö¡¨ÐÁÕºÔµà»ÅÂՋ ¹Ê¶Ò¹Ðà¡´Ô ¢Ö¹Œ ÊÁ‹ÓàÊÁÍà¾Õ§¾Í à¾×͋ ·Õ‹¨Ð·ÓãËéÃкºä·ÁÁԋ§Ã¤Ô ¿Ñ àÇÍÐÃÕ (timing recovery) ÊÒÁÒö·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊ·Ô ¸ÀÔ Ò¾ µÑÇÍÂÒè §àª¹è ¶Òé ÅӴѺ¢éÍÁÙÅ·‹Õ¨Ðà¢Õ¹ŧä»ã¹ÊÍ׋ º¹Ñ ·¡Ö ¤Í× ···11111 ··· 11111···ÅÓ´ºÑ ¢Íé ÁÅÙ ¹ÕŒ¶×ÍÇÒè ໚¹ÅӴѺ¢éÍÁÅÙ ·Õ‹äÁè´Õ à¹Í‹× §¨Ò¡ ¨Ð·ÓãËéà¡Ô´»­˜ ËÒ ISI ÍÂÒè §Ãعáç ã¹·Ò§µÃ§¡Ñ¹¢Òé Á ¶éÒÅÓ´ºÑ ¢Íé ÁÙÅ·‹¨Õ Ðà¢Õ¹ŧä»ã¹Ê‹Í× ºÑ¹·Ö¡ ¤×Í ···00000 ··· 00000···¡ç¨Ð¶Í× ÇèÒ໹š ÅӴѺ¢éÍÁÅÙ ·‹ÕäÁè´Õàªè¹¡¹Ñ à¹×͋ §¨Ò¡ ¨Ð·ÓãËéà¡´Ô »­˜ ËÒàÃ׋ͧ¡ÒÃà¢Òé ¨Ñ§ËÇÐ (synchronization) ¢Í§Ãкºä·ÁÁÔ§‹ ÃԤѿàÇÍÐÃÕ à¾ÃÒЩй¹ÑŒ à¾Í׋ ËÅÕ¡àŋÕ§ÅӴѺ¢éÍÁÅÙ ·§ŒÑ 2 Ẻ¹ÕŒ ¨§Ö ÁÕ¤ÇÒÁ¨Ó໚¹·‹Õ¨Ðµéͧà¢Òé ÃËÊÑ ÅӴѺ¢Íé ÁÅÙ ´éÇÂÃËÊÑ RLL «§Ö‹ ã¹·Ò§»¯ÔºµÑ ÔáÅÇé ¡ÒÃà¢Òé áÅжʹÃËÑÊ´Çé ÂÃËÑÊ RLL ÊÒÁÒö·Óä´é§Òè Ââ´Â¡ÒÃãªé “µÒÃÒ§¤¹é ËÒ (lookup table)” 㹡ÒÃà¢Òé áÅжʹÃËÑÊ¢Íé ÁÅ٠û٠·Õ‹ 8.1 áÊ´§áºº¨ÓÅͧ¡ÒÃà¢Òé ÃËÊÑ RLL â´Â·‹Õ “굄 ÃÒÃËÑÊ (code rate)” ¨Ð¹ÂÔ ÒÁâ´Â ¨Ó¹Ç¹ºÔµÍÔ¹¾Øµ m ËÒôéǨӹǹºµÔ àÍÒµ¾ì µØ n ¹¹‹Ñ ¤Í× R = m ≤ 1 (8.1) n

8.2. ¨Ó¹Ç¹ÅÓ´ºÑ ¢éÍÁÅÙ ·ÑŒ§ËÁ´·‹ÊÕ Í´¤ÅÍé §¡Ñºà§‹×͹䢺§Ñ ¤Ñº (D, K ) 153à¹×‹Í§¨Ò¡ ¨Ó¹Ç¹ºÔµàÍÒµ¾ì ص n ·‹Õä´é¨Ò¡¡ÒÃà¢éÒÃËÊÑ ¨ÐÁըӹǹÁÒ¡¡ÇèÒËÃ×Íà·Òè ¡Ñº¨Ó¹Ç¹ºÔµÍÔ¹¾Øµm àÊÁÍ ´Ñ§¹ÑŒ¹ ¢éÍàÊÕ¢ͧ¡ÒÃà¢éÒÃËÑÊ RLL ·Õ‹à˹ç ä´éªÑ´à¨¹¡ç¤Í× ¨Ð·ÓãËàé ¡Ô´ “ºÔµÊÇè ¹à¡Ô¹ (redundant bit)” «Ö‹§¨Ð·ÓãËéÊÙ­àÊÕÂà¹Í׌ ·Õ‹¡ÒèѴà¡çº¢Íé ÁÙÅ·‹Õµéͧ¡ÒÃã¹ÎÒÃ´ì ´ÊÔ ¡ìä´Ã¿ì仺ҧÊÇè ¹ ´Ñ§¹Œ¹Ñ㹡ÒÃàÅÍ× ¡ÃËÑÊ RLL ã´ÁÒãªé§Ò¹ ¡ç¤Ç÷Ջ¨ÐàÅÍ× ¡ãªéÃËÑÊ RLL ·‹ÕÁÕÍѵÃÒÃËÊÑ R à¢éèÒã¡Åé¤èÒ 1ãËéÁÒ¡·‹ÊÕ ´Ø à¾×͋ Å´¡ÒÃÊÙ­àÊÕÂà¹ÍŒ× ·Õ‹¡ÒÃ¨Ñ´à¡ºç ¢Íé ÁÙŷՋµÍé §¡Òà ÊÓËÃºÑ à¹Œ×ÍËÒ㹺·¹ÕŒ¨Ð͸ԺÒ¶֧¢ÑŒ¹µÍ¹¡ÒÃÍ͡ẺÃËÊÑ RLL ÍÂÒè §§èÒ àÁ‹Í× ¡Ó˹´¾ÒÃÒÁàÔ µÍÃì m, n, d, áÅÐ k ÁÒãËé8.2 ¨Ó¹Ç¹ÅÓ´ºÑ ¢éÍÁÙŷь§ËÁ´·‹ÊÕ Í´¤Åéͧ¡ºÑ à§Í‹× ¹ä¢º§Ñ ¤Ñº (d, k)¡Ó˹´ãËéÅÓ´ºÑ ¢éÍÁÙÅÁÕ ¤ÇÒÁÂÒǷь§ÊÔ¹Œ L ºµÔ ¨Ó¹Ç¹ÅӴѺ¢Íé ÁÅÙ ·§ÑŒ ËÁ´ ·‹ÕÊÍ´¤ÅÍé §¡Ñºà§‹Í× ¹ä¢ºÑ§¤ºÑ (constraint) (d, k) ÊÒÁÒöËÒä´¨é Ò¡ÊÁ¡ÒõÍè 仹ŒÕ [9]N (L) = L + 1, 1 ≤ L ≤ d + 1 (8.2) (8.3)N (L) = N (L − 1) + N (L − d − 1), d + 1 ≤ L ≤ k (8.4) k (8.5)N (L) = d + k + 1 − L + N (L − i − 1), k < L ≤ d + kN (L) = i=d k N (L − i − 1), L > d + k i=dàÁÍ‹× N (L) = 0 ÊÓËÃºÑ L < 0 áÅÐ N (0) = 1 㹡óշՋ¾ÒÃÒÁàÔ µÍÃì k = ∞ ¨Ó¹Ç¹ÅӴѺ¢éÍÁÙÅ·§ÑŒ ËÁ´·Õ‹ÊÍ´¤ÅÍé §¡Ñºà§Í‹× ¹ä¢º§Ñ ¤ºÑ (d, ∞)¨ÐÊÒÁÒöËÒä´é¨Ò¡ÊÁ¡ÒõÍè 仹ŒÕNd(L) = L + 1, 1 ≤ L ≤ d + 1 (8.6)Nd(L) = Nd(L − 1) + Nd(L − d − 1), L > d + 1 (8.7)àÁ×͋ Nd(L) = 0 ÊÓËÃѺ L < 0 áÅÐ Nd(0) = 1 µÒÃÒ§·Õ‹ 8.1 áÊ´§µÇÑ ÍÂèÒ§¨Ó¹Ç¹ÅӴѺ¢éÍÁÅÙ·§ŒÑ ËÁ´ Nd(L) ·‹ÁÕ Õ¤ÇÒÁÂÒÇ L ·‹ÊÕ Í´¤Åéͧ¡Ñºà§×‹Í¹ä¢º§Ñ ¤Ñº (d, ∞)

154 ȹ٠Âìà·¤â¹âÅÂÕÍÔàÅ¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃìààË§è ªÒµÔµÒÃÒ§·‹Õ 8.1: µÇÑ ÍÂÒè §¨Ó¹Ç¹ÅÓ´ºÑ ¢Íé ÁÙÅ·ŒÑ§ËÁ´ Nd(L) ·Õ‹ÁÕ¤ÇÒÁÂÒÇ L ·‹ÕÊÍ´¤Åéͧ¡Ñºà§Í׋ ¹ä¢ºÑ§¤ºÑ (d, ∞) d L = 4 L = 5 L = 6 L = 7 L = 8 L = 9 L = 10 18 13 21 34 55 89 144 26 9 13 19 28 41 60 35 7 10 14 19 26 36 45 6 8 11 15 20 26 55 6 7 9 12 16 21 àÁ‹Í× ·ÃÒº¨Ó¹Ç¹ÅÓ´ºÑ ¢Íé ÁÙÅ·ŒÑ§ËÁ´ N (L) ·‹ÕÊÍ´¤Åéͧ¡Ñºà§×‹Í¹ä¢ºÑ§¤ºÑ (d, k) áÅÇé ¨Ó¹Ç¹ºµÔ·Œ§Ñ ËÁ´ K ·Ê‹Õ ÒÁÒö¹ÓÁÒãªáé ·¹ÅÓ´ºÑ ¢Íé ÁÙÅáµÅè ÐÅӴѺ¨ÐÁÕ¤èÒà·èÒ¡ºÑ K = log2 {N (L)} (bits) (8.8)àÁ‹Í× x á·¹¨Ó¹Ç¹àµçÁºÇ¡·‹Õ¹éÍ·Õʋ Ø´ ·‹ÕÁÕ¤Òè ÁÒ¡¡ÇÒè ËÃÍ× à·èÒ¡ºÑ ¤Òè x àªè¹ ¶éÒ N4(6) = 8 ¡çÊÒÁÒöãªé¢Íé ÁÅÙ ºÔµ¨Ó¹Ç¹ 3 ºÔµ {000, 001, 010, 011, 100, 101, 110, 111} 㹡ÒÃá·¹ÅӴѺ¢éÍÁÅÙ áµèÅÐẺ8.3 ¤ÇÒÁ¨¢Ø ͧÃËÊÑ RLL à຺ (d, k)ã¹·ÄɯբͧÃкºÊÍ‹× ÊÒà “¤ÇÒÁ¨Ø (capacity)” ËÁÒ¶§Ö ¤Òè ʧ٠ÊØ´¢Í§ÍµÑ ÃÒÃËÊÑ R ·Õ‹ÊÒÁÒö·ÓãËéÊÁÑ Ä·¸Ô¼Åä´é «‹§Ö ¨Ð¹ÔÂÒÁâ´Â [9] C (d, k) = lim 1 log2{N (L)} (8.9) n L→∞àÁ‹Í× N (L) ¤×Í ¨Ó¹Ç¹ÅӴѺ¢Íé ÁÅÙ ·Ñ§Œ ËÁ´·‹ÕÊÍ´¤ÅÍé §¡ºÑ à§Í‹× ¹ä¢º§Ñ ¤Ñº (d, k) ¹Í¡¨Ò¡¹ÕŒ ¤Òè ¤ÇÒÁ¨ØC (d, k) Âѧ໚¹¾ÒÃÒÁÔàµÍÃì·Õ‹º§è ºÍ¡¶§Ö ¤ÇÒÁÊÒÁÒö㹡Òè´Ñ à¡çº¢Íé ÁÙÅ¢èÒÇÊÒâͧ¼Ùãé ªé·‹Õµéͧ¡ÒèÐà¢Õ¹ŧä»ã¹Ê×͋ º¹Ñ ·Ö¡ (äÁè¹ÑººÔµÊÇè ¹à¡Ô¹) ¹‹¹Ñ ¤Í× ¶éÒ¤Òè C (d, k) ‹ԧÁÒ¡ ¡çáÊ´§ÇÒè ÃкºÊÒÁÒö¨´Ñ à¡çº¢Íé ÁÙÅ¢èÒÇÊÒâͧ¼éãÙ ªäé ´éÁÒ¡àª¹è ¡Ñ¹

8.3. ¤ÇÒÁ¨Ø¢Í§ÃËÊÑ RLL à຺ (D, K) 155¹Í¡¨Ò¡¹ŒãÕ ¹¡ÒÃà»ÃÂÕ ºà·ÂÕ º»ÃÐÊ·Ô ¸ÔÀÒ¾¢Í§ÃËÑÊ RLL ẺµèÒ§æ ÊÒÁÒö·Óä´âé ´Â¡ÒþԨÒóҷդ‹ Òè “»ÃÐÊ·Ô ¸Ô¼Å¢Í§ÃËÑÊ (code eciency)” «‹§Ö ¹ÂÔ ÒÁâ´Â η = R (8.10) C(d, k)¡ÅÒè ǤÍ× ÃËÑÊ RLL ·Õ‹Á¤Õ Òè »ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÊÑ ÁÒ¡ ¡áç Ê´§ÇÒè Á»Õ ÃÐÊÔ·¸ÔÀҾ㹡ÒÃãªé§Ò¹ÊÙ§8.3.1 굄 ÃÒ¢Òè ÇÊÒÃàªÔ§àÊ鹡ӡѺ¢Í§ÃËÑÊ RLL à຺ (d, k)๋×ͧ¨Ò¡ ¡ÒäӹdzËÒ¤èÒ¤ÇÒÁ¨Ø C (d, k) ã¹ÊÁ¡Òà (8.9) àÁ×͋ L → ∞ ·Óä´é¤è͹¢Òé §ÅÓºÒ¡´Ñ§¹Œ¹Ñ â´Â·Ñ‹Çä» ¨Ö§¹ÔÂÁ¤Ó¹Ç³ËÒ¤Òè C (d, k) ¨Ò¡ “ÍѵÃÒ¢Òè ÇÊÒÃàªÔ§àÊ鹡ӡºÑ (asymptotic information rate)” «§‹Ö ¹ÔÂÒÁâ´Â [58] C(d, k) = log2{λmax} (8.11)àÁ×‹Í λmax ¤Í× ÃÒ¡¨Ó¹Ç¹¨Ã§Ô (real root) ·Á‹Õ ¤Õ Òè ÁÒ¡ÊØ´ ¢Í§ÊÁ¡Òà (8.12) xk+2 − xk+1 − xk−d+1 + 1 = 0, k < ∞ (8.13) xd+1 − xd − 1 = 0, k = ∞µÒÃÒ§·‹Õ 8.2 áÊ´§ÍѵÃÒ¢èÒÇÊÒÃàª§Ô àÊ鹡ӡºÑ C (d, k) ¢Í§ÃËÊÑ RLL Ẻ (d, k) µèÒ§æ ·Õ‹ä´é¨Ò¡¡ÒÃá¡éÊÁ¡Òà (8.11) – (8.13) áÅÐàÁÍ‹× ¾Ô¨ÒóҤÒè C (d, k) ã¹µÒÃÒ§·‹Õ 8.2 ¨Ð¾ºÇèÒ ÃËÑÊ RLL ·Õ‹ãª·é ыÇ仨ÐÁÕ¤Òè ¾ÒÃÒÁÔàµÍÃì d ≤ 2 àÊÁÍ à¾Í‹× ·¨Õ‹ ÐÃѺ»ÃС¹Ñ ä´Çé Òè 굄 ÃÒÃËÑÊ R ≥ 1/28.3.2 ÍѵÃÒ¤ÇÒÁ˹Òàà¹è¹ÍѵÃÒ¤ÇÒÁ˹Òá¹è¹ DR (density ratio) ËÃ×Í ¤ÇÒÁ˹Òá¹¹è ¡ÒúÃÃ¨Ø (packing density) ໹š¾ÒÃÒÁàÔ µÍÃì·Õ‹º§è ºÍ¡¶Ö§ÃÐÂзҧ·Ò§¡ÒÂÀÒ¾ (physical distance) ÃÐËÇÒè §µÓá˹觢ͧ¡ÒÃà»ÅÕ‹ ¹Ê¶Ò¹Ð·‹µÕ ´Ô ¡¹Ñ 2 µÓá˹§è ¢Í§ÅÓ´ºÑ ¢éÍÁÅÙ ·àՋ ¢éÒÃËÊÑ RLL «§‹Ö ¹ÂÔ ÒÁâ´Â DR = (1 + d)R (8.14)

156 ÈÙ¹Âìà·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹¡Ô Êàì àÅФÍÁ¾ÇÔ àµÍÃàì àËè§ªÒµÔ µÒÃÒ§·‹Õ 8.2: 굄 ÃÒ¢èÒÇÊÒÃàªÔ§àÊ鹡ӡѺ¢Í§ÃËÊÑ RLL Ẻ (d, k) µÒè §æ k d=0 d=1 d=2 d=3 d=4 d=5 1 0.6942 2 0.8792 0.4057 3 0.9468 0.5515 0.2878 4 0.9752 0.6174 0.4057 0.2232 5 0.9881 0.6509 0.4650 0.3218 0.1823 10 0.9997 0.6909 0.5418 0.4460 0.3746 0.3158 15 0.9999 0.6939 0.5501 0.4615 0.3991 0.3513 ∞ 1.0000 0.6942 0.5515 0.4650 0.4057 0.3620â´Â·‹Õ R ¤Í× ÍµÑ ÃÒÃËÑÊ µÒÃÒ§·‹Õ 8.3 áÊ´§¤ÇÒÁÊÑÁ¾¹Ñ ¸ìÃÐËÇÒè §¤ÇÒÁ¨Ø C (d, k) áÅÐÍѵÃÒ¤ÇÒÁ˹Òá¹¹è DR ¨ÐàËç¹ä´éÇèÒàÁ׋ͤÇÒÁ¨Ø C (d, k) Ŵŧ ¤èÒ굄 ÃÒ¤ÇÒÁ˹Òá¹¹è DR ¡ç¨Ðà¾Áԋ ¢Œ¹Ö ¤ÇÒÁÊÑÁ¾Ñ¹¸ì¹ÕŒÊÒÁÒö͸ԺÒÂä´é´§Ñ µÍè 仹Ռ ¨Ò¡ÊÁ¡Òà (8.14) àÁÍ‹× ¾ÒÃÒÁàÔ µÍÃì d ྋÁÔ ¢¹ÖŒ ¤Òè DR ¡¨ç Ðà¾ÔÁ‹ ¢¹ŒÖ áµè¾ÒÃÒÁàÔ µÍÃì d ·‹àÕ ¾Á‹Ô¢ŒÖ¹¹ŒÕ ÁÕ¤ÇÒÁËÁÒÂÇÒè ¢éÍÁÙŷՋ¶Ù¡à¢éÒÃËÑʨÐÁÕºÔµÊÇè ¹à¡¹Ô à¾Á‹Ô ÁÒ¡¢ÖŒ¹ (à¾ÃÒÐÇèÒ ¾ÒÃÒÁàÔ µÍÃì d ¤×ͨӹǹºÔµ 0 ¹éÍÂÊ´Ø ·Õ‹ÍÂÙèÃÐËÇèÒ§ºÔµ 1) ¶Òé ¾Ô¨ÒóÒÇÒè ÊÍ׋ º¹Ñ ·¡Ö ÁÕà¹Í׌ ·‹Õ㹡Òè´Ñ à¡çº¢Íé ÁÙŷՋ¨Ó¡´Ñ´Ñ§¹¹ÑŒ ÃкºÊÒÁÒö·Õ¨‹ ШѴà¡çº¢éÍÁÙÅ¢èÒÇÊÒâͧ¼ãÙé ªäé ´¹é Íé Âŧ ๋Í× §¨Ò¡ µéͧàËÅ×Íà¹Í׌ ·ºÕ‹ Ò§ÊèǹäÇéÊÓËÃѺ¨´Ñ à¡ºç ºµÔ ÊÇè ¹à¡Ô¹ à¾ÃÒЩйѹŒ ¨Ö§Ê§è ¼Å·Óãˤé èÒ¤ÇÒÁ¨Ø C (d, k) ·‹¤Õ ӹdzä´Áé Õ¤Òè ¹Íé Âŧ8.4 à¤Ã׋ͧʶҹШӡѴ¢Í§ÃËÊÑ RLLà¤Ã׋ͧʶҹШӡѴ (FSM: nite state machine) ¢Í§ÃËÑÊ RLL ¨ÐáÊ´§ãËàé Ë繶֧ ¡ÒÃà»Å‹ÂÕ ¹á»Å§¢Í§Ê¶Ò¹Ðã¹ÃËÑÊ RLL µÒÁোÍ× ¹ä¢º§Ñ ¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì (d, k) µÇÑ ÍÂÒè §àª¹è ÃËÑÊ RLL Ẻ(d, k) ¨ÐÁÕà¤Ã×͋ §Ê¶Ò¹Ð¨Ó¡Ñ´µÒÁÃÙ»·‹Õ 8.2 àÁÍ‹× Si ¤×Í Ê¶Ò¹Ð i áÅеÑÇàÅ¢·á‹Õ Ê´§ÍµèÙ ÒÁàʹé ÅÙ¡Èä×Í ¢Íé ÁÅÙ ºÔµàÍÒµì¾Øµ·Õ‹ÊÍ´¤Åéͧ¡ºÑ ো×͹䢺§Ñ ¤ºÑ ¢Í§¾ÒÃÒÁÔàµÍÃì (d, k) ¨Ò¡Ã»Ù ·‹Õ 8.2 ʶҹÐàËÁÔ µ¹é

8.4. à¤Ã‹×ͧʶҹШӡѴ¢Í§ÃËÊÑ RLL 157µÒÃÒ§·‹Õ 8.3: ¤ÇÒÁÊÑÁ¾¹Ñ ¸ìÃÐËÇÒè §¤ÇÒÁ¨Ø C (d, k) áÅÐÍѵÃÒ¤ÇÒÁ˹Òá¹¹è DR d C(d, ∞) DR = (1 + d)C(d, ∞) 1 0.6942 1.3884 2 0.5515 1.6545 3 0.4650 1.8600 4 0.4057 2.0285 5 0.3620 2.1720 0 S2 0 Sd 0 Sd+1 0 0S1 1 Sk Sk+1 11 û٠·‹Õ 8.2: à¤Ã׋ͧʶҹШӡѴ¢Í§ÃËÑÊ RLL Ẻ (d, k)¨ÐÍÂèÙ·‹ÊÕ ¶Ò¹Ð S1 «§‹Ö ãËé¶×ÍÇÒè à»èš¹à˵ءÒó·ì ‹àÕ ¨ÍºÔµ 1 µÇÑ ááã¹ÅӴѺ¢éÍÁÅÙ à¾ÃÒЩйѹŒ ºÔµµÍè 仨еéͧ໹š ºÔµ 0 ໚¹¨Ó¹Ç¹ÍÂÒè §¹éÍ d µÑǵ´Ô µèÍ¡¹Ñ (¹¹‹Ñ ¤Í× Ê¶Ò¹Ð S1 ¡ç¨Ðà´¹Ô ·Ò§à»¹š àÊ¹é µÃ§ä»ÂѧʶҹРSd+1) ¾ÍÅÓ´ºÑ ¢éÍÁÅÙ ÁÕºÔµ 0 ¤Ãº d µÑÇáÅÇé ¨Ò¡à§×͋ ¹ä¢º§Ñ ¤Ñº (d, k) áÊ´§ÇèÒ ºÔµµÑǶѴä»ÊÒÁÒö໹š ä´é·Œ§Ñ ºµÔ 0 ËÃÍ× ºÔµ 1 «‹§Ö ¶Òé ໹š ºµÔ 1 àÁÍ׋ ã´ Ãкº¡ç¨ÐµéͧNjԧ¡ÅѺä»àËÁÔ µ¹é ·Õ‹Ê¶Ò¹Ð S1 ãËÁè áµè¶Òé ໚¹ºµÔ 0 ¡ç¨ÐÁÕºµÔ 0 ä´Íé ¡Õ äÁèà¡¹Ô k − d µÑÇ áÅÐàÁ‹Í× ÁºÕ Ôµ 0 µ´Ô µÍè ¡Ñ¹¤Ãº kµÑÇáÅéÇ ºÔµµÇÑ ¶´Ñ 仨еéͧ໚¹ºµÔ 1 à·èÒ¹ŒÑ¹ ¹¹‹Ñ ¤×Í Ãкº¨Ð¶Ù¡º§Ñ ¤ºÑ ãËé¡ÅºÑ ä»àÃÁԋ µ¹é ·Õ‹Ê¶Ò¹Ð S1ãËÁèâ´Â굄 â¹ÁѵԵÑÇÍÂèÒ§·Õ‹ 8.1 ¨§áÊ´§á¼¹ÀÒ¾à¤ÃÍ‹× §Ê¶Ò¹Ð¨Ó¡´Ñ ¢Í§ÃËÊÑ RLL µÒÁà§×͋ ¹ä¢º§Ñ ¤Ñº¢Í§¾ÒÃÒÁÔàµÍÃì(d, k) = (1, 3)ÇÔ¸Õ·Ó ¾ÒÃÒÁàÔ µÍÃì (1, 3) ËÁÒ¶֧ ÅӴѺ¢Íé ÁÅÙ ¨ÐÁÕºÔµ 0 ÍÂÒè §¹éÍÂ˹§‹Ö µÑÇ ËÃ×ÍÍÂÒè §ÁÒ¡ÊÒÁµÑÇ

158 ÈÙ¹Âìà·¤â¹âÅÂÍÕ àÔ Å¡ç ·Ã͹¡Ô Êàì àÅФÍÁ¾ÔÇàµÍÃìààË§è ªÒµÔ 0 S2 0 S3 0 S4 S1 1 1 1 û٠·‹Õ 8.3: à¤ÃÍ׋ §Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÊÑ RLL Ẻ (1, 3)µÔ´µÍè ¡Ñ¹ ·Í‹Õ ÂèÃÙ ÐËÇèÒ§ºÔµ 1 «‹§Ö ÊÒÁÒöà¢Õ¹໚¹à¤Ã×͋ §Ê¶Ò¹Ð¨Ó¡Ñ´ä´é µÒÁÃÙ»·Õ‹ 8.38.5 àÁ·Ã¡Ô «ì¡ÒÃà»ÅÕ‹ ¹Ê¶Ò¹Ðà¤ÃÍ‹× §Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÊÑ RLL Ẻ (d, k) ÊÒÁÒöà¢Õ¹ãËéÍÂèÙã¹ÃÙ»¢Í§ “àÁ·ÃÔ¡«ì¡ÒÃà»Å‹Õ¹ʶҹР(state transition matrix)” ä´é «§‹Ö ¹ÂÔ ÒÁâ´Â àÁ·Ã¡Ô «ì D ·Õ‹Á¢Õ ¹Ò´ (k + 1) á¶Ç áÅÐ (k + 1)á¹Çµ§ÑŒ â´Â·Õ‹ ÊÁÒª¡Ô ¢Í§àÁ·Ã¡Ô «ì D(i, j) ¹¹‹Ñ ¤Í× á¶Ç·Õ‹ i áÅÐá¹Çµ§ŒÑ ·‹Õ j ¨Ð¶¡Ù ¡Ó˹´â´Â D(i, 1) = 1, i ≥ d + 1 (8.15)  1, j = i + 1 D(i, j) =  0, elseµÑÇÍÂÒè §àªè¹ à¤Ã‹×ͧʶҹШӡѴ¢Í§ÃËÑÊ RLL Ẻ (1, 3) µÒÁû٠·Õ‹ 8.3 ÊÒÁÒöà¢ÂÕ ¹à»š¹àÁ·Ã¡Ô «ì¡ÒÃà»ÅÂՋ ¹Ê¶Ò¹Ðä´é´Ñ§¹ÕŒ  D =  0 1 0 0  (8.16) 1 0 1 0 1 0 0 1 1000 àÁ·ÃÔ¡«ì D ã¹ÊÁ¡Òà (8.16) ÊÒÁÒöÊÃÒé §ä´é´Ñ§µÍè 仹Ռ ¶Òé ¡Ó˹´ãËéáµèÅÐá¶Ç᷹ʶҹÐáµÅè ÐʶҹР¡ÅèÒǤ×Í á¶Ç ·Õ‹ ˹֧‹ ãªé ᷹ʶҹРS1 áÅÐá¶Ç ·Õ‹ Êͧ ãªé ᷹ʶҹРS2 ໹š µé¹àªè¹à´ÕÂÇ¡¹Ñ ãËéáµÅè Ðá¹Çµ§ŒÑ ᷹ʶҹÐáµèÅÐʶҹР¡ÅèÒǤ×Í á¹Çµ§ÑŒ ·Õ‹Ë¹§‹Ö ãªé᷹ʶҹРS1 áÅÐ

8.5. àÁ·Ã¡Ô «ì¡ÒÃà»Å‹ÂÕ ¹Ê¶Ò¹Ð 159á¹ÇµÑ§Œ ·Õ‹Êͧãªé᷹ʶҹРS2 ໹š µ¹é ´Ñ§¹Œ¹Ñ 㹡ÒÃÊÃÒé §àÁ·ÃÔ¡«ì¡ÒÃà»ÅÂՋ ¹Ê¶Ò¹Ð¨Ò¡à¤ÃÍ׋ §Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÊÑ RLL Ẻ (1, 3) µÒÁÃÙ»·‹Õ 8.3 ãËé¾Ô¨ÒóҷÅÕ Ðá¹ÇµŒÑ§ àªè¹ ã¹á¹ÇµÑŒ§·Õ‹Ë¹‹Ö§(ʶҹРS1) ãËé´ÙÇÒè ÁÕàÊé¹ÅÙ¡ÈèҡʶҹРSi ã´ºÒé §·Õ‹ÇÔ§‹ à¢Òé ÁҷՋʶҹРS1 ¨Ò¡Ã»Ù ·Õ‹ 8.3 ¨Ð¾ºÇèÒ ÁÕàÊé¹Å¡Ù ÈèҡʶҹРS2, S3, áÅÐ S4 ´Ñ§¹¹ÑŒ ã¹á¹ÇµÑŒ§·Õ‹Ë¹§‹Ö ¹ÕŒ ¤èÒ 1 ¨Ð¶¡Ù ãÊèà¢Òé ä»ã¹á¶Ç·Õ‹Êͧ, á¶Ç·Ê‹Õ ÒÁ, áÅÐá¶Ç·‹ÕÊՋ Êèǹá¶Ç·‹Õ˹֧‹ ¨ÐãËàé »¹š ¤èÒ 0 㹷ӹͧà´ÕÂǡѹ ¶éÒ¾Ô¨ÒóҷՋá¹Çµ§ÑŒ·‹ÕÊͧ (ʶҹРS2) ãËé´ÙÇÒè ÁÕàʹé ÅÙ¡ÈèҡʶҹРSi ã´ºéÒ§·Õ‹Ç§‹Ô à¢Òé ÁÒ·Ê‹Õ ¶Ò¹Ð S2 ¨Ò¡Ã»Ù ·‹Õ 8.3 ¨Ð¾ºÇÒè ÁÕàÊé¹Å¡Ù ÈèҡʶҹРS1 àÊé¹à´ÕÂÇ·‹ÕNj§Ô ÁҷՋʶҹРS2 ´Ñ§¹Ñ¹Œ ¤èÒ 1 ¨Ð¶¡Ù ãÊèà¢Òé ä»ã¹á¶Ç·Õ‹Ë¹Ö§‹ Êèǹá¶Ç͹׋ æ ¨ÐÁ¤Õ èÒ໚¹¤Òè 0 ໚¹µ¹é ÊÓËÃѺ㹡óշ‹Õ¾ÒÃÒÁàÔ µÍÃì k = ∞ à¤ÃÍ‹× §Ê¶Ò¹Ð¨Ó¡´Ñ ¢Í§ÃËÑÊ RLL Ẻ (d, ∞) ÊÒÁÒöà¢Õ¹ãËÍé ÂãÙè ¹Ã»Ù ¢Í§àÁ·Ã¡Ô «¡ì ÒÃà»ÅÂ‹Õ ¹Ê¶Ò¹Ð D ·Á‹Õ Õ¢¹Ò´ (d + 1) á¶Ç áÅÐ (d + 1) á¹ÇµÑŒ§ â´Â·‹Õ ÊÁÒªÔ¡¢Í§àÁ·Ã¡Ô «ì D(i, j) ¨Ð¶¡Ù ¡Ó˹´â´Â D(i, j) = 1, j = i + 1 (8.17)D(d + 1, 1) = D(d + 1, d + 1) = 1 D(i, j) = 0, elseµÇÑ ÍÂÒè §·‹Õ 8.2 ¨§áÊ´§á¼¹ÀÒ¾à¤ÃÍ‹× §Ê¶Ò¹Ð¨Ó¡´Ñ áÅÐàÁ·Ã¡Ô «¡ì ÒÃà»ÅՋ¹ʶҹР¢Í§ÃËÊÑ RLLµÒÁà§×͋ ¹ä¢º§Ñ ¤ºÑ ¢Í§¾ÒÃÒÁÔàµÍÃì (d, k) = (0, 3)ÇÔ¸Õ·Ó ¾ÒÃÒÁÔàµÍÃì (0, 3) ËÁÒ¶§Ö ÅӴѺ¢Íé ÁÅÙ ¨ÐÁÕºÔµ 0 ÍÂÒè §¹éÍÂ˹‹Ö§µÇÑ ËÃÍ× ÍÂèÒ§ÁÒ¡ÊÒÁµÇÑ µÔ´µèÍ ¡Ñ¹ ·Õ͋ ÂèÙ ÃÐËÇèÒ§ ºµÔ 1 «‹Ö§ ÊÒÁÒö à¢Õ¹ ໚¹ à¤Ã‹Í× § ʶҹР¨Ó¡Ñ´ ä´é µÒÁ û٠·‹Õ 8.4 â´Â ·‹ÕàÁ·ÃÔ¡«¡ì ÒÃà»ÅÕ‹Â¹Ê¶Ò¹Ð·Ê‹Õ Í´¤ÅÍé §¡ºÑ à¤Ã׋ͧʶҹШӡ´Ñ ¹ŒÕ ¤Í×  D =  1 1 0 0  1 0 1 0 1 0 0 1 1000

160 ÈÙ¹Âìà·¤â¹âÅÂÕÍÔàÅ¡ç ·Ã͹ԡÊàì àÅФÍÁ¾ÔÇàµÍÃìààË§è ªÒµÔ 1 0 S2 0 S3 0 S4 S1 11 1 û٠·‹Õ 8.4: à¤ÃÍ׋ §Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÊÑ RLL Ẻ (0, 3)8.5.1 ¡ÒÃËÒÍѵÃÒ¢Òè ÇÊÒÃàª§Ô àÊ¹é ¡Ó¡ºÑàÁ·ÃÔ¡«¡ì ÒÃà»Å‹Õ¹ʶҹРD ÊÒÁÒö¹ÓÁÒãªé㹡ÒäӹdzËÒ굄 ÃÒ¢èÒÇÊÒÃàªÔ§àÊ鹡ӡºÑ C (d, k)¨Ò¡ÊÙµÃã¹ÊÁ¡Òà (8.11) ¹¹‹Ñ ¤×Í C(d, k) = log2 λmDax (8.18)â´Â·Õ‹ λmDax ¤Í× ¤Òè ÅѡɳÐ੾ÒШӹǹ¨Ã§Ô (real eigenvalue) ·Á‹Õ ¤Õ èÒÁÒ¡Ê´Ø ¢Í§àÁ·ÃÔ¡«¡ì ÒÃà»ÅÂՋ ¹Ê¶Ò¹Ð D «§Ö‹ ËÒä´é¨Ò¡¡ÒÃá¡éÊÁ¡Òà det(D − λI) = 0 (8.19)àÁ×‹Í det(·) ¤Í× ¡ÒÃËÒ¤èÒ´àÕ ·ÍÃÁì Ôá¹¹µì (determinant), I ¤×Í àÁ·Ã¡Ô «àì Í¡Å¡Ñ É³ì (identity matrix)·Õ‹Á¢Õ ¹Ò´à·èÒ¡ºÑ àÁ·Ã¡Ô «ì D, áÅÐ λ ¤×Í ¤èÒÅ¡Ñ É³Ð੾ÒÐ8.5.2 ÅÓ´ºÑ ¢éÍÁÅÙ ·Ê‹Õ Í´¤Åéͧ¡ºÑ à¤ÃÍ׋ §Ê¶Ò¹Ð¨Ó¡´Ñ ¢Í§ÃËÑÊ RLL à຺ (d, k)¨Ò¡à¤Ã׋ͧʶҹШӡ´Ñ ¢Í§ÃËÑÊ RLL Ẻ (d, k) ·‹ÕáÊ´§ã¹ÃÙ»·‹Õ 8.2 àÁ‹×Í Si ¤×Í Ê¶Ò¹Ð i ´Ñ§¹Œ¹Ñ¨Ó¹Ç¹ÅӴѺ¢Íé ÁÅÙ ·à‹Õ »¹š ä»ä´·é Œ§Ñ ËÁ´·ÕÁ‹ Õ¤ÇÒÁÂÒÇ L ºÔµ ·Í‹Õ Í¡¨Ò¡Ê¶Ò¹Ð Si áÅéÇä»Ê¹ŒÔ ÊØ´·ÊՋ ¶Ò¹ÐSj ¨ÐÁ¤Õ Òè à·Òè ¡ºÑ ¤Òè ¢Í§ÊÁÒª¡Ô á¶Ç·‹Õ i áÅÐá¹Çµ§ŒÑ ·‹Õ j ¢Í§àÁ·Ã¡Ô «ì DL ¹¹‹Ñ ¤×Í DL(i, j)µÇÑ ÍÂÒè §·‹Õ 8.3 à¤Ã׋ͧʶҹШӡ´Ñ ¢Í§ÃËÊÑ RLL Ẻ (0, 2) áÊ´§ã¹ÃÙ»·Õ‹ 8.5 ¨§ËҨӹǹÅÓ´ºÑ¢Íé ÁÙÅ·‹Õ໚¹ä»ä´é·ÑŒ§ËÁ´·‹ÕÁÕ¤ÇÒÁÂÒÇ 2 ºÔµ ·‹ÕÍÍ¡¨Ò¡Ê¶Ò¹Ð Si áÅÇé ä»ÊŒÔ¹Ê´Ø ·Õ‹Ê¶Ò¹Ð Sj ÊÓËúÑ

8.5. àÁ·ÃÔ¡«¡ì ÒÃà»ÅÕ‹ ¹Ê¶Ò¹Ð 161 1 0 S2 0 S1 S3 11 û٠·‹Õ 8.5: à¤ÃÍ‹× §Ê¶Ò¹Ð¨Ó¡Ñ´¢Í§ÃËÊÑ RLL Ẻ (0, 2)0 ≤ i, j ≤ 3Ç¸Ô Õ·Ó à¤Ã‹×ͧʶҹШӡ´Ñ ¢Í§ÃËÊÑ RLL Ẻ (0, 2) ã¹Ã»Ù ·Õ‹ 8.5 ÊÒÁÒöà¢Õ¹ãËéÍÂèÙã¹Ã»Ù ¢Í§àÁ·ÃÔ¡«¡ì ÒÃà»ÅՋ¹ʶҹРD ä´é ¤Í×   D =  1 1 0  (8.20) 1 0 1 100´Ñ§¹¹ÑŒ ¨Ó¹Ç¹ÅÓ´ºÑ ¢éÍÁÙŷՋ໚¹ä»ä´é·Œ§Ñ ËÁ´·Õ‹Á¤Õ ÇÒÁÂÒÇ 2 ºµÔ ËÒä´¨é Ò¡ D2 «Ö‹§Á¤Õ Òè à·èÒ¡ºÑ  D2 =  2 1 1  (8.21) 2 1 0 110ÊÁ¡Òà (8.21) ºÍ¡ãËé·ÃÒºÇÒè • ÅӴѺ¢Íé ÁÅÙ ·‹ÍÕ Í¡¨Ò¡Ê¶Ò¹Ð S1 → S1 Áըӹǹà·èÒ¡ºÑ D(1, 1) = 2 µÑÇ ¤Í× {01, 11} • ÅÓ´ºÑ ¢éÍÁÅÙ ·Õ‹ÍÍ¡¨Ò¡Ê¶Ò¹Ð S2 → S1 Á¨Õ ӹǹà·èҡѺ D(2, 1) = 2 µÇÑ ¤×Í {01, 11} • ÅӴѺ¢éÍÁÙÅ·‹ÍÕ Í¡¨Ò¡Ê¶Ò¹Ð S3 → S1 Áըӹǹà·èҡѺ D(3, 1) = 1 µÇÑ ¤×Í {11} • ÅӴѺ¢Íé ÁÙÅ·Í‹Õ Í¡¨Ò¡Ê¶Ò¹Ð S1 → S2 Á¨Õ ӹǹà·èҡѺ D(1, 2) = 2 µÑÇ ¤Í× {10}

162 ȹ٠Âàì ·¤â¹âÅÂÕÍÔàÅç¡·Ã͹¡Ô Êàì àÅФÍÁ¾ÇÔ àµÍÃìààË§è ªÒµÔ8.6 ¢Ñ¹Œ µÍ¹¡ÒÃÍÍ¡à຺ÃËÑÊ RLLã¹ÊÇè ¹¹Œ¨Õ ÐáÊ´§¢ÑŒ¹µÍ¹¡ÒÃÍ͡ẺµÒÃÒ§¤¹é ËÒ à¾×‹Íãªé㹡ÒÃà¢éÒáÅжʹÃËÊÑ RLL â´Â㪵é ÑÇÍÂèÒ§´Ñ§µÍè 仹ŒÕµÑÇÍÂèÒ§·Õ‹ 8.4 ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃѺ¡ÒÃà¢éÒáÅжʹÃËÊÑ RLL Ẻ (0, 2) â´Â·Õ‹¢Íé ÁÙÅáµÅè ФÌѧ·‹¼Õ èÒ¹¡ÒÃà¢Òé ÃËÑÊáÅÇé ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡ºÑ n = 3 ¾ÃéÍÁ·§ÑŒ ËÒ»ÃÐÊ·Ô ¸¼Ô ŢͧÃËÑÊ ηÇ¸Ô ·Õ Ó ¡ÒÃÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃѺ¡ÒÃà¢éÒáÅжʹÃËÑÊ RLL ÊÒÁÒöáºè§Í͡໹š 4 ¢Œ¹Ñ µÍ¹ ´§Ñ ¹ÕŒ¢¹ŒÑ µÍ¹·Õ‹ 1: ãË¾é ¨Ô ÒóҴÙÇÒè ¢Íé ÁÅÙ 3 ºÔµÁ·Õ ѧŒ ËÁ´¡Õ‹áºº «§‹Ö ¨Ðä´Çé èÒ ÁÕ·Œ§Ñ ËÁ´ 8 Ẻ ¤Í× {000, 001, 010, 011, 100, 101, 110, 111}¢Ñ¹Œ µÍ¹·‹Õ 2: ãËé¾Ô¨ÒóҴÙÇèÒ ÁÕ¢Íé ÁÅÙ ªØ´ä˹ºÒé §·‹ÕäÁèÊÍ´¤Åéͧ¡Ñºà§‹Í× ¹ä¢º§Ñ ¤Ñº (0, 2) «§‹Ö ¨Ð¾ºÇÒè Á¢Õ éÍÁÙŷь§ËÁ´ 7 Ẻ·Õ¼‹ èҹো×͹䢺§Ñ ¤Ñº (0, 2) ¹‹Ñ¹¤Í× {001, 010, 011, 100, 101, 110, 111}¢ÑŒ¹µÍ¹·Õ‹ 3: ãËéÅͧ¹Ó¢éÍÁÅÙ ·ä‹Õ ´¨é Ò¡¢¹ÑŒ µÍ¹·‹Õ 2 áµÅè еÇÑ ÁÒ·Ó¡Òõè͡ѹ·Ñ§Œ ·Ò§«Òé ÂáÅзҧ¢ÇÒáÅÇé ´ÙÇèÒ ÁÕ¢Íé ÁÙŵÑÇä˹ºéÒ§·Õ‹àÁÍ‹× ¹ÓÁÒµÍè ¡Ñ¹áÅÇé ¨ÐäÁèÊÍ´¤Åéͧ¡Ñºà§×‹Í¹ä¢º§Ñ ¤Ñº (0, 2) 㹷Ջ¹ŒÕ¨Ð¾ºÇèÒ ¢éÍÁÅÙ 001 áÅÐ 100 àÁÍ‹× ¹Ó仵è͡Ѻ¢Íé ÁÅÙ µÇÑ Í×¹‹ ¨Ð·ÓãËéà§×͋ ¹ä¢ºÑ§¤Ñº (0, 2) ¼Ô´ä» ´Ñ§¹¹ŒÑ¢Íé ÁÙÅ 001 áÅÐ 100 ¨ÐµÍé §¶¡Ù µ´Ñ ·Ô§Œ ä» ·ÓãËé¢éÍÁÙÅ·‹ÕËŧàËÅÍ× ÍÂÙèÁÕà¾ÂÕ § 5 Ẻ ·‹Õ¼Òè ¹à§‹Í× ¹ä¢º§Ñ ¤Ñº (0, 2) ¹¹‹Ñ ¤Í× {010, 011, 101, 110, 111}«‹§Ö ¢Íé ÁÅÙ àËÅÒè ¹Õ¡Œ ç¤×Í ¢éÍÁÙÅ·ÊՋ ÒÁÒö¹ÓÁÒãªàé »¹š ¢éÍÁÙÅ·‹Õ¼Òè ¹¡ÒÃà¢éÒÃËÑÊ RLL áÅéÇ¢¹ŒÑ µÍ¹·Õ‹ 4: ¨Ò¡¢Íé ÁÙÅ·ŒÑ§ 5 Ẻ·Õ‹ä´éã¹¢Œ¹Ñ µÍ¹·‹Õ 3 ãËéàÅ×Í¡ÁÒ 4 Ẻ (Ẻ㴡äç ´)é à¾×‹Íãªé㹡ÒÃÊÃéÒ§µÒÃÒ§¤é¹ËÒ ÊÓËÃºÑ ¡ÒÃà¢éÒáÅжʹÃËÊÑ ¢éÍÁÅÙ Í¹Ô ¾Øµ·ÅÕ Ð 2 ºÔµ ¹‹Ñ¹¤×Í {00, 01, 10,11} «‹§Ö ¨Ðä´é µÒÁµÒÃÒ§·Õ‹ 8.4 áÅШÐä´éÇèÒ ÍѵÃÒÃËÑÊ ¤Í×

8.6. ¢¹ŒÑ µÍ¹¡ÒÃÍÍ¡à຺ÃËÊÑ RLL 163 µÒÃÒ§·Õ‹ 8.4: µÒÃÒ§¤é¹ËÒÊÓËÃѺ¡ÒÃà¢éÒáÅжʹÃËÊÑ RLL Ẻ (0, 2) ¢éÍÁÙÅÍ¹Ô ¾µØ ¢éÍÁÅÙ àÍÒµì¾Øµ 00 010 01 011 10 101 11 110 R = 2 3 㹷ӹͧà´ÕÂÇ¡¹Ñ ¡ÒÃËÒ»ÃÐÊÔ·¸¼Ô ŢͧÃËÊÑ RLL ÊÒÁÒöËÒä´éµÒÁ¢Œ¹Ñ µÍ¹µÍè 仹Ռ àÃԋÁµé¹ãËéÊÃÒé §à¤Ã‹×ͧʶҹШӡ´Ñ ¢Í§ÃËÑÊ RLL Ẻ (0, 2) «‹Ö§¨Ðä´éµÒÁÃÙ»·Õ‹ 8.5 ¨Ò¡¹Œ¹Ñ ãËéÊÃéÒ§àÁ·ÃÔ¡«ì¡ÒÃà»Å‹ÂÕ ¹Ê¶Ò¹Ð·Õ‹ÊÍ´¤Åéͧ¡Ñºà¤Ã‹Í× §Ê¶Ò¹Ð¨Ó¡Ñ´ã¹Ã»Ù ·Õ‹ 8.5 «§Ö‹ ¨Ðä´é¼ÅÅѾ¸ìµÒÁÊÁ¡Òà (8.20)¹‹¹Ñ ¤Í×  D =  1 1 0  1 0 1 100¢¹ŒÑ µÍ¹µèÍÁÒ ¤Í× ¡ÒÃËÒ¤èÒÅѡɳÐ੾ÒТͧàÁ·Ã¡Ô «ì D «§‹Ö ÊÒÁÒöËÒä´é¨Ò¡á¡éÊÁ¡Òà (8.19)¹¹‹Ñ ¤Í×     det  1 1 0  − λ  1 0 0  = 0 1 0 1 0 1 0 100 001   det  1−λ 1 0  = 0 1 −λ 1 1 0 −λ −λ3 + λ2 + λ + 1 = 0 (8.22)

164 ÈÙ¹Âìà·¤â¹âÅÂÍÕ àÔ Å¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃìààË觪ҵÔâ´Â¡ÒÃá¡Êé Á¡Òà (8.22) àÃÒ¨Ðä´Çé èÒ λ = 1.8393, −0.4196 + 0.6063i, −0.4196 − 0.6063i´§Ñ ¹ŒÑ¹ λDmax = 1.8393 ¨Ð¶¡Ù ¹ÓÁÒãªé㹡ÒäӹdzËÒ¤ÇÒÁ¨Ø C(d, k) µÒÁÊÁ¡Òà (8.18) ¹¹‹Ñ ¤×Í C(d, k) = log2{λmax} = log2{1.8393} = 0.87916áÅлÃÐÊÔ·¸¼Ô ŢͧÃËÊÑ η ËÒä´¨é Ò¡ÊÁ¡Òà (8.10) «‹§Ö ¨Ðä´Çé Òè η = R = 2/3 = 0.7583 C(d, k) 0.879168.7 µÇÑ ÍÂèÒ§ÃËÊÑ RLL à຺µèÒ§æÃËÊÑ RLL ÁËÕ ÅÒÂẺ¢Ö¹Œ ÍÂÙè¡Ñº¾ÒÃÒÁÔàµÍÃì (d, k) áÅÐ굄 ÃÒÃËÑÊ R ·Õ‹ãªé ã¹Â¤Ø àËÁÔ µ¹é ¢Í§Í»Ø ¡Ã³ìÎÒÃ´ì ´ÔÊ¡ìä´Ã¿ì ÃËÑÊ RLL ·‹Õãªé¨ÐÁÕªÍ‹× ÇèÒ “ÃËÑÊ FM (frequency modulation)” â´ÂÁÕµÒÃÒ§¤¹é ËÒÊÓËÃѺ¡ÒÃà¢Òé áÅжʹÃËÊÑ µÒÁû٠·‹Õ 8.6(a) â´ÂÃËÑÊ FM ¹ŒÕ¨Ðãªé§Ò¹ÃÇè Á¡ÑºÇ§¨ÃµÃǨËҨشʧ٠ʴØ(peak detector) áÅÐÁÍÕ µÑ ÃÒÃËÑÊ R = 1/2 «‹Ö§¨Ð·ÓãËéµÍé §Ê­Ù àÊÕ¾¹Œ× ·Õ㋠¹ÎÒÃì´´ÔÊ¡ìä´Ã¿äì »»ÃÐÁÒ³50% ྋÍ× à¡çº¢Íé ÁÅÙ ºµÔ Êèǹà¡Ô¹ µÇÑ ÍÂÒè §¡ÒÃà¢Òé ÃËÊÑ àª¹è ¶Òé ÅӴѺ¢Íé ÁÅÙ Í¹Ô ¾µØ ¤Í× {110000} ÅÓ´ºÑ¢éÍÁÙŷՋä´é¨Ò¡¡ÒÃà¢Òé ÃËÑÊ FM ¤×Í {11 11 01 01 01 01} Ê§Ñ à¡µ¨Ð¾ºÇÒè ÃËÑÊ FM ÂÍÁãËÅé Ó´ºÑ ¢éÍÁÙÅ·Õà‹ ¢éÒÃËÑÊáÅéÇÁÕºÔµ 1 µ´Ô ¡¹Ñ ä´é «‹Ö§¨Ð¡èÍãËéà¡Ô´»˜­ËÒàÃÍ׋ § ISI ´Ñ§¹ŒÑ¹ ¨Ö§Á¡Õ ÒþѲ¹ÒÃËÑÊãËÁè·à‹Õ ÃÕ¡ÇèÒ “ÃËÑÊ MFM (modied frequency modulation)”ËÃ×ͺҧ¤Ãь§àÃÕ¡ÇèÒ “ÃËÑÊÁÔÅàÅÍÃì (Miller code)” «‹§Ö ÁµÕ ÒÃÒ§¤¹é ËÒÊÓËÃºÑ ¡ÒÃà¢Òé áÅжʹÃËÑÊ µÒÁû٠·Õ‹ 8.6(b) â´Â·Õ‹ x = 0 ¶Òé ºÔµ¡Íè ¹Ë¹Òé ºÔµ x ÁÕ¤Òè ໹š ºÔµ 1 ¹Í¡¹ÑŒ¹ x = 1 ÃËÑÊ MFM ¹ŒÕ¶×ÍÇèÒ໹š ÃËÑÊ RLL Ẻ (1, 3) áÅÐÁÕ굄 ÃÒÃËÑÊ R = 1/2 â´Â¨ÐÁÕ»ÃÐÊÔ·¸¼Ô ŢͧÃËÊÑ η =0.5/0.5515 = 0.9066 µÑÇÍÂÒè §¡ÒÃà¢Òé ÃËÑÊ àª¹è ¶Òé ÅӴѺ¢Íé ÁÙÅÍ¹Ô ¾Øµ ¤×Í {1100011} ÅӴѺ¢Íé ÁÙÅ·‹äÕ ´é¨Ò¡¡ÒÃà¢éÒÃËÑÊ MFM ¤Í× {01 01 00 10 10 01 01} ໹š µ¹é ¹Í¡¨Ò¡¹ŒÕ û٠·‹Õ 8.6(c) áÅÐ 8.6(d)áÊ´§µÑÇÍÂèÒ§ÃËÊÑ RLL ẺµèÒ§æ ·‹Õãªéã¹ÎÒÃì´´ÊÔ ¡ìä´Ã¿ì ¨Ò¡ÇÔÇѲ¹Ò¡Òâͧ¡Òþ²Ñ ¹ÒÃËÑÊ RLL

8.7. µÑÇÍÂÒè §ÃËÊÑ RLL à຺µèÒ§æ 165user bits coded bits user bits coded bits0 01 0 x01 11 1 01 (a) FM code (b) MFM codeuser bits coded bits user bits coded bits00 101 10 010001 100 11 100010 001 000 00010011 010 010 1001000000 101000 011 0010000001 100000 0010 001001001000 001000 0011 000010001001 010000(c) 2/3 (1,7) RLL code (d) 1/2 (1,7) RLL codeû٠·‹Õ 8.6: µÇÑ ÍÂÒè §ÃËÊÑ RLL ẺµèÒ§æ ·‹ãÕ ªãé ¹ÎÒÃ´ì ´ÊÔ ¡äì ´Ã¿ì¨Ð¾ºÇèÒ ¾ÒÃÒÁÔàµÍÃì d ·‹Õãªéã¹ÃËÑÊ RLL ¨Ð¤èÍÂæ Ŵŧ à¾×‹ÍÅ´¨Ó¹Ç¹ºÔµÊÇè ¹à¡¹Ô ·ÓãËéÊÒÁÒö¨´Ñ à¡çº¢Íé ÁÅÙ ·Õ‹µéͧ¡ÒÃã¹ÎÒÃì´´ÊÔ ¡ìä´Ã¿ìä´Áé Ò¡¢Ö¹Œ 㹡ÒõѴÊÔ¹ã¨ÇÒè ¨ÐàÍÒÃËÊÑ RLL ã´ÁÒãªé§Ò¹ã¹Ãкº¨Ð¢Ö¹Œ ÍÂè¡Ù ºÑ »˜¨¨ÑÂËÅÒÂæ ÍÂèÒ§ ´Ñ§¹ŒÕ 1) ¾ÒÃÒÁÔàµÍÃì (d, k) 2) 굄 ÃÒÃËÊÑ R = m/n 3) ¤ÇÒÁ¨Ø C(d, k) 4) »ÃÐÊ·Ô ¸¼Ô ŢͧÃËÑÊ η 5) ÍѵÃÒ¤ÇÒÁ˹Òá¹è¹ DR

166 ȹ٠Âàì ·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃàì àË§è ªÒµÔ«‹Ö§â´Â·Ñ‹Çä»áÅÇé ¨Ó໚¹µÍé §»Ãй»Õ ÃйÍÁ»˜¨¨Ñ·ѧŒ ËÁ´ãËéàËÁÒÐÊÁ¡ºÑ ÊÀÒ¾áÇ´ÅéÍÁ㹡Ò÷ӧҹ¢Í§Ãкº ÃËÊÑ RLL ·Õ‹à¤Âãªéã¹ÎÒÃì´´ÔÊ¡ìä´Ã¿ì àªè¹ ÃËÊÑ RLL Ẻ 1/2 (2, 7), ÃËÊÑ RLL Ẻ4/5 (0, 2), áÅÐÃËÑÊ RLL Ẻ 8/9 (0, 3) ໹š µ¹é Ê§Ñ à¡µ¨Ð¾ºÇèÒ ÃËÑÊ RLL ·Õ㋠ªé¨ÐÁÍÕ µÑ ÃÒÃËÊÑ à¢Òéã¡Å¤é Òè 1 àÃ×͋ Âæ à¾×͋ Å´¨Ó¹Ç¹ºÔµÊèǹà¡Ô¹ áÅоÒÃÒÁàÔ µÍÃì d ·Õ㋠ª¡é ç¨ÐÁ¤Õ èÒ໚¹¤èÒ 0 ¹¹Ñ‹ ¤Í× ÂÍÁãËéÁÕºÔµ 1 µÔ´¡Ñ¹ä´é «Ö§‹ ¶§Ö áÁéÇèҨСÍè ãËéà¡Ô´»˜­ËÒàÃ׋ͧ ISI áµèÃкº¡çÊÒÁÒö¨Ñ´¡ÒáºÑ ISI ¹ÕŒä´é´éÇÂà·¤¹¤Ô PRML µÒÁ·ÍՋ ¸ºÔ ÒÂ㹺··Õ‹ 48.8 ÃËÊÑ (0, G/I ) ÊÓËÃºÑ ªÍè §ÊÑ­­Ò³ PRMLÊÓËÃºÑ ªÍè §Ê­Ñ ­Ò³ PRML ·Õ‹ãªé·ÒÃìࡵç Ẻ PR4, H (D) = 1 − D2, ¢Íé ÁÙÅàÍÒµì¾µØ ªèͧÊÑ­­Ò³(·Õä‹ ÁèÁÕÊ­Ñ ­Ò³Ãº¡Ç¹) ³ àÇÅÒ k Á¤Õ èÒà·èÒ¡ºÑ ¼ÅµÒè §ÃÐËÇèÒ§¢Íé ÁÙÅÍ¹Ô ¾µØ 2 µÑÇ ³ àÇÅÒ k áÅÐ k−2´§Ñ ¹ÑŒ¹ ªèÍ§Ê­Ñ ­Ò³¹ÕŒ¨ÐÁդسÊÁºµÑ Ô¾ÔàÈɷՋÇÒè ÅӴѺ¢éÍÁÅÙ ÂèÍÂàÅ¢¤Õ‹ (odd subsequence) ¨Ð໹šÍÊÔ ÃШҡÅӴѺ¢Íé ÁÙÅÂèÍÂàÅ¢¤èÙ (even subsequence) ´Ñ§¹Ñ¹Œ à¾×‹Í·Õ‹¨ÐŴ˹èǤÇÒÁ¨ÓàÊ¹é ·Ò§ (pathmemory) ¢Í§Ç§¨ÃµÃǨËÒÇÕà·Íúì Ô ¨Ó¹Ç¹¢Í§ºµÔ 0 ·Õ‹àÃÂÕ §µÔ´µÍè ¡Ñ¹¢Í§áµÅè ÐÅÓ´ºÑ ¢Íé ÁÙÅÂÍè ¨еéͧÁÕä´äé Áè èà¡Ô¹ I µÑÇ áÅÐà¾Í׋ ªÇè ·ÓãËéÃкºä·ÁÁԋ§ÃÔ¤¿Ñ àÇÍÐÃÕÊÒÁÒö·Ó§Ò¹ä´éÍÂèÒ§ÁÕ»ÃÐÊ·Ô ¸ÀÔ Ò¾áÅШӹǹ¢Í§ºÔµ 0 ·à‹Õ ÃÕ§µ´Ô µè͡ѹã¹ÅÓ´ºÑ ¢Íé ÁÅÙ ÃÇÁ (ÅÓ´ºÑ ¢éÍÁÙÅÂèÍÂàÅ¢¤Á‹Õ ÒÃÇÁ¡ÑºÅӴѺ¢éÍÁÅÙÂèÍÂàÅ¢¤Ùè) ¨ÐµéͧÁÕä´éäèÁèà¡Ô¹ G µÇÑ àËÁÍ× ¹¡ºÑ ¾ÒÃÒÁàÔ µÍÃì k ã¹ÃËÊÑ RLL Ẻ (d, k) ÊÓËÃºÑ ¤èÒ0 ã¹ÃËÑÊ (0, G/I ) ¹Œ¹Ñ ¨ÐËÁÒ¶§Ö ÃкºÍ¹Ø­ÒµãËéÅӴѺ¢éÍÁÙÅÃÇÁÊÒÁÒöÁÕºÔµ 1 àÃÕ§µÔ´µÍè ¡Ñ¹ä´é àËÁÍ× ¹¡Ñº¾ÒÃÒÁàÔ µÍÃì d ã¹ÃËÊÑ RLL Ẻ (d, k) [9, 59, 60] à¾ÃÒÐÇÒè ǧ¨ÃµÃǨËÒ PRMLÁ¤Õ ÇÒÁÊÒÁÒö㹨´Ñ ¡ÒáºÑ ISI ·Õ‹à¡´Ô ¢ÖŒ¹ä´é ¶Òé ¡Ó˹´ãËé γ = {γ1, γ2, . . . , γn} ໚¹ÅÓ´ºÑ ¢Íé ÁÙÅẺ亹ÒÃÕ·‹ÕÁ¤Õ ÇÒÁÂÒÇ n ºµÔ à¾ÃÒЩй¹ÑŒÅӴѺ¢éÍÁÅÙ ÂèÍÂàÅ¢¤‹Õ γo áÅÐÅӴѺ¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè γe ¨Ð¹ÔÂÒÁâ´Â [60] γo = {γ1, γ3, γ5, . . . , γ2 n/2 −1} γe = {γ2, γ4, γ6, . . . , γ2 n/2 }àÁ‹Í× x á·¹¨Ó¹Ç¹àµçÁºÇ¡·ÁՋ Ò¡·Õ‹ÊØ´ ·Á‹Õ ¤Õ èÒ¹Íé ¡ÇèÒËÃ×Íà·Òè ¡ºÑ ¤èÒ x ´Ñ§¹ŒÑ¹ ¨Ðä´Çé Òè ÅÓ´ºÑ ¢éÍÁÅÙÂÍè ÂàÅ¢¤Õ‹ γo áÅÐÅÓ´ºÑ ¢éÍÁÙÅÂèÍÂàÅ¢¤Ùè γe ¨ÐÁ¤Õ ÇÒÁÂÒÇà·èҡѺ n/2 áÅÐ n/2 µÒÁÅӴѺ ÅӴѺ

8.9. ÊÃ»Ø ·Òé º· 167¢Íé ÁÅÙ γ ¨Ð¶Ù¡àÃÕ¡ÇÒè ໹š ÅÓ´ºÑ ¢éÍÁÅÙ ·‹ÕÊÍ´¤ÅÍé §¡ºÑ à§×͋ ¹ä¢ºÑ§¤Ñº (0, G/I ) ¡çµèÍàÁ×‹Í ÅÓ´ºÑ ¢éÍÁÙÅÃÇÁ γ ÁÕºÔµ 0 àÃÕ§µÔ´µèÍ¡¹Ñ ä´éäÁèà¡Ô¹ G µÑÇ áÅÐÅӴѺ¢Íé ÁÙÅÂèÍ γo áÅÐ γe ÁÕºÔµ 0 àÃÕ§µÔ´µÍè¡Ñ¹ä´éäÁèà¡Ô¹ I µÇÑ àÁÍ׋ G áÅÐ I ໚¹àÅ¢¨Ó¹Ç¹àµÁç ºÇ¡µÇÑ ÍÂèÒ§·‹Õ 8.5 ¡Ó˹´ãËé γ = {110100101000110011} ¤Í× ÅÓ´ºÑ ¢Íé ÁÙŷՋ¶¡Ù à¢éÒÃËÑÊ´Çé ÂÃËÑÊRLL Ẻ (0, G/I ) ¨§ËÒ¤Òè ¾ÒÃÒÁàÔ µÍÃì G áÅÐ I ¢Í§ γÇÔ¸Õ·Ó ¨Ò¡ÅӴѺ¢éÍÁÙÅ γ ·‹Õ¡Ó˹´ãËéÁÒ ¨Ðä´éÇÒè γo = {100110101} áÅÐ γe = {110000101}à¾ÃÒЩй¹ÑŒ ¨Ó¹Ç¹ºÔµ 0 ·Õ‹àÃÂÕ §µ´Ô ¡¹Ñ ÁÒ¡·‹ÕÊ´Ø ¢Í§ γ, γo, áÅÐ γe ¤Í× 3, 2, áÅÐ 4 µÒÁÅÓ´ºÑ´Ñ§¹ŒÑ¹ ¨Ð¾ºÇèÒ G = 3 áÅÐ I = 4 ¹¹‹Ñ ¤×Í ÅÓ´ºÑ ¢éÍÁÙÅ γ ¶¡Ù à¢Òé ÃËÑÊ´Çé ÂÃËÊÑ RLL Ẻ (0, 3/4) ¨Ò¡µÑÇÍÂÒè §·‹Õ 8.5 ¨ÐÊѧࡵà˹ç ä´Çé èÒ ÅӴѺ¢Íé ÁÅÙ ·Õ‹¶Ù¡à¢éÒÃËÊÑ ´éÇÂÃËÊÑ RLL Ẻ (0, G/I )·‹Õ¶¡Ù µÍé §¹ÑŒ¹ ¤èÒ¾ÒÃÒÁàÔ µÍÃì G ≤ 2I àÊÁÍ µÇÑ ÍÂèÒ§ÃËÑÊ (0, G/I ) ·‹Õãªéã¹Ãкº¡ÒûÃÐÁÇżÅÊÑ­­Ò³¢Í§ÎÒÃì´´ÊÔ ¡ìä´Ã¿ì હè ÃËÑÊ 8/9 (0, 4/4) áÅÐÃËÑÊ 16/17 (0, 6/6) ໚¹µé¹8.9 ÊÃØ»·éÒº·â´Â·Ç‹Ñ ä» ÃËÊÑ RLL ÁÕËÅÒÂÃٻẺ 㹺·¹ÕŒä´é͸ºÔ Ò¶§Ö ËÅ¡Ñ ¡Ò÷ӧҹáÅТŒ¹Ñ µÍ¹¡ÒÃÍ͡ẺÃËÊÑ RLL (runlength limited) µÒÁà§Í׋ ¹ä¢ºÑ§¤Ñº (d, k) â´Â·Õ‹ ¾ÒÃÒÁÔàµÍÃì d ¨Ð໹š µÑÇ¡Ó˹´¨Ó¹Ç¹·Õ‹¹éÍÂ·Ê‹Õ Ø´¢Í§ºÔµ 0 ·‹ÕÍÂÙèÃÐËÇèÒ§ºµÔ 1 (µÒÁû٠Ẻ NRZI) áÅоÒÃÒÁàÔ µÍÃì k ¨Ð໚¹µÑÇ¡Ó˹´ÁÒ¡·Õ‹Ê´Ø ¢Í§ºµÔ 0 ·Õ‹ÍÂÙèÃÐËÇÒè §ºÔµ 1 à¹×‹Í§¨Ò¡ ºµÔ 1 á·¹¡ÒÃà»Å‹ÂÕ ¹Ê¶Ò¹Ð¢Í§¡ÃÐáÊ俿҇ à¢Õ¹ ´Ñ§¹ŒÑ¹ ¾ÒÃÒÁÔàµÍÃì d ¨Ö§ªÇè ÂÅ´¼Å¡Ãзº·Õ‹à¡Ô´¨Ò¡ ISI ã¹¢³Ð·‹Õ ¾ÒÃÒÁàÔ µÍÃì k ¨ÐÃѺ»ÃСѹÇÒè ÅÓ´ºÑ ¢Íé ÁÅÙ ·‹Õà¢ÂÕ ¹Å§ã¹Ê‹Í× º¹Ñ ·Ö¡¨ÐÁÕ¡ÒÃà»ÅÕ‹ ¹Ê¶Ò¹Ð໚¹ÃÐÂÐæ ྋ×ͪÇè ·ÓãËÃé кºä·ÁÁ§Ô‹ Ã¤Ô Ñ¿àÇÍÐÃÕÊÒÁÒö·Ó§Ò¹ä´Íé ÂèÒ§ÁÕ»ÃÐÊÔ·¸ÔÀÒ¾ ÍÂÒè §äáµç ÒÁ ã¹»¨˜ ¨ºØ ¹Ñ ¹ÕŒ ÃËÊÑ RLL ·Õ¹‹ ÔÂÁãªÁé ¡Ñ ¨ÐÍÂèãÙ ¹ÃÙ»¢Í§ÃËÊÑ (0, G/I ) «Ö‹§à»š¹ÃËÊÑ ·‹¶Õ Ù¡Í͡ẺÁÒãËé㪧é Ò¹¡ÑºÃкº PRML ¢Í§ÎÒôì´ÔÊ¡äì ´Ã¿ì

168 ȹ٠Âàì ·¤â¹âÅÂÕÍàÔ Åç¡·Ã͹¡Ô ÊìààÅФÍÁ¾ÇÔ àµÍÃàì àË§è ªÒµÔ ã¹¡ÒÃàÅ×Í¡ÃËÊÑ RLL ÁÒãªé§Ò¹¨Ðµéͧ¤Ó¹Ö§¶§Ö »¨˜ ¨ÂÑ µÒè §æ ä´éá¡è ¾ÒÃÒÁÔàµÍÃì (d, k), ÍѵÃÒÃËÑÊR, ¤ÇÒÁ¨Ø C (d, k), »ÃÐÊ·Ô ¸Ô¼Å¢Í§ÃËÑÊ η, áÅÐ ÍµÑ ÃÒ¤ÇÒÁ˹Òá¹¹è DR ໹š µ¹é ྋÍ× ãËéä´éÃËÊÑRLL ·Õ‹´ÕÊØ´ÊÓËÃѺ§Ò¹»ÃÐÂ¡Ø µì¹Œ¹Ñ æ ¢éÍÊ§Ñ à¡µ·‹Õ¾º¢Í§ÃËÑÊ RLL ·‹Õ¹ÓÁÒãªé§Ò¹ã¹ÎÒÃ´ì ´ÔÊ¡ìä´Ã¿ìã¹»˜¨¨ºØ ¹Ñ ¤Í× ¾ÒÃÒÁàÔ µÍÃì d ¨Ð¤Íè Âæ ŴŧÁÒ໚¹¤Òè 0 áÅÐ굄 ÃÒÃËÊÑ R ¢Í§ÃËÊÑ RLL ·‹Õãªé ¡çÁÕ¤Òè à¢éÒã¡Å¤é èÒ 1 ÁÒ¡¢Œ¹Ö àÃÍ‹× Âæ ·ŒÑ§¹àŒÕ ¾Í׋ ໹š ¡ÒÃÅ´¨Ó¹Ç¹ºÔµÊÇè ¹à¡¹Ô ·Õ‹à¡´Ô ¢ÖŒ¹ã¹Ãкº ·ÓãËÊé ÒÁÒö¨´Ñ à¡çº¢Íé ÁÙÅ¢Òè ÇÊÒâͧ¼éÙãªéä´Áé Ò¡¢¹ÖŒ8.10 à຺½ƒ¡Ë´Ñ ·éÒº· 1. ¨§¤Ó¹Ç³ËҨӹǹÅӴѺ¢éÍÁÙÅ·§ŒÑ ËÁ´·‹ÁÕ Õ¤ÇÒÁÂÒÇ·§ŒÑ ʹŒÔ L ºÔµ ·Õʋ Í´¤Åéͧ¡Ñºà§‹×͹䢺§Ñ ¤ºÑ (d, k) àÁÍ‹× 1.1) d = 0, k = 2, áÅÐ L = 5 1.2) d = 1, k = 3, áÅÐ L = 6 1.3) d = 1, k = 7, áÅÐ L = 10 1.4) d = 2, k = 7, áÅÐ L = 10 1.5) d = 2, k = ∞, áÅÐ L = 10 2. ¨§áÊ´§á¼¹ÀÒ¾à¤Ã׋ͧʶҹШӡ´Ñ áÅФӹdzËÒàÁ·ÃÔ¡«ì¡ÒÃà»ÅÂ‹Õ ¹Ê¶Ò¹Ð ¢Í§ÃËÊÑ RLL µÒÁোÍ× ¹ä¢º§Ñ ¤ºÑ ¢Í§¾ÒÃÒÁÔàµÍÃì (d, k) àÁ‹Í× 2.1) d = 1 áÅÐ k = 5 2.2) d = 1 áÅÐ k = 7 2.3) d = 2 áÅÐ k = 5 2.4) d = 2 áÅÐ k = 7 3. ¨Ò¡â¨·Âìã¹¢éͷՋ 2 ¨§¤Ó¹Ç³ËÒ¤ÇÒÁ¨Ø C (d, k) â´ÂãªéÊÁ¡Òà (8.12) ¾ÃÍé Á·§ŒÑ à»ÃÕºà·Õº ¼ÅÅѾ¸·ì ‹äÕ è´¡é Ѻ C (d, k) ·¤‹Õ ӹdzä´é¨Ò¡ÊÁ¡Òà (8.18)

8.10. à຺½ƒ¡Ë´Ñ ·éÒº· 1694. ¨§ËҨӹǹÅӴѺ¢éÍÁÅÙ ·‹Õ໚¹ä»ä´é·§ŒÑ ËÁ´·Õ‹ÁÕ¤ÇÒÁÂÒÇ L ºµÔ ·‹ÕÍÍ¡¨Ò¡Ê¶Ò¹Ð Si áÅÇé ä» ÊÔ¹Œ Ê´Ø ·Õ‹Ê¶Ò¹Ð Sj ¢Í§ÃËÊÑ RLL µÒÁà§Í‹× ¹ä¢ºÑ§¤ºÑ ¢Í§¾ÒÃÒÁàÔ µÍÃì (d, k) àÁ‹×Í 4.1) d = 0, k = 2, áÅÐ L = 5 4.2) d = 1, k = 3, áÅÐ L = 5 4.3) d = 1, k = 7, áÅÐ L = 10 4.4) d = 2, k = 7, áÅÐ L = 105. ¡Ó˹´ãËÅé Ó´ºÑ ¢éÍÁÙÅ·‹Õ¶Ù¡à¢éÒÃËÑÊ´éÇÂÃËÑÊ RLL Ẻ (0, G/I ) ¨§ËÒ¤èÒ¾ÒÃÒÁÔàµÍÃì G áÅÐ I ¢Í§ γ ´Ñ§µÍè 仹ŒÕ 5.1) γ = {10101000101001100101} 5.2) γ = {10010100001101001100111101} 5.3) γ = {11100011001010001001100101}6. ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃºÑ ¡ÒÃà¢Òé áÅжʹÃËÊÑ RLL Ẻ (0, 1) â´Â·‹Õ ¢Íé ÁÅÙ áµèÅФçь ·‹Õ ¼Òè ¹¡ÒÃà¢éÒÃËÊÑ áÅÇé ¨ÐÁÕ¤ÇÒÁÂÒÇà·èÒ¡ºÑ L = 2 ¾ÃÍé Á·Ñ§Œ ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÊÑ7. ¨§ÊÃéÒ§µÒÃÒ§¤é¹ËÒÊÓËÃºÑ ¡ÒÃà¢éÒáÅжʹÃËÊÑ RLL Ẻ (1, 2) â´Â·Õ‹ ¢éÍÁÅÙ áµèÅФçь ·Õ‹ ¼Òè ¹¡ÒÃà¢Òé ÃËÑÊáÅÇé ¨ÐÁÕ¤ÇÒÁÂÒÇà·Òè ¡ºÑ L = 3 ¾ÃÍé Á·ÑŒ§ËÒ»ÃÐÊÔ·¸Ô¼Å¢Í§ÃËÊÑ8. ¨§ÊÃéÒ§µÒÃÒ§¤¹é ËÒÊÓËÃºÑ ¡ÒÃà¢éÒáÅжʹÃËÑÊ RLL Ẻ (1, 3) â´Â·‹Õ ¢Íé ÁÅÙ áµÅè Фçь ·‹Õ ¼Òè ¹¡ÒÃà¢éÒÃËÊÑ áÅéǨÐÁÕ¤ÇÒÁÂÒÇà·Òè ¡ºÑ L = 4 ¾ÃÍé Á·ÑŒ§ËÒ»ÃÐÊ·Ô ¸Ô¼Å¢Í§ÃËÊÑ

170 ȹ٠Âàì ·¤â¹âÅÂÍÕ àÔ Å¡ç ·Ã͹ԡÊàì àÅФÍÁ¾ÇÔ àµÍÃàì àË觪ҵÔ

ÀÒ¤¼¹Ç¡ ¡µÒÃÒ§¿§˜ ¡ìªÑ¹ Q¿§˜ ¡ìªÑ¹ Q(x) ໚¹¿§˜ ¡ªì ¹Ñ ·Õ‹ÊÒÁÒö¨Ñ´ãËéÍÂÙèã¹Ã»Ù ¢Í§¿˜§¡ªì ѹ¡ÒÃᨡᨧÊÐÊÁ¢Í§µÇÑ á»ÃÊØèÁẺà¡ÒÊàì «ÕÂ¹ä´«é ‹§Ö ໚¹·¹Õ‹ ÂÔ Á㪧é Ò¹·Ò§´éҹʶԵÈÔ ÒʵÃìáÅдÒé ¹ÇÔÈÇ¡ÃÃÁÈÒʵÃì â´Â¿˜§¡ìªÑ¹ Q(x) ¨Ð¹ÔÂÒÁ´§Ñ ¹ÕŒ Q(x) = √1 ∞ − y2 dy (¡.1) 2π x 2 exp«§‹Ö ໹š ¡ÒÃËÒ¤Òè »Ã¾Ô ¹Ñ ¸Êì èǹËÒ§¢Í§¿˜§¡ªì ¹Ñ ¤ÇÒÁ˹Òá¹¹è ¤ÇÒÁ¹èÒ¨Ð໹š Ẻà¡ÒÊàì «ÂÕ ¹àÁ‹×Í exp{·}¤Í× ¿˜§¡ìª¹Ñ àÅ¢ªŒÕ¡ÓÅѧ (exponential function) â´Â·‹ÇÑ ä» ¤èҢͧ¿§˜ ¡ªì ¹Ñ Q(x) ÊÓËÃºÑ ¤Òè x µÒè §æÊÒÁÒöËÒä´¨é Ò¡µÒÃÒ§¤¹é ËÒ (lookup table) áµãè ¹¡Ã³Õ·Õ‹ x 3 ¿§˜ ¡ìª¹Ñ Q(x) ÊÒÁÒö»ÃÐÁÒ³¤Òè ä´é´Ñ§¹ŒÕ Q(x) ≈ √1 exp − x2 (¡.2) x 2π 2µÒÃÒ§µèÍ仹¨ŒÕ ÐáÊ´§¤Òè ¢Í§¿§˜ ¡ìªÑ¹ Q(x) ÊÓËÃºÑ 0 ≤ x ≤ 3.59 171

172 ÈÙ¹Âìà·¤â¹âÅÂÕÍàÔ Å¡ç ·Ã͹¡Ô ÊìààÅФÍÁ¾ÔÇàµÍÃìààË§è ªÒµÔ x Q(x) x Q(x) x Q(x) x Q(x) x Q(x) 0 0.50000 0.36 0.35942 0.72 0.23576 1.08 0.14007 1.44 0.0749340 0.01 0.49601 0.37 0.35569 0.73 0.23270 1.09 0.13786 1.45 0.0735290 0.02 0.49202 0.38 0.35197 0.74 0.22965 1.10 0.13567 1.46 0.0721450 0.03 0.48803 0.39 0.34827 0.75 0.22663 1.11 0.133500 1.47 0.070781 0.04 0.48405 0.40 0.34458 0.76 0.22363 1.12 0.131360 1.48 0.069437 0.05 0.48006 0.41 0.34090 0.77 0.22065 1.13 0.129240 1.49 0.068112 0.06 0.47608 0.42 0.33724 0.78 0.21770 1.14 0.127140 1.50 0.066807 0.07 0.47210 0.43 0.33360 0.79 0.21476 1.15 0.125070 1.51 0.065522 0.08 0.46812 0.44 0.32997 0.80 0.21186 1.16 0.123020 1.52 0.064255 0.09 0.46414 0.45 0.32636 0.81 0.20897 1.17 0.121000 1.53 0.063008 0.10 0.46017 0.46 0.32276 0.82 0.20611 1.18 0.119000 1.54 0.061780 0.11 0.45620 0.47 0.31918 0.83 0.20327 1.19 0.117020 1.55 0.060571 0.12 0.45224 0.48 0.31561 0.84 0.20045 1.20 0.115070 1.56 0.059380 0.13 0.44828 0.49 0.31207 0.85 0.19766 1.21 0.113140 1.57 0.058208 0.14 0.44433 0.50 0.30854 0.86 0.19489 1.22 0.111230 1.58 0.057053 0.15 0.44038 0.51 0.30503 0.87 0.19215 1.23 0.109350 1.59 0.055917 0.16 0.43644 0.52 0.30153 0.88 0.18943 1.24 0.107490 1.60 0.054799 0.17 0.43251 0.53 0.29806 0.89 0.18673 1.25 0.105650 1.61 0.053699 0.18 0.42858 0.54 0.29460 0.90 0.18406 1.26 0.103830 1.62 0.052616 0.19 0.42465 0.55 0.29116 0.91 0.18141 1.27 0.102040 1.63 0.051551 0.20 0.42074 0.56 0.28774 0.92 0.17879 1.28 0.100270 1.64 0.050503 0.21 0.41683 0.57 0.28434 0.93 0.17619 1.29 0.098525 1.65 0.049471 0.22 0.41294 0.58 0.28096 0.94 0.17361 1.30 0.096800 1.66 0.048457 0.23 0.40905 0.59 0.27760 0.95 0.17106 1.31 0.095098 1.67 0.047460 0.24 0.40517 0.60 0.27425 0.96 0.16853 1.32 0.093418 1.68 0.046479 0.25 0.40129 0.61 0.27093 0.97 0.16602 1.33 0.091759 1.69 0.045514 0.26 0.39743 0.62 0.26763 0.98 0.16354 1.34 0.090123 1.70 0.044565 0.27 0.39358 0.63 0.26435 0.99 0.16109 1.35 0.088508 1.71 0.043633 0.28 0.38974 0.64 0.26109 1.00 0.15866 1.36 0.086915 1.72 0.042716 0.29 0.38591 0.65 0.25785 1.01 0.15625 1.37 0.085343 1.73 0.041815 0.30 0.38209 0.66 0.25463 1.02 0.15386 1.38 0.083793 1.74 0.040930 0.31 0.37828 0.67 0.25143 1.03 0.15151 1.39 0.082264 1.75 0.040059 0.32 0.37448 0.68 0.24825 1.04 0.14917 1.40 0.080757 1.76 0.039204 0.33 0.37070 0.69 0.24510 1.05 0.14686 1.41 0.079270 1.77 0.038364 0.34 0.36693 0.70 0.24196 1.06 0.14457 1.42 0.077804 1.78 0.037538 0.35 0.36317 0.71 0.23885 1.07 0.14231 1.43 0.076359 1.79 0.036727

173x Q(x) x Q(x) x Q(x) x Q(x) x Q(x)1.80 0.035930 2.16 0.0153860 2.52 0.0058677 2.88 0.00198840 3.24 0.000597651.81 0.035148 2.17 0.0150030 2.53 0.0057031 2.89 0.00192620 3.25 0.000577031.82 0.034380 2.18 0.0146290 2.54 0.0055426 2.90 0.00186580 3.26 0.000557061.83 0.033625 2.19 0.0142620 2.55 0.0053861 2.91 0.00180710 3.27 0.000537741.84 0.032884 2.20 0.0139030 2.56 0.0052336 2.92 0.00175020 3.28 0.000519041.85 0.032157 2.21 0.0135530 2.57 0.0050849 2.93 0.00169480 3.29 0.000500941.86 0.031443 2.22 0.0132090 2.58 0.0049400 2.94 0.00164110 3.30 0.000483421.87 0.030742 2.23 0.0128740 2.59 0.0047988 2.95 0.00158890 3.31 0.000466481.88 0.030054 2.24 0.0125450 2.60 0.0046612 2.96 0.00153820 3.32 0.000450091.89 0.029379 2.25 0.0122240 2.61 0.0045271 2.97 0.00148900 3.33 0.000434231.90 0.028717 2.26 0.0119110 2.62 0.0043965 2.98 0.00144120 3.34 0.000418891.91 0.028067 2.27 0.0116040 2.63 0.0042692 2.99 0.00139490 3.35 0.000404061.92 0.027429 2.28 0.0113040 2.64 0.0041453 3.00 0.00134990 3.36 0.000389711.93 0.026803 2.29 0.0110110 2.65 0.0040246 3.01 0.00130620 3.37 0.000375841.94 0.026190 2.30 0.0107240 2.66 0.0039070 3.02 0.00126390 3.38 0.000362431.95 0.025588 2.31 0.0104440 2.67 0.0037926 3.03 0.00122280 3.39 0.000349461.96 0.024998 2.32 0.0101700 2.68 0.0036811 3.04 0.00118290 3.40 0.000336931.97 0.024419 2.33 0.0099031 2.69 0.0035726 3.05 0.00114420 3.41 0.000324811.98 0.023852 2.34 0.0096419 2.70 0.0034670 3.06 0.00110670 3.42 0.000313111.99 0.023295 2.35 0.0093867 2.71 0.0033642 3.07 0.00107030 3.43 0.000301792.00 0.022750 2.36 0.0091375 2.72 0.0032641 3.08 0.00103500 3.44 0.000290862.01 0.022216 2.37 0.0088940 2.73 0.0031667 3.09 0.00100080 3.45 0.000280292.02 0.021692 2.38 0.0086563 2.74 0.0030720 3.10 0.00096760 3.46 0.000270092.03 0.021178 2.39 0.0084242 2.75 0.0029798 3.11 0.00093544 3.47 0.000260232.04 0.020675 2.40 0.0081975 2.76 0.0028901 3.12 0.00090426 3.48 0.000250712.05 0.020182 2.41 0.0079763 2.77 0.0028028 3.13 0.00087403 3.49 0.000241512.06 0.019699 2.42 0.0077603 2.78 0.0027179 3.14 0.00084474 3.50 0.000232632.07 0.019226 2.43 0.0075494 2.79 0.0026354 3.15 0.00081635 3.51 0.000224052.08 0.018763 2.44 0.0073436 2.80 0.0025551 3.16 0.00078885 3.52 0.000215772.09 0.018309 2.45 0.0071428 2.81 0.0024771 3.17 0.00076219 3.53 0.000207782.10 0.017864 2.46 0.0069469 2.82 0.0024012 3.18 0.00073638 3.54 0.000200062.11 0.017429 2.47 0.0067557 2.83 0.0023274 3.19 0.00071136 3.55 0.000192622.12 0.017003 2.48 0.0065691 2.84 0.0022557 3.20 0.00068714 3.56 0.000185432.13 0.016586 2.49 0.0063872 2.85 0.0021860 3.21 0.00066367 3.57 0.000178492.14 0.016177 2.50 0.0062097 2.86 0.0021182 3.22 0.00064095 3.58 0.000171802.15 0.015778 2.51 0.0060366 2.87 0.0020524 3.23 0.00061895 3.59 0.00016534

174 ȹ٠Âàì ·¤â¹âÅÂÍÕ àÔ Å¡ç ·Ã͹ԡÊàì àÅФÍÁ¾ÇÔ àµÍÃàì àË觪ҵÔ

ÀÒ¤¼¹Ç¡ ¢Êٵä³ÔµÈÒʵ÷ì ՋÊÓ¤­ÑÀÒ¤¼¹Ç¡¹ÕŒ¨ÐáÊ´§Êٵä³µÔ ÈÒʵÃì·ã‹Õ ªéºèÍÂÊÓËÃºÑ ¡ÒÃÇàÔ ¤ÃÒÐËìÃкº¡ÒûÃÐÁÇżÅÊÑ­­Ò³¢Í§ÎÒÃ´ì ´ÊÔ ¡äì ´Ã¿ì¢Í§Ë¹Ñ§ÊÍ× àÅÁè ¹ŒÕ¢.1 µÃÕ⡳ÁÔµÔ (Trigonometric)sin(−α) = − sin(α)cos(−α) = cos(α)sin(α) = cos(α − π/2)sin2(α) + cos2(α) = 1sin(α ± β) = sin(α) cos(β) ± cos(α) sin(β)cos(α ± β) = cos(α) cos(β) ∓ sin(α) sin(β)sin(α) sin(β) = 1 cos(α − β) − 1 cos(α + β) 2 2sin(α) cos(β) = 1 sin(α + β) + 1 sin(α − β) 2 2cos(α) cos(β) = 1 cos(α − β) + 1 cos(α + β) 2 2cos(α) sin(β) = 1 sin(α + β) − 1 sin(α − β) 2 2 175

176 ÈÙ¹Âàì ·¤â¹âÅÂÍÕ ÔàÅç¡·Ã͹ԡÊàì àÅФÍÁ¾ÔÇàµÍÃàì àË§è ªÒµÔsin(2α) = 2 sin(α) cos(α)cos(2α) = cos2(α) − sin2(α) = 1 − 2 sin2(α) = 2 cos2(α) − 1sin2(α) = 1 {1 − cos(2α)} 2cos2(α) = 1 {1 + cos(2α)} 2ejα = cos(α) + j sin(α)sin(α) = (ejα − e−jα)/(2j)cos(α) = (ejα + e−jα)/2¢.2 »Ã¾Ô ѹ¸ìäÁè¨Ó¡´Ñ ࢵ (Indenite Integral) u dv = uv − v du àÁ×͋ u áÅÐ v ໹š ¿˜§¡ªì ѹ¢Í§ x xn dx = xn+1/(n + 1) àÁ×͋ n = −1 x−1 dx = ln(x) eax dx = eax/a ln(x) dx = x ln(x) − x xeax dx = eax(ax − 1)/a2 x2eax dx = eax(a2x2 − 2ax + 2)/a3 sin(ax) dx = −(1/a) cos(ax) cos(ax) dx = (1/a) sin(ax) sin2(ax) dx = x/2 − sin(2ax)/4a x sin(ax) dx = (1/a2){sin(ax) − ax cos(ax)} cos2(ax) dx = x/2 + sin(2ax)/4a x cos(ax) dx = (1/a2){cos(ax) + ax sin(ax)}

ÀÒ¤¼¹Ç¡ ¤¡ÒÃËÒ͹ؾѹ¸ì¢Í§àÇ¡àµÍÃàì àÅÐàÁ·Ã¡Ô «ìÀÒ¤¼¹Ç¡¹Õ¨Œ ÐÊÃ»Ø ÊµÙ Ã¡ÒÃËÒ͹ؾ¹Ñ ¸ì (dierentiation) ¢Í§àÇ¡àµÍÃìáÅÐàÁ·ÃÔ¡«ì«§Ö‹ ¨Ð໚¹»ÃÐ⪹ìµÍè ¡ÒÃÇàÔ ¤ÃÒÐËìÃкº¡ÒûÃÐÁÇżÅÊÑ­­Ò³¢Í§ÎÒÃ´ì ´ÔÊ¡ìä´Ã¿ìã¹Ë¹Ñ§ÊÍ× àÅÁè ¹ŒÕ ¡Ó˹´ãËé u áÅÐ x ໹š àÇ¡àµÍÃìá¹ÇµÑŒ§ (column vector) ¢¹Ò´ k × 1 (¹¹‹Ñ ¤Í× Áըӹǹk á¶Ç áÅÐ 1 á¹ÇµÑŒ§) áÅÐãËé A ໹š àÁ·ÃÔ¡«¨ì µÑ ÃØ ÊÑ (square matrix) ¢¹Ò´ k × k ´§Ñ ¹¹ÑŒ¨Ò¡¡ÒÃËÒ͹ؾѹ¸ì¢Í§àÇ¡àµÍÃàì àÅÐàÁ·ÃÔ¡«ì¨Ðä´é¤ÇÒÁÊÑÁ¾¹Ñ ¸ì´Ñ§¹ŒÕ xTu = uTx (¤.1) (¤.2) ∂ xTu =x (¤.3) ∂u (¤.4) ∂ (Au) = AT (¤.5) ∂u (¤.6) ∂ (Au) = A ∂uTáÅÐ uTAu ∂u ∂ = A + AT u¶éÒàÁ·ÃÔ¡«ì A ໹š àÁ·ÃÔ¡«·ì ‹ÕÊÁÁҵà (symmetric) ¹¹‹Ñ ¤×Í A = AT ¨Ðä´éÇÒè ∂ uTAu = 2Au ∂u 177