รศ.ดร.ปยะ โควินททวีวัฒน โปรแกรมวศิ วกรรมโทรคมนาคม คณะวิทยาศาสตรและเทคโนโลยี มหาวิทยาลัยราชภัฏนครปฐม
กสาำรหปรรบั ะกมาวรลจผดั ลเกสบ็ ญั ขญอ้ มาณูลด ิจทิ ัลเลม่ 3 : การออกแบบวงจรภาครับขั้นสงู VSioglnuaml ePrIoIIce:sAsidnvgafnocreDdiRgietcaeliDveartaDSetsoigrnageสงวนลขิ สทิ ธิต์ ามพระราชบัญญตั ิลขิ สิทธ์ิหา้ มลอกเรยี นแบบไมว่ า่ ส่วนใด สว่ นหนึง่ ในหนงั สอื เล่มน้ี ไม่ว่าในรปู แบบใดๆนอกจากจะไดร้ บั อนุญาตเป็นลายลักษณอ์ กั ษรจากผเู้ ขียนเท่าน้ันข้อมูลทางบรรณานุกรมของหอสมุดแห่งชาติปิยะ โควินท์ทวีวฒั น์ การประมวลผลสัญญาณสำหรับการจัดเกบ็ ข้อมลู ดจิ ทิ ัล เลม่ 3 : การออกแบบวงจรภาครับข้นั สงู ./ ปิยะ โควนิ ทท์ ววี ฒั น.์ —นครปฐม: โปรแกรมวิศวกรรมโทรคมนาคม คณะวิทยาศาสตรแ์ ละ เทคโนโลยี มหาวิทยาลัยราชภัฏนครปฐม, 2554 ISBN : 978-974-350-900-1พิมพค์ รง้ั ท่ี 1 สงิ หาคม 2554 348 หนา้ ราคา 270 บาทผ้จู ดั พิมพ ์ : รศ.ดร.ปิยะ โควินทท์ วีวัฒน์พมิ พ์ที ่ : บรษิ ัท เพชรเกษม พร้ินต้ิง กรุป๊ จำกัด 18/49 ถ.ทรงพล ต.ลำพยา อ.เมือง จ.นครปฐม 73000 โทรศัพท์ : 0-3425-9758-9, 0-3425-9111 โทรสาร : 0-3425-3465
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message ECC modulation recorded modulator write current waveformbits encoder encoder bits write head/medium/read head assemblyestimated ECC modulation reproduced read channelmessage bits decoder decoder bits readback voltage waveform subsystem A ¥»Ê· 1.1 â´ §¯É ¯¥²´¥³ ÂÉ n¯£»§¶¶ ³§Å°´¥q¶¬Æq ¥¡q [9, 10] ¬Ï´¥³ ¥²©´¥¯m´¯n £§» ³©¯m´ (read head) ²¯m´n¯£»§´¬Ê¹¯³¸Ä¤Â£Ê¹¯©³ ¯´m §ʹ¯Ê£· ´¸ ¥Â¶ ©Ê£· ·´¥Â§Ê·¤Ã§¬¢´ ©´£ÂÉãm夃 (magnetization) ɲÅn§§³ ¯q ¯£´Âɬ³´¥»§Ê¹Ã¥³Æ¡¡n´Ê·Â¥·¤³³©Ê Æ©m´ “¬³´¯m´§³ (readbacksignal)” ´³Ë¬³ ´¯m´§³²»¬m´n Æ¥²£©§§Åm¯¬³´¯´m ʸ¥²¯©n ¤¶Ë ¬m©m´È Âm ©¥¥¯m´Ê´Ï (LPF: low-pass filter), ©¥³³©¯¤m´ (sampler ¥¹¯analog-to-digital converter), ¯· ©¯Æ§Â¯¥q (equalizer), 粩¥¥©´¬³§³«q (symboldetector) ÂÉn Ĥn¯£»§Â¯´q º·ÊÆnɲ»Ï´´¥¯¥³¬n©¤©¥¯¥³¬£¯»Â§³(modulation decoder) 粩¥¯¥³¬ÃnÆn¯¶ §´ (ECC decoder) ´£§Ï´³  ʹ¯´m´¥²£´¯¶m´©¬´¥Ê· ¯n ´¥²Ï´£´Ån´ 1.2 Ã´Ï §¯m¯¬³´¯°´¥q¶¬qÆ¥¡q ¥²¤m¯¤ A (subsystem A) Å¥»Ê· 1.1 ¬´£´¥Ã¬Ån¯¤m»Å¥» ¯Ã´Ï §¯´¶ª´¬¥q Æn´£¥» Ê· 1.2 [1, 10] £ʹ¯§Ï´³ n¯£»§¯¶ ºÃÆ´¥· ak {0, 1} Ê£· · ´Â©§´¯¶Âm´³ T m©¤ » ¬m m´Æ¤³ ©¥¯ º ³ ¯q º£¶ (ideal differentiator) Ê·£·¥» º´£Âm´³ 1 – D £ʯ¹ D ¹¯©³ ϴ¶´¥m©Â©§´ T m©¤ Ï´ÅnÆnÂɧϴ³n¯£»§Â§Ê·¤¬´² (transition sequence) bk {–1, 0, 1} £ʹ¯ bk = r1 £´¤¸´¥Â§·Ê¤¬´²Ã©¥¹¯Ã§ (positive or negative transition) ç² bk = 0 £´¤¸Æ£m£·´¥Â§Ê·¤¬´² (no transition) ´³Ë§Ï´³n¯£»§Â§Ê·¤¬´² bk ²»¬mm´Æ¤³m¯¬³´Ê·£·§¯¬¯¯¶£ ³§¬q Âm´³¬³´ ³§¬q§ʷ¤¬´² g(t) ç²»¥©n©¤¬³´¥© n(t) ´Ï ÅnÆnÂÉ ¬³ ´¯m´§³ r(t) ʸ ¬´£´¥Â¤· Âɬ£´¥¶ª´¬¥qÆn ¯¹2 การประมวลผลสัญญาณสำหรับการจัดเกบ็ ขอมูลดจิ ิทัล Signal Processing for Digital Data Storage
n t ak bk g t r t aˆk m t H D ¥» Ê· 1.2 Ã´Ï §¯m¯¬³´¯°´¥q ¬¶ qÆ¥¡q r t bkg t kT n t (1.1) k´³ËÊ©· ¥¢´¥³ ¬³ ´¯m´§³ r(t) ²» ¬m´m Ƥ³ ©¥¥¯m´ÏÊ´ (LPF)  ʹ¯Ï´³¬³´¥©Ê·¯¤»m¯Ã©´£Ê· ç²»´Ï ´¥³³©¯¤m´ ©§´Ê·»©º£n©¤¥²Æ££Ê¶¥¶³¡Â©¯¥· (timing recovery) [10] n¯£»§Â¯´q º¯©¥³³©¯¤m´É²»¬mƤ³¯·©¯Æ§Â¯¥q粩¥¥©´¬³§³«q  ʹ¯´§Ï´³n¯£»§¯¶ ºÊ·©¥²Âɬ»¬º aˆk (¥¹¯´m ¥²£´¯ ak ) ¬Ï´¥³¥²´¥³¸Ãé¯ (longitudinal recording) ¬³´ ³§¬q§ʷ¤¬´²¥¯¹ Ê·¥n» ³ ³³©Ê Æ©m´¬³ ´ ³§¬q Lorentzian £·¥»¬£´¥¯¹ [11] g t 1 2t 1 2 (1.2) / PW50Ĥʷ PW50 ¹¯©´£©n´¯¬³´ ³§¬q g(t) ©³ Ï´ÃmÊ·¬³´ ³§¬q£·©´£¬»Âɥʸ ʸ¯©´£¬» ¬»¬º Ųʷ¬³´ ³§¬q§ʷ¤¬´²¯¥²´¥³¸Ãé³Ë(perpendicular recording) £·¥» ¬£´¥¹¯ [12] g t erf 2t ln 2 ¬® (1.3) PW50£ʹ¯ ln(.) ¹¯§¯´¥¶¸£¥¥£´¶ (natural logarithm), PW50 ¹¯©´£©n´¯ ³§¬q g a t ¥¹¯ บทนำ¯ º ³q ¯ g(t) ©³ ´Ï ÃmÊ·¬³´ ³§¬q£·©´£¬»Âɥʸʸ¯©´£¬»¬»¬º, ç² 1erf(.) ¹¯¡³q³¯n ¶ §´ (error function) ʸ ¶¤´£Ä¤ บทที่ เลม 3 : การออกแบบวงจรภาครับขั้นสงู 3 Volume III : Advanced Receiver Design
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¥» Ê· 1.4 ¬³´ ³§¬Æq ¶ ¬Ï´¥³ ´¥³¸ (a) Ãé¯ ç² (b) Ãé³Ë³Ã¬Å¥»Ê· 1.4 Ĥ§¯¬¯Æ¶·Ë²¹¯©m´Âɳ©Ã¯ “m¯¬³´ (channel)”¯¥²´¥³ ¸ n¯£»§Å°´¥q¬¶ qÆ¥¡q Ĥ³©Ê Æ©¥¥©´¬³§³ «qÊ· ¶¤£ÅnÅ¥²´¥³ ¸ ãÂm §É¹¯ ©¥¥©´©·Â¯¥q¶ (Viterbi detector) [10, 13] Âʹ¯´©´£³n¯¯©¥¥©´©·Â¯¥q¶²Â ʶ£Ë¸Ã§·Ë Ï´§³´£Ï´©m©¤©´£Ï´¯m¯¬³´ (channel memory) ³³Ë¯·©¯Æ§Â¯¥q¸ Âɬʶ ´Ï ÂÉÊ· ¯n Ï´£´ÅÂn ʯ¹ ¥³¥»¥m´§¯¬¯¥©£¯³Ë ¥²ÅnÂÉÆ´£§¯¬¯Ê·n¯´¥Ê·Â¥·¤©m´ “§¯¬¯´¥qÂÉ1 (target response)” H(D) [10, 11, 14] ç²m©¤§©´£³n¯¯©¥¥©´©·Â¯¥q¶Æn Å´¶³¶´¥qÂÉ·ËÂ¥·¤³³Ê©Æ©m´ “´¥qÂÉ篬¯´¬m©” ¥¯¹ ´¥qÂÉ Ã PR (partial response) Ĥ´¥qÂÉà PR Ê·ÂÉʤ· ¯£¥³Å¥²´¥³ ¸ Ã鯣¥· »¬£´¥¯¹ [11] H D 1D 1 Dn (1.7)ç²Å¥²´¥³¸Ãé³Ë £¥· » ¬£´¥¹¯ [14, 15] (1.8) H D 1 Dn£ʯ¹ n ¹¯Â§´Ï ©Â£É © บทนำ1 ´¥qÂÉÅ´°´¥q¶¬Æq ¥¡q £´¤¸ ©¥¥¯Ã¶¬nÊ£· · ´Ï ©ÃÉ (tap) n¯¤ ç²»¯¯ÃÅ£n ·§¯ 1 ¬¯Â¶©´£Ê·Â£¯¹ ³§¯¬¯¯m¯¬³´ (ƶ) Å£n ´Ê·¬º Ĥ¥´ª´´¥¤´¤¬³´¥© บทที่ เลม 3 : การออกแบบวงจรภาครับขน้ั สูง 5 Volume III : Advanced Receiver Design
¥» Ê· 1.5 §¯¬¯Â¶ ©´£Ê· ¯´¥qÂÉôm È ¬´Ï ¥³ ¯m ¬³´´¥³¸ (a) Ãé¯ ç² (b) Ãé³Ë ¥»Ê· 1.5 Â¥·¤Â·¤§¯¬¯Â¶©´£Ê· (frequency response) ¯´¥qÂÉà m´È Ĥ§¯¬¯Â¶©´£Ê·¯m¯¬³´É¹¯ §´¥Ã§¡»Â¥·¤¥q (Fourier transform) ¯¬³´ ³§¬qƶ [1] Ŭ£´¥ (1.6) ç²³©Â§Ê·¯¤»mÅ¥ʹ¯£´¤©Â§É¬Ê·Â§Ê·¤£ [] ì´m ¬£³ ¥²¬¶ ¶ÃÎ m§²Ãɯ´¥Âq É ³©¯¤´m Âm PR4 [1 0 –1] £´¤¸ ´¥qÂÉà PR4 (PR class-IV) Ê·£·¡³q³m´¤Ä¯ÅÄ£ D [1] ¹¯ H(D) = 1 – D2, ¥¯¹ EEPR2 [1 4 6 4 1] £´¤¸´¥qÂÉà EEPR2 Ê·£·¡³q³m´¤Ä¯ÅÄ£ D ¹¯ H(D) = 1 + 4D + 6D2 + 4D3 + D4 ÂÉn ´¥» Ê· 1.5 ©´m £ʯ¹ ¯m ¬³´£·m´ ND  ʣ¶ ¸Ë ´¥Âq É ÊÅ· n É ©¥£· ´Ï ©ÃÉ£´¸Ë (£·m´ n £´Ë¸ )  ʹ¯Ån§¯¬¯¯´¥qÂÉ£·§³«²Â£¹¯³§¯¬¯¯m¯¬³´ Ån£´Ê·¬º ʸ²m©¤´Ï Ån©¥¥©´©·Â¯¥q¶´Ï ´Æn¯¤m´£·¥²¬¶¶¢´ £´¸Ë (ª¸«´ ¥´¤§²Â¯·¤Â ʶ£Â¶£ÆnÅÊ· 3 ¯ [10]) ¯´·Ë´¬£´¥ (1.7) ç² (1.8) ©m´m´¬³£¥²¬¶¶Î ¯´¥qÂÉà PR º³© ²Âɧϴ©ÂÉ£ ¯¤m´Æ¥É´£n´Ån´¥qÂÉÊ·£·m´¬³£¥²¬¶¶ÂΠɧϴ©¥¶Ê¸Â¥·¤©m´ “´¥qÂÉà GPR (generalized partial response target)” ¬£¥¥²¥©£¯¥²Ê·Æn²·©m´ ´¥Ån´¥Âq É Ã PR £´ »n¬Å¬´£´¥ª¸ «´Â¶´¥¯¯Ã¯·©¯Æ§Â¯¥qç²´¥qÂÉ Ê·Â£´²³m¯¬³ ´¯°´¥q¶¬qÆ¥¡qÆÅn [10, 14, 15]6 การประมวลผลสญั ญาณสำหรบั การจดั เกบ็ ขอ มลู ดิจิทลั Signal Processing for Digital Data Storage
ak H D sk q t w t aˆk r t¥» Ê· 1.6 ÃÏ´§¯m¯¬³ ´¯º£¶1.3 Ã´Ï §¯m¯¬³´¯º £¶ÃÏ´§¯m¯¬³´Å¥»Ê· 1.2 ¹¯©m´ÂÉ “Ã´Ï §¯m¯¬³´Â¬£¹¯¥¶ (realisticchannel model)”  ¥´²£·§³«²´¥Ï´´Å§n·¤³¥²¥¶Ê¸¥²¯n©¤¶Ë ¬m©Ê·¬Ï´³Ê£· ¯· ¤Å»m ¬´³¤¥¥£¯m ¬³´¯m´¯°´¥q ¶¬qÆ¥¡q [1] ų©n¯·Ë²¯¶´¤ “ÃÏ´§¯m¯¬³´¯º£¶ (ideal channel model)” ʸ¶¤£ÅnÅ´¥ª¸«´Ã§²©¶Â¥´²q ˹´´¥Ï´´¯¥²´¥¥²£©§§¬³´¯°´¥q¶¬qÆ¥¡q  ¥´²ÂÉÃÏ´§¯Ê·Æ£m³n¯Ã§²m´¤¯m ´¥Ï´©´£Â´n Å ³³Ë´n ¬££º¶Ån¥²£·¥²©´¥¯·©¯Æ§Â³Ã¬£»¥q (perfect equalization)ÃÏ´§¯Å¥» 1.2 ɲ¬´£´¥§¥»ÆnÂÉÃÏ´§¯m¯¬³´¯º£¶Å¥»Ê· 1.6 Ĥ§Ï´³n¯£»§¯¶ ºÃÆ´¥· ak ·Ê£·´Â©§´¯¶Âm´³ T ²»¬mÂn´Æ¤³m¯¬³´H D i hiDi £ʹ¯ hi ¹¯m´¬³£¥²¬¶¶Î ³©·Ê i ¯m¯¬³´ ç²»§Ï´Ë ¬³´(modulate) ³¬³´ ³§¬qÆ©¶¬q¯º£¶ (ideal Nyquist pulse) q(t) = sin(St/T)/(St/T)[16] ç²»¥©©n ¤¬³´¥© w(t) ´Ï ÅnÆnÂɬ³´¯m´§³r t skq t kT w t (1.9) kĤʷ sk = ak hk ¹¯¯n £»§Â¯´q º¯m¯¬³´ ç² ¹¯³©Ï´Â¶´¥¯Ä©§»³ (con- บทนำvolution operator) ´³ËÊ·©¥¢´¥³ ¬³´¯m´§³ r(t) ²»¬mm´Æ¤³©¥¥¯m´´ÏÊ Ã§²» ´Ï ´¥³ ©³ ¯¤´m ©§´Ê·»©º£Ä¤¥²Æ££Ê¶¥¶³¡Â©¯¥· m¯²¬mn¯£»§Â¯´q º¯©¥³³©¯¤m´Æ¤³©¥¥©´¬³§³«q ʹ¯Ï´´¥´§Ï´³n¯£»§¯¶ ºÊ·©¥²Âɬ» ¬º 1 บทท่ี เลม 3 : การออกแบบวงจรภาครบั ขน้ั สูง 7 Volume III : Advanced Receiver Design
1.4 ´¥¯¥³¬Ã©´ÏË ÃÏ´§¯m¯¬³´Å¥»Ê· 1.2 ÂÉÃÏ´§¯¯ “¥²Ê·Æ£m»Ân´¥³¬ (uncoded system)” ¯¤m´Æ¥É´£©¥¢´¥³Ê·Ån¥¶Å§´¤È ´¥²¤ºq²Ån³Ë ´¥¯·©¯Æ§Â³ (equalization)  ʹ¯³´¥³´¥§¯ (distortion) ¯m¯¬³´ ç²´¥Ân´¥³¬ÃnÆn¯¶ §´ (error correction coding)  ʹ¯³´¥³n¯¶ §´Ê·Â¶¸Ë´m¯¬³´ Ĥ³Ê©Æ¥²Ê·£·´¥ Ån´¥³¬ ECC ²Â¥·¤©m´ “¥²Ê· » ´n ¥³¬ (coded system)” ¥²´¥¥²£©§§¬³´¯°´¥q¶¬qÆ¥¡q¥¶ (»¥»Ê· 1.1) ²£·´¥Ån´¥³¬ ÃÆn n¯¶ §´©n ¤Âm ³ (ʸ²Å¥n ¬³ RS  ¥´²¬´£´¥ÃnÆn¯¶ §´Ê·¶³§´¤¶ Æn) §m´©¹¯¶m´©¬´¥²»¬mÂn´Æ¤³©¥Ân´¥³¬ÃnÆn¯¶ §´Ã§²©¥Ân´¥³¬£¯»Â§³ ɲÆnÂɧϴ³n¯£»§¯¶ º ak Å¥»Ê· 1.2 ´³ËÊ·©¥¢´¥³ §Ï´³n¯£»§¯¶ ºÊ·¥©´ Æn aˆk Å¥»Ê· 1.2 ɲ»¬mƤ³©¥¯¥³¬£¯»Â§³Ã§²©¥¯¥³¬ÃnÆn¯¶ §´  ʹ¯ÅnÆnÂÉm´¥²£´¯¶m´©¬´¥Ê·²Ï´ÆÅn´Æn ´¥Ï´´¯¥²´¥¥²£©§§ ¬³´¯°´¥q¶¬qÆ¥¡qŧ³«²·Ë¶¤£Ån³Ë Ãm¯·¸³º³Ê¸¹¯©m´ÂÉ´¥¥²£©§ §Ã´Â·¤© (one-way processing) ³Ê¹¯©¥¥©´¬³§³«q²Ï´´Âɯ¶¬¥²´ ©¥¯¥¬³ ECC ¯¤m´Æ¥É´£´©¶³¤ [2 – 5] ìÅnÂÉ©m´ “´¥¯¥³¬Ã©Ï´Ë (iterative decoding)” ʸÂÉ´¥´Ï ´¥m©£³¥²©m´©¥¥©´¬³§³«q粩¥¯¥³¬ ECC ¬´£´¥m©¤Â Ê£¶ ¬£¥¥²¥©£¯¥²ÆÂn ɯ¤m´£´ °´¥q¶¬qÆ¥¡qÊ·Ån¥²´¥¥²£©§§ ¬³´Ã©´ÏË ²£·Ä¥¬¥n´´£¥»Ê· 1.7 Ĥ£·´¥Â ʶ£©¥Ân´¥³¬Ã©Ï´Ë (iterative encoder) 粩¥¯¥³¬Ã SISO2 (soft-input soft-output) Ân´ÆÅ¥² ¯´·Ë©¥ ¥©´¬³§³«qÊ·ÅnÅ¥²¤m¯¤ A ²n¯Â§Ê·¤´©¥¥©´©·Â¯¥q¶ÂÉ©¥¥©´ à SISO Ĥʩ· ¥Â´n ¥³¬Ã©Ï´Ë ɹ¯©¥Ân´¥³¬ÃÆn n¯¶ §´¥²Â¢Ê¸3ʸ ¶¤£ Ån¥³¬ LPDC (low-density parity-check code) [17]  ¥´²ÂÉ¥³¬ ECC Ê·£·¬£¥¥²£´¬º [2, 5] (ª¸ «´¥´¤§²Â¯·¤Âʤ· ©¥³¬ LPDC ÆnÅÊ· 4) ³ º³·Ë°´¥q¶¬qÆ¥¡q¥mºÅ£mÈ Ænϴ¶´¥¯¥³¬Ã©´ÏË £´Ån´Ã§n© (´£¥»Ê· 1.7) ʸ²£·´¥Ã§Â§Ê·¤m´©¬´¥Ã¯¡q (soft information) [2] ¥²©m´©¥ 2 ©¥¥©´Ã SISO 粩¥¯¥¬³ à SISO ²´Ï ´Ä¤Ån ¯n £»§¯¶ º Ê·ÂÉm´©¬´¥Ã¯¡q (soft information) ç²Ånn¯£»§Â¯´q º Ê· Ém´©¬´¥Ã¯¡qÂm³ (ª¸ «´¥´¤§²Â¯·¤ÆnÅÊ· 2 – 3) 3 ¥¬³ Reed Solomon Æ£m¶¤£Ï´£´ÅÅn ´¥¯¥¬³ Ã©Ï´Ë ³³Ë°´¥q ¶¬Æq ¥¡qÊÅ· ¥n ²´¥¥²£©§§ ¬³ ´Ã©Ï´Ë ¸ ´Ï Âɯn  ʶ£©¥Â´n ¥¬³ é´ÏË (iterative encoder) Ân´ÆÅ¥²8 การประมวลผลสญั ญาณสำหรบั การจดั เกบ็ ขอมูลดิจทิ ลั Signal Processing for Digital Data Storage
¥»Ê· 1.7 â´ §¯É ì´¥´Ï ´¯¥²´¥¥²£©§§¬³ ´Ã©´ÏË ¯°´¥q¬¶ Æq ¥¡q¥©´Ã SISO 粩¥¯¥³¬Ã SISO Ĥʷ©¥¥©´Ã SISO Ê·Ån³´¥¯¥³¬Ã©Ï´Ë ¬´£´¥ ³´Æn´¯³§¯¥¶¸£ BCJR [18] ¥¹¯ SOVA (soft-output Viterbialgorithm) [19] (ª¸«´¥´¤§²Â¯·¤ÆnÅÊ· 2 – 3) Ųʷ©¥¯¥³¬Ã SISO Ê·Ån¯¥³¬¯n £§» Ê· » Ân´¥¬³ ©n ¤¥¬³ LDPC ² ³´£´´¯³§¯¥¶¸£´¥m´m´©¬´¥ (messagepassing algorithm) [17] (ª¸ «´¥´¤§²Â¯·¤ÆnÅ©³ n¯Ê· 4.4.4) ´¥Ï´´¯Â¶´¥¯¥³¬Ã©Ï´Ë ¥ʶ£´ ©¥¥©´Ã SISO Ï´´¥¥©´n¯£»§Ê·Æn¥³ çn©¬m§§³ qÊ·Æn (ʸÂÉm´©¬´¥Ã¯¡q) Ƥ³©¥¯¥³¬ÃSISO ´³Ë©¥¯¥³¬Ã SISO ɲ¬m§§³ qÊ·Æn´´¥¯¥³¬n¯£»§§³ÆÅn©¥¥©´Ã SISO  ʹ¯ÅnÅ´¥¥©´n¯£»§Å£m¯·¥³Ë ʸ ¥²©´¥·Ë²Ï´Â¶´¥Æ¥ʹ¯¤È ¥²³Ê ¥´£´Ï ©¥¯ (iteration) ¯´¥©Ï´Ë Ê·Ï´ ©¥¯¥³¬Ã SISO¸ ²¬m¯n £»§Â¯´q ºÊ·ÆnƤ³©¥¯¥³¬£¯»Â§³Ã§²©¥¯¥³¬ RS  ʹ¯Ï´´¥¯¥³¬¯n £»§¯m Æ£´¤Âº ´¥»Ê· 1.7 ² ©´m £· ´¥Ån´³Ë ¥¬³ RS ç²¥³¬ LDPC ¯¤m´Æ¥É´£Å´¶³¶ ©m´ [20] £ʹ¯£·´¥Ån´¥³¬ LPDC Å´¥¯¥³¬Ã©Ï´Ë çn© ɯ´²Æ£mÏ´Âɯn Ån¥¬³ RS ÆÉ n ³ ³Ë»nŬn ´£´¥Â§¹¯Ån´¥¬³ RS ç²¥³¬ LDPC ¥m©£³ ¥¹¯Ån¥³¬LDPC  ¤· ¯¤´m ·¤© ɤ³Å¬n £¥¥²ÊÅ· §n·¤³1.5 ˹´Ã§²´Ï ª³ qÊ· m´¬Å บทนำų©n¯·Ë²¯¶´¤ ˹´Ã§²´Ï ª³ qÊ·m´¬ÅÊ·ÂÊ·¤©n¯³´¥¯¥³¬Ã©´ÏË Â Ê¹¯Ån»n¯´m Ân´Å©´££´¤¯´Ï §´m ·Ë m¯ª¸ «´Â˹¯´ÅÊ· 2 – 4 1 บทที่ เลม 3 : การออกแบบวงจรภาครับขน้ั สูง 9 Volume III : Advanced Receiver Design
1.5.1 ´¥³ ¬¶ Åð´¥qç²Ã¯¡q ©¥¢´¥³¯¥²¬Ê¯¹ ¬´¥¶¶ ³§ ©¥¥©´Ã§²©¥¯¥³¬¬´£´¥Â§¹¯Ån´Æn³Ë´¥³¬¶Åð´¥q (hard decision) ç²´¥³ ¬¶Åï¡q (soft decision) £ʹ¯ ´¥³¬¶Åð´¥q ¹¯´¥´m´¥²£´¯¶n¯£»§¥¹¯¬³§³«q (symbol) ·ÊÆn ´©¥¥©´¥¹¯©¥¯¥³¬ Ĥ§§³ q·ÊÆn²Â¥·¤©m´ “m´©¬´¥Ã°´¥q (hard information)” Âm n´©¥¥©´Æn¥³n¯£»§Ê·£·m´Âm´³ 0.9 ɯ´²³¬¶Å©m´¶n¯£»§ ʬ· m£´´©¥¢´¬m ¯¹ ¶ 1 ´¥³ ¬¶Åï¡q ¹¯´¥´´m ©´£m´Âʹ¯¹¯ (reliability) ¯¶ n¯£»§¥¹¯¬³§³«q ÊÆ· n´©¥¥©´¥¹¯©¥¯¥¬³ Ĥ¯´ª¤³ n¯£»§Ê©· ¥¢´¥³£·³Ë £ 粧§³ qÊ· Æn²Â¥¤· ©´m “´m ©¬´¥Ã¯¡q (soft information)” ³©¯¤´m Âm ´n ©¥¯¥³¬Ån§§³ q ÂÉm´©¬´¥Ã¯¡qÊ·£·m´£´ Éì©m´m´¥²£´¯¶n¯£»§¥¹¯¬³§³«qÊ·Æn´ ©¥¯¥³¬·Ë£· ©´£m´Âʹ¯¯¹ ¥¹¯©´£ÂÉÆÆn Ê·²» ¯n ¬» ¬Ï´¥³ ¥²¬Ê¹¯¬´¥ÃÆ´¥· ©´£m´Âʯ¹ ¯¹ ¯¶¯n £»§²©³´ “¯³¥´¬m©©¥²ÂÉ篴¥¶ £¸ (LLR: log-likelihood ratio)” ³Ê¹¯´n ´Ï Ån x {0, 1} ÂÉ©³ Ã¥¬m£º Æ´¥· ³³Ë´m LLR ¯ x ¶¤´£Ä¤ M x ln p x 10®¬ (1.10) p x £ʹ¯ ln(.) ¹¯§¯´¥¶¸£¥¥£´¶ (natural logarithm) ç² p(x) ¹¯¡³q³©´£´Ãm©´£m´²ÂÉ (pdf: probability density function) ¯ x ¯´·Ëm´¬³£»¥q (absolute value)¯ M x ¯¹ ´m ©¬´¥Ã¯¡q ¥¯¹ m´©´£m´Âʯ¹ ¹¯¯¶¯n £§» x ç²Â¥Ê¯¹ £´¤¯ M x ɹ¯´m ©¬´¥Ã°´¥q ¥¹¯´m ¥²£´¯¶ n¯£»§ x ³Ê¹¯ xˆ ¦£¦¥¤¦¦10,, if M x p 0 (1.11) if M x 01.5.2 ¯³ ¥´¬©m ©¥²ÂÉ篴¥¶ £¸¯³ ¥´¬m©©¥²ÂÉ篴¥¶¸£ (LLR) ¯¹ ÂÉ£¥¶ (metric) ¥¹¯³©·©Ë ³m´©¬´¥ÊÅ· n£´Å¯§³ ¯¥¶£¸ ´m È ÊÅ· nÅ¥²©´¥¯¥³¬Ã©´ÏË Âm ¯§³ ¯¥¶¸£ BCJR, SOVA, ç²LDPC ÂÉn ų¬¹¯·Ë²Ån¬³§³ «q M x Ãm´ LLR ¯¶ ¯n £»§ x {0, 1} ʸ10 การประมวลผลสัญญาณสำหรบั การจัดเก็บขอ มลู ดจิ ิทัล Signal Processing for Digital Data Storage
Log-likelihood ratio (LLR)8 6 4 2 0 -2 -4 -6 -8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p(a = +1)¥» Ê· 1.8 m´ LLR ¯¶n¯£»§ a £ʯ¹ ·¤³ ©´£m´²ÂÉ p(a = +1)ɯ¹ m´§¯´¥¶¸£¥¥£´¶¯Âª«¬©m ¥²©´m ©´£m´²Âɯ¶ 1 粶 0 ´£Ê·¶¤´£Å¬£´¥ (1.10) ¬´Ï ¥³¥²¬Ê¹¯¬´¥Ê·Ånn¯£»§¯¶ ºÆ´¥·Ã¶³©Ë ³Ê¹¯ a {–1, 1} m´ LLR²¶¤´£Ä¤ M a ln p a 11¬® (1.12) p a ʸ ¶¤£Å£n ´Å¯³§¯¥¶ ¸£´¥¯¥¬³ (decoding algorithm)  ¥´²Â¥Ê¹¯£´¤¯m´ M a บทนำ·Ë¬´£´¥Ï´£´ÅnÂÉm´¥²£´¯¶n¯£»§ a (¥¹¯m´©¬´¥Ã°´¥q) Æn³· ÅÏ´¯ 1·¤©³´¯ M a ÅÉ Ân ɳ©¯¸©´£m´Âʹ¯¹¯¯¶n¯£»§ a (¥¹¯m´©¬´¥Ã¯¡q) บทที่¥»Ê· 1.8 ìm´ LLR ¯¶n¯£»§ a £ʹ¯Â·¤³©´£m´²ÂÉ p(a = +1) Ĥ M a £·m´Âɩ£ʹ¯ p(a = +1) > 0.5 ³Ê¹¯¶n¯£»§ a £·©´£m´Âʹ¯¹¯Ê·²Âɶ 1 £´©m´¶ –1ç² M a £·m´Âɧ£ʹ¯ p(a = +1) < 0.5 ³Ê¹¯¶n¯£»§ a £·©´£m´Âʹ¯¹¯Ê·²Âɶ –1£´©´m ¶ 1 ¯´·Ë´n p(a = +1) = 0.5 É ²Ï´Ån M a 0 ʸ£´¤©´£©m´¶n¯£»§ a£·Ä¯´¬Ê· ²ÂÉÆn³Ë ¶ 1 粶 –1 ©n ¤©´£m´²ÂÉÂm´³ Âʹ¯´ p(a = +1) = 1 – p(a = –1) ³³Ë¬£´¥ (1.12) ³¥» Å£mÆnÂÉ เลม 3 : การออกแบบวงจรภาครบั ข้ันสูง 11 Volume III : Advanced Receiver Design
eM a p a 1 (1.13) 1 p a 1 (1.14) (1.15)ç² (1.16) p eM a 1 e M a / 2 a 1 1 eM a 1 eM a eM a/2 eM a/2 p eM a 1 e M a / 2 a 1 1 e M a 1 e M a eM a/2 eM a/2´¬£´¥ (1.14) ç² (1.15) ¬¥º Æn©´m ¬Ï´¥³ C {–1, +1} ²Æn©m´ p a C eCM a / 2 2 eM a/2 eM a/1.5.3 ¯n £§» ¯´q º ï¡q ¯m¯¬³´ ¶´¥´¥²¬Ê¹¯¬´¥ÃÆ´¥· £ʹ¯¶n¯£»§ x {0, 1} »¬mƤ³©¥Ân´»m (mapper)  ʹ¯Ã§ÅnÂɶn¯£»§ u {–1, 1} çn©¬mm´m¯¬³´Ê·Æ£m£·m©¤©´£Ï´ ʸϴÅn¬³´Ê·©¥¢´¥³Æn¥³£·m´Âm´³ y = u + n £ʹ¯ n ¹¯¬³´¥©Â´¬q¬·´©Ã© (AWGN:additive white Gaussian noise) Ê£· · ´m §ʷ¤Âm´³ ª» ¤Ãq §²©´£Ã¥¥©Â´m ³ V2 ¶¤´£¡³q³©´£´Ãm©´£m´²ÂÉã·Âʹ¯Æ (conditional probabilitydensity function) p y | x ¹¯¡³q³©´£´Ãm©´£m´²Âɯ³©Ã¥¬mº£ y £ʹ¯Ï´m´ x £´Ån Å´§³³n´Ï´m´ y £´Ån ɲÆn©m´ p y | x Ê·ÂÉ¡³q³¯³©Ã¥ x²»Â¥·¤©m´ “¡³q³©¥²ÂÉ (likelihood function)” [4] Å´¶³¶m¯Ê·©¥¢´¥³²Æn¥³n¯£»§ y ©´£m´²Âɯ² ¶¥¶¯¯¥¶ (a prioriprobability) ¯ x ²£· m´Âm´³ p x 1 ç² p x 0 ¯¤m´Æ¥É´£§³ ´Ê·©¥¢´¥³Æn¥³n¯£»§ y ©´£m´²ÂÉ p x 1 | y ç² p x 0 | y ²Â§Ê·¤ÂÉ©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶ (APP: a posteriori probability) ç²´¯Â¬q (Bayes’ rule) Ï´ÅÆn n©´m p x i | y p x i; y / p y p y | x ip x i / p y (1.17)12 การประมวลผลสญั ญาณสำหรบั การจัดเกบ็ ขอมลู ดจิ ทิ ัล Signal Processing for Digital Data Storage
£ʹ¯ i {0, 1} ç² p a; b ¯¹ ¡³q³ ©´£´Ãm©´£m´²ÂÉ¥m©£ (joit pdf) ¥²©m´©³ Ã¥¬m£º a ç² b ³ ³Ë´m LLR ¯¶n¯£§» x £ʹ¯Ï´m´ y £´Ån ²¶¤´£Ä¤ M x | y ln p x 10 || yy®¬ (1.18) p x ´¯Â¬q ²Æn©m´ ln p x 1 ||yy®¬ ln p y | x 10¬® ln p x 10®¬ p x 0 p y | x p x Lcy M x (1.19)£ʹ¯ Lc ¹¯n¯£»§Â¯´q ºÃ¯¡q¯m¯¬³´Ê¸¹¯ÂÉm´©¬´¥Ã¯¡q·Ê¬¯§n¯³¶n¯£»§ x Ê·Æn£´´n¯£»§ y ç² M x Â¥·¤©m´ “m´©¬´¥¯² ¶¥¶¯¯¥¶ (a priori information)”¯¹ m´©¬´¥Ê·ÂÊ·¤©³¶n¯£»§ x m¯Ê·©¥¢´¥³Æn¥³n¯£»§ y Ĥť·Ê·©¥¢´¥³Æ£m£·m´©¬´¥¯² ¥¶ ¯¶ ¯¥¶ É ²Ï´Ån M x 0 Ĥ³©Ê Æm´ Lc Ŭ£´¥ (1.19) ²Â¥·¤©m´©´£m´Âʯ¹ ¹¯¯m¯¬³´ (channelreliability) ʸ˸³§³«²¯m¯¬³´ ³©¯¤m´Âm Å¥·Ê· nk ¹¯¬³´¥©AWGN ɲƩn ´m ln p y | x 10¬® w ln p y | u 11¬® p y | x p y | u ln exp 1 y 12 ®¬ 2 exp 2T2 T2 y (1.20) 1 y 12 2T2³Ê¹¯ Lc 2 / T21.5.4 ©¥¯¥¬³ à SISO บทนำ©¥¯¥³¬Ã SISO (soft-input soft-output) ¹¯©¥¯¥³¬n¯£»§Ê·´Ï ´³m´©¬´¥ 1ï¡q Ĥ²¥³n¯£»§¯¶ ºÊ·ÂÉm´©¬´¥Ã¯¡qÂn´£´¥²£©§§ ç²Ånn¯£»§Â¯´q ºÂÉm´©¬´¥Ã¯¡q บทที่ เลม 3 : การออกแบบวงจรภาครับขน้ั สูง 13 Volume III : Advanced Receiver Design
nk Ma xk xk uk yk Mp xk xˆk\0,1^ M xk | y \o1^ ¥» Ê· 1.9 ¥²¬Ê¯¹ ¬´¥¶ ¶§³ Ê·Å©n ¥¯¥¬³ à SISO ¶´¥´¥²¬Ê¹¯¬´¥Å¥»Ê· 1.9 £ʹ¯§Ï´³n¯£»§ xk {0, 1} »¬mƤ³©¥Ân´¥³¬(encoder) 粩¥Â´n »m (mapper)  ʹ¯ÅnÆÂn ɧϴ³n¯£»§ uk {–1, 1} ´³Ë©¥¯¥³¬Ã SISO ²Ï´´¥¯¥³¬n¯£»§¯¬³´ yk = uk + nk Ĥʷ nk ¹¯¬³´¥©AWGN Ĥ¯´ª³¤©´£©m ¤Â§¯¹ ´§Ï´³ ¯n £»§ Ma xk £ʹ¯ Ma xk ¯¹ ´m LLR ï² ¶¥¶¯¯¥¶(a priori LLR) ¯¶¯n £»§ xk ³Ê¯¹ M xk ln p xk 10®¬ (1.21) a p xk ʸ£´¤¸ m´©¬´¥Ê·ÂÊ·¤©³ ¶¯n £»§ xk m¯Ê©· ¥¢´¥³²Æ¥n ³§´Ï ³ ¯n £»§ y ¥¯¹ n¯£§» yk³Ë £ (³Ê¹¯Âɯ¶¬¥²´ y) ÅÏ´¯Â·¤©³n´©¥¢´¥³Æ£m£·m´©¬´¥¯² ¶¥¶¯¯¥¶ ɲϴÅn M xk 0 ¬´Ï ¥³ ºm´ k ʸ £´¤©´£©m´¶ ¯n £§» xk º©³ £·©´£m´²ÂÉÊ·² a¶˸ Âm´³ ´³Ë©¥¯¥³¬Ã SISO ²Ån¯n £»§Â¯´q ºÂÉm´ LLR ï²Ä ¬Â¯¥¶¯¯¥¶(a posteriori LLR) ¯¶ ¯n £§» xk ³Ê¯¹ Mp xk ln p xk 1 | yy¬® (1.22) p xk 0 |Ĥʷ m´¥²£´¯¶n¯£»§ xk ¬´£´¥´Æn´´¥¬mm´ M xk m´Ân´Æ¤³©¥¥©´ p·Â¥Ê¶£Â§Ê·¤ (threshold detector) ´£©´£¬³£ ³q³·Ë xˆk ¤¦¦¦¦¥£10,, if M x k p 0 (1.23) p if M x k 0 p£´¤Âº ¬´Ï ¥³´m LLR ¯¶ n¯£§» x ³Ê¯¹ M x ų¬¹¯Â§m£·Ë²¶¤´£³ ·Ë14 การประมวลผลสญั ญาณสำหรับการจดั เกบ็ ขอมูลดิจิทัล Signal Processing for Digital Data Storage
n´m´ LLR £· ©³ ¯n ¤ (subscript) ÂÉ ´¥´£¶Â¯¥q a Âm Ma x ²£´¤¸´m LLR à ¯² ¶¥¯¶ ¯¥¶ (a priori LLR) ¯¶ n¯£§» x n´´m LLR £· ³©¯n ¤ÂÉ ´¥´£Â¶ ¯¥q p Âm M x ²£´¤¸m´ LLR ï²Ä ¬Â¯¥¯¶ ¯¥¶ p (a posteriori LLR) ¯¶ ¯n £»§ x1.6 ¬¥ºn´¤Å·ËÆn¯¶ ´¤Ã´Ï §¯m¯¬³ ´¯´m ÊÅ· nÃ¥²´¥³¸ ¶ ãÂm §É (³Ë ÃÏ´§¯m¯¬³ ´Â¬£¹¯¥¶Å¥» Ê· 1.2 ç²Ã´Ï §¯¯m ¬³´¯º £¶Å¥»Ê· 1.6)  ʹ¯Ån»n¯m´¬´£´¥Ï´ÃÏ´§¯·ËÆÅÅn ´¥©¶Â¥´²q¥²´¥¥²£©§¬³ ´¯°´¥q ¶¬Æq ¥¡q Âʹ¯´°´¥q ¶¬Æq ¥¡q¥ºm Å£mÈ Ê£· ·´Ï m´¤Ån¯§´²Ån¶´¥¯¥³¬Ã©´ÏË (iterative decoding)  ¥´²¬´£´¥m©¤Â ʶ£¬£¥¥²¯¥²Æn·¤Ê¶Ë¸ ³³Ëŷ˸ Ưn ¶ ´¤Ã©¶Ã§² ˹ ´¯Â¶´¥¯¥³¬Ã©Ï´Ë ¥©£³Ë ©´££´¤¯ SISO©´£m´²Âɯ² ¶¥¶¯¯¥¶ ©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶ m´©¬´¥Ã¯¡q 粯³¥´¬m©©¥²ÂÉ篴¥¶¸£ (LLR) ÂÉn  ʹ¯Â¥·¤£©´£ ¥n¯£¯»n¯m´m¯Ê·²ª¸«´§³´¥Ï´´¯©¥¥©´Ã§²©¥¯¥¬³ à SISO ʸ ²¯¶´¤m¯ÆÅÊ· 2 – 41.7 ø ³ n´¤ บทนำ1. ¯¶´¤§³ ´¥´Ï ´¯¥²´¥³ ÂÉn¯£§» ¶¶ §³ Å°´¥q ¶¬Æq ¥¡qÅ¥»Ê· 1.12. Ånĥå£ SCILAB ©´¥»¯m Æ·Ë (http://home.npru.ac.th/piya/webscilab ¥¹¯ http://www.scilab.org) 2.1) ¬³ ´ §³ ¬Âq §¤Ê· ¬´² m´ ND ´m È ´£¥» Ê· 1.3 2.2) §¯¬¯Æ¶ m´ ND m´È ´£¥» Ê· 1.43. ì©m´§´¥Ã§¡»Â¥·¤¥q¯§¯¬¯Æ¶ m(t) Ŭ£´¥ (1.6) ¯¥² ´¥³¸Ã鯣· m´Â´m ³ M 8 exp\Q 8 ND^ 1exp\j 2Q8^ 粯¥²´¥³ ¸Ãé³Ë £· m´Âm´³ 1 บทที่ เลม 3 : การออกแบบวงจรภาครับขน้ั สูง 15 Volume III : Advanced Receiver Design
M 8 T exp ¦¤¦¦£¥¦ Q 282 ND2 ¦¦¦»¼²¦ 1 exp\j 2Q8^ jQ8 ln 16 £ʹ¯ exp{.} ¹¯¡³q ³Â§·Ë ´Ï §³, : = fT ¹¯©´£Ê·Ã¯¥£q ¯§Æ§q (normalized fre- quency), f ¯¹ ©´£Ê£· · m©¤ÂÉ°¶¥,q |x | ¯¹ m´¬£³ »¥q¯ x, ç² j 14. ´§´¥Ã§¡»Â¥¤· ¥q¯§¯¬¯Æ¶Ån¯ 3 ©´¥»§¯¬¯Â¶ ©´£Ê· ¯ ¯m ¬³ ´ m´ ND m´È Å¥» Ê· 1.5 ĤÅÄn ¥Ã¥£ SCILAB5. ¯¶ ´¤©´£Ãm´¥²©m´Ã´Ï §¯¯m ¬³ ´Â¬£¯¹ ¥¶Å¥» Ê· 1.2 ç²ÃÏ´§¯ ¯m ¬³´¯º £Å¶ ¥» Ê· 1.66. ¯¶ ´¤§³´¥´Ï ´¯¥²´¥¥²£©§§¬³´Ã©´ÏË ¯°´¥q ¬¶ qÆ¥¡qÅ ¥» Ê· 1.77. ¯¶´¤©´££´¤¯´m ©¬´¥Ã¯¡q (soft information)8. ¯¶ ´¤©´££´¤¯¯³¥´¬m©©¥²ÂÉ篴¥¶¸£ (LLR: log-likelihood ratio)9. ¯¶´¤©´££´¤¯´m LLR ï² ¥¶ ¯¶ ¯¥¶ ç²´m LLR ï²Ä ¬Â¯¥¶¯¯¥¶10. ¯¶´¤©´££´¤¯©¥¥©´Ã SISO 粩¥¯¥³¬Ã SISO16 การประมวลผลสญั ญาณสำหรบั การจัดเกบ็ ขอ มลู ดิจิทัล Signal Processing for Digital Data Storage
Ê· 2¥³¬Â¯¥qÄųº³¥³¬ÃÆn n¯¶ §´ [2 – 5] £Å· n§¹¯Ån´Ï´©£´´£§³«²´¥Ån´¯ บทนำ ร ัหสเทอ รโบçm ²´¥²¤ºq Ĥ©³Ê Æ´¥²¤ºqÊ· n¯´¥©´£¬´£´¥Å´¥ÃnÆn¯¶ §´¬» ɲn¯Ån©¥Ân´¥³¬Ã§²¯¥³¬Ê·£·©´£³n¯¬»£´Âm³ ©¶·´¥Ãn³´¯¤m´m´¤É¹¯ 2´¥Ån ´¥Ân´¥³¬Ãm¯³ (concatenated coding) ʸÂÉ´¥Ân´¥³¬n¯£»§Ä¤Ån©¥Ân´¥³¬ 1บทท่ี£´©m´Ê¸©¥£´m¯³Ã¯º¥£¥¹¯Ã´ Ĥ¯´ª³¤©´£m©¤Â§¹¯¯©¥¯¶Â¯¥q§·¡Â©¯¥q (interleaver) ´³Ën¯£»§Ê·»Ân´¥³¬É²»Ï´´¥¯¥³¬n©¤©¥¯¥³¬Ãm§² บทที่³© ¸ ãn©´m §§³ q ÊÆ· n ´©¶·´¥·Ë¹¯©m´ÂÉ㴲ʷ¬ºÃ¥¯ (sub-optimal) Ãm©¶·´¥·Ë²¥²·¥²¯£¥²©m´©´£¬´£´¥Å´¥ÃÆn ¯n ¶ §´Ã§²©´£³n¯¯¥²©´¥Â´n ¥¬³ 粯¥¬³ ¶´¥¯¥³¬Ã©´ÏË (iterative decoding) [2, 3] ¹¯Âɶʷ¬´£´¥m©¤§¯³ ¥´n¯¶ §´¯¶ (BER: bit-error rate) ¯¥²Ånn¯¤§©m´Â¶£Æn ´¥¯¥³¬¯n £»§¯¥³¬Â¯¥qÄ (turbo code) [3] ¹¯ÂÉ©³ ¯¤m´¯´¥¯¥³¬Ã©Ï´Ë ʸųº³Æ£n ·´¥Ï´£´Ånŧ´¤´¥²¤ºq ÆÃn m ¥²Ä¥ª ³ q§ʯ¹ Ê· ç²¥²¬Ê¯¹ ¬´¥m´´©Â·¤£ÂÉn ¯´·Ë§³´¥Â¯¥qÄ (turbo principle) Ê·ÅnÅ´¥¯¥³¬n¯£»§Ã¯¥qĤ³¬´£´¥Ï´£´¥²¤ºqÅn³¥²©´¥¯·©¯Æ§Â³ (equalization) Æn Ĥ²Â¥·¤Â¶·Ë©m´“¯·©¯Æ§Â³Ã¯¥qÄ (turbo equalization)” [21] ʸ¹¯ÂÉ¥²©´¥¯¥³¬Ã©Ï´Ë Ê·ÆnÏ´£´Ån¥¶Å°´¥q¶¬qÆ¥¡q¥ºmÅ£mÈ Ã§n© [6] ʸ£·¬£¥¥²·©m´°´¥q¶¬qÆ¥¡qů·ÊÆ· £Æm nÅn¶´¥¯¥³¬Ã©Ï´Ë ·Ë²Â¥Ê£¶ n¯¶´¤¥³¬¯Ä©§»³ 粯³§¯¥¶ £¸ BCJR [18] ʸ ¯¹ Âɬm©¬Ï´³¯¥³¬Â¯¥qÄ Â Ê¹¯Ån»n¯m´Ân´Å¶´¥Ân´¥³¬Ã§²´¥¯¥³¬Ã©Ï´Ë ·ÊÅnÅ¥²´¥¥²£©§§¬³´¯°´¥q ¬¶ qÆ¥¡q เลม 3 : การออกแบบวงจรภาครบั ข้ันสูง 17 Volume III : Advanced Receiver Design
2.1 ¥³¬¯Ä©§»³¥¬³ ÃÆn ¯n ¶ §´¥¹¯¯´Â¥¤· ©´m ¥³¬ÃÆn ¯n ¶ §´Ã´n n´ (FEC: forward error-correction code) ¶¤£Ï´£´Ånų´¥³ ¬³´¥©Ã§²¯n ¶ §´Ê·Â¶´m¯¬³´Ä¤³©Ê Æ¥³¬ÃÆn ¯n ¶ §´¬´£´¥Ãm¯¯ÆnÂɬ¯Ã¹¯ ¥³¬§É¯ (block code) ç²¥³¬¯Ä©§»³ (convolutional code) [2] ¯´·Ë¤³£·¥³¬ ECC ÃÅ£mÊ·¯´ª³¤Â¶´¥¯¥³¬Ã©Ï´Ë Âm ¥³¬Â¯¥qÄ [3] ç²¥³¬ LDPC [17] ÂÉn ʸ£·¬£¥¥²Ân´Å§n©´£ºm¯¬³´¯Ã¯4 (Shannon’s channel capacity) £´©m´¥³¬¯Ä©§»³Å³©n¯·Ë²¬¥º§³´¥Ï´´¯¥³¬¯Ä©§»³Â ¥´²ÂÉ¶Ë ¬m©Ê·¬Ï´³¯¥³¬Â¯¥qÄʸ²§m´©m¯Æų©n¯Ê· 2.32.1.1 ´¥Â´n ¥³¬©¥Ân´¥³¬¯Ä©§»³ (convolutional encoder) ²ÅnÂ¥¶¬Â¯¥qçʹ¯ (shift register) 粩¥©Ã£¯ºÄ§¬¯5 (modulo-2 adder) Å´¥Ân´¥³¬n¯£»§ Ĥ²´Ï ´¥Ân´¥³¬§Ï´³n¯£»§¯¶ º (input data sequence) ʸº ç²Å§n ´Ï ³ ¯n £§» ¯´ q º Ï´©£´©m´¥¹¯Â´m ³Ê¸º Ĥʷ´n ©¥Â´n ¥³¬¯Ä©§»³ ´n ¥¬³ n¯£»§¯¶ º 1 ¶ çn©Ï´Ån¶n¯£»§Â¯´q ºÏ´© n ¶ ì©m´©¥Ân´¥³¬¯Ä©§»³·Ë£·¯³¥´¥³¬ (code rate) Âm´³ R 1/ n ¥»Ê·2.1 쩳 ¯¤´m ©¥Ân´¥³¬¯Ä©§»³ Ê·£·¯³ ¥´¥¬³ R = 1/2 £ʹ¯ D ¯¹ ©³ ´Ï ¶´¥m©Â©§´Ê¸m©¤ (unit delay operator) ʸ ÅnÃÂ¥¬¶ ¯¥Ãq §ʹ¯ Å´¶³©¶ ¥Ân´¥¬³¯Ä©§»³ ²Â¤· Ãn©¤ º ´£³©Ï´Â¶ (generator polynomial) ʸ£·¥»¬£´¥¯¹ [1] N (2.1)G D giDi i 0£ʹ¯ P ¹¯Ï´©m©¤©´£Ï´¯©¥Ân´¥³¬¯Ä©§»³ (¥¹¯Ï´©Â¥¶¬Â¯¥qçʹ¯)ç² gi = 1 n´¶n¯£»§¯¶ ºÊ·»m©Â©§´Æ i m©¤ £·§m¯´¥Â¶¯¶n¯£»§Â¯´q º ©§´³º ³ ³©¯¤m´Âm ©¥Ân´¥¬³ ¯Ä©§» ³ Å¥» Ê· 2.1 () £ · º´£©³ ϴ¶¹¯G D ¢¡ G1 D, G2 D¯°± ¡¢ 1 D, 1 D2 °±¯ (2.2) 4 ¥» ´¤§²Â¯·¤Â¥Ê¹¯©´£º m¯¬³ ´ (channel capacity) ÆÅn ³©n¯Ê· 5.1.3 ¯ [1] 5 n´Ån ¹¯©³ ϴ¶´¥©Ã£¯Äº §¬¯ ³³Ë 0 0 = 0, 0 1 = 1, 1 0 = 1, ç² 1 1 = 018 การประมวลผลสญั ญาณสำหรับการจัดเก็บขอ มลู ดิจิทัล Signal Processing for Digital Data Storage
yk1xk yk2¥» Ê· 2.1 () ©¥Â´n ¥¬³ ¯Ä©§»³, () ©¥Â´n ¥¬³ ¯Ä©§»³ ã·¥², ç² () ©¥Ân´¥³¬¯Ä©§» ³Ã£¥· ²Â©·¤Â¶Â£Ê¹¯ ¹¯©³ ´Ï ¶´¥©Ã£¯ºÄ§¬¯, G1(D) ¹¯ º´£³©Ï´Â¶¯n¯£»§Â¯´q º yk1 , ร ัหสเทอ รโบG2(D) ¹¯ º´£³©´Ï ¶¯n¯£§» ¯´q º yk2 , ç²£· m©¤©´£Ï´ P = 2 m©¤ 2 ¯´·Ë©¥Ân´¥³¬¯Ä©§»³Ã£·¥² (systematic convolutional encoder) บทที่¹¯©¥Ân´¥³¬¯Ä©§»³Ê·´Ï Ånn¯£»§Â¯´q ºÊ¸º£·m´Âm´³n¯£»§¯¶ º ´£Ê·Ã¬Å¥» Ê· 2.1 () ʸ£· º´£³©Ï´Â¶¹¯ ¡ ¢1, 1 D2 ±°¯ ¬Ï´¥³©¥Ân´¥³¬¯Ä©§»³Ã£·¥²Ê£· ·´¥n¯§³ ©n ¤²Â¥·¤©m´©¥Ân´¥¬³ ¯Ä©§»³Ã£·¥²Â©¤· ¶ (recursive systematic convolutional encoder) ´£¥»Ê· 2.1 () ʸ£· º´£³©Ï´Â¶¹¯ ¡¢1, 1/ 1 D2 ±°¯ Ĥ³©Ê Æ©¥Ân´¥³¬¯Ä©§»³Ã£·¥²Â©·¤Â¶²ÂÉÊ·¶¤£Ån´£´©m´©¥Ân´¥³¬¯Ä©§»³Ã¯Ê¹È [2] Ĥ³Ê©Æ´¥©¶Â¥´²q¥³¬¯Ä©§»³²¯´ª³¤Â¥Ê¹¯¬´²Ï´³ (FSM: finite statemachine) ʸÂÉÃÏ´§¯Ê·Ã¬ÅnÂɸ´¥Â§Ê·¤Ã§¯n¯£»§¯¶ º, ¬´²Â¥Ê¶£n(start state), ¬´²m¯Æ (next state), ç²n¯£»§Â¯´q º ¯¥² (ª¸«´¥´¤§²Â¯·¤Ænų©n¯Ê· 4.3.1 ¯ [10]) ¥»Ê· 2.2 (n´¤) ì¥ʹ¯¬´²Ï´³¯©¥Ân´¥³¬¯Ä©§»³Å¥»Ê· 2.1 () ʸ£·³Ë £ 2P = 4 ¬´²¹¯ 00, 01, 10 ç² 11 Ĥ·Ê¬n§»ª¥²Ã¬Â¬n´´¥Â§Ê·¤¬´² ç²m´ x / y1y2 Ê·¯¤m»¶³Â¬n§»ª¥²ÅnÃm´n¯£»§¯¶ º¶ x粯n £§» ¯´q º¶ y1 ç² y2 ¯´·Ëⴠ¥§§¶¬ (trellis diagram) ʸÅn촥§ʤ· ¬´²ÅÃm§²©m ©§´¬É ´£´¥Ån¯¶´¤´¥´Ï ´¯¥¬³ ¯Ä©§»³ÆnÂm³ ¥»Ê·2.2 (©´) ìⴠ¥§§¬¶ ¯©¥Ân´¥³¬¯Ä©§»³ Å¥»Ê· 2.1 () ³Ê¹¯Ã¢´ เลม 3 : การออกแบบวงจรภาครบั ข้นั สูง 19 Volume III : Advanced Receiver Design
¥» Ê· 2.2 â´ ¥ʹ¯¬´²Ï´³ ç²Ã¢´ Â¥§§¶¬¯¥»Ê· 2.1 ()Â¥§§¬¶ Å¥²¤²Ê· k ²Ã¬´¥Â§Ê·¤¬´²Ê·ÂÉÆÆn ³Ë £¯©¥Ân´¥³¬´¬´²Ê¸ ©§´ k Ƥ³¯·¬´²Ê¸ ©§´ k + 1 Ĥm´Ê·¯¤m»¶³Â¬n§»ª¥É¹¯m´ x / y1y2 Ê·¯¤»mÅ¥ʯ¹ ¬´²´Ï ³ ³Ê¯ Âʹ¯´Â¬n´ (path) ʷ¶ƴ£Ã¢´ Â¥§§¶¬²£´¤¸º ¯Â¬n¬´´ (branch) Ê·¥²¯n©¤Ê¸Â¬n¬´´m¯Ê¸¥²¤² ³³ËÏ´¥³¬ (codeword)º Ï´ (¥¯¹ n¯£»§Â¯´q º ¯©¥Ân´¥¬³ ¯Ä©§»³) ²¯n ¬¯§¯n ³Â¬n´Ê·ÂÉÆn ·¤Ê¸Â¤· © (unique path) Åⴠ¥§§¬¶ (¥» » Ê· 2.5)©³ ¯¤m´Ê· 2.1 ì³Ë ¯´¥Â´n ¥¬³ ¯©¥ Y1Ân´¥¬³ ¯Ä©§» ³ Å¥» Ê· 2.1 () £ʹ¯¶n¯£§» X D S1 D S2¯¶ º¹¯ {x0, x1, x2, x3} = {1 0 1 1}©¶·´Ï ¥» Ê· 2.1 () ìţmÆn´£¥»´n ©´£¹¯ Y2ʸ£ʹ¯Ï´¶n¯£»§ {xk} £´Ân´¥³¬n©¤©¥Ân´¥³¬¯Ä©§» ³ ²£· ³Ë ¯´¥´Ï ´³ ·Ë³Ë ʷʸ Ï´Ån¬´²¯Â¥¶¬Â¯¥qçʹ¯³Ë £ ³Ê¹¯ S1 ç² S2 £·m´ÂÉ 0 (Ï´ÅnÂɬ´² 00) Ĥ³Ë ¯·ËÂÉ ·¤´¥Â¥·¤£©´£ ¥n¯£¯©¥Ân´ ¥³¬Ã§²¤³ Æ£m£·´¥n¯¶ n¯£§» ´n Æ20 การประมวลผลสัญญาณสำหรบั การจดั เกบ็ ขอ มลู ดิจิทลั Signal Processing for Digital Data Storage
³Ë Ê·¬¯ ¥ʶ£n¯¶Ã¥Ê¸£·m´ÂÉ 1 (³Ê¹¯ x0 = 1) Ân´¬m»©¥ ÉÏ´Ånm´ Y1 = X S1 = 1 0 = 1 ç² Y2 = X S2 = 1 0 = 1 ʸ¹¯n¯£»§Â¯´q º·ÊÆn´ ´¥Â´n ¥³¬¯¶ Ã¥³Ê¯³Ë ʬ· ´£ ¥ʶ£n¯¶Ê·¬¯Ê¸£·m´ÂÉ 0 Ân´¬m»©¥ m´m´È Å©¥É²Â§Ê¹¯Æʸ¶ ³Ë £ ( ©§´·Ë S1 = 1 ç² S2 = 0) Ï´Ånm´ Y1 = X S1 = 0 1 = 1 ç² Y2 = X S2 = 0 0 = 0 ʸ ¹¯§Ê·Æn ´´¥Ân´¥³¬¯¶Ê·¬¯³Ë ʬ· Ê· ¥ʶ£n¯¶Ê·¬´£Ê¸£·m´ÂÉ 1 Ân´¬m»©¥ m´m´È Å©¥É²Â§Ê¹¯Æʸ¶ ³Ë £ ( ©§´·Ë S1 = 0 ç² S2 = 1) Ï´Ånm´ Y1 = X S1 = 1 0 = 1 ç² Y2 = X S2 = 1 1 = 0 ʸ ¹¯§Ê·Æn ´´¥Ân´¥¬³ ¯¶ Ê·¬´£³Ë Ê· n´ ¥ʶ£n¯¶Ê·¬Ê·Ê¸£·m´ÂÉ 1 Ân´¬»m©¥ m´m´È Å©¥É²Â§Ê¹¯Æʸ¶³Ë £ ( ©§´·Ë S1 = 1 ç² S2 = 0) Ï´Ånm´ Y1 = X S1 = 1 1 = 0 ç² Y2 = X S2 = 1 0 = 1 ʸ¹¯§Ê·Æn ´´¥Â´n ¥¬³ ¯¶ Ê·¬Ê·³Ë Ê· ¬³Â©m´¬´²¯©¥Ân´¥³¬¯Ä©§»³Æ£mÆn§³Æ¬m»¬´²Â¥Ê¶£n·ÊÂÉ ª»¤q £ ( ¯·Ë¯¤m»Å¬´² 11) n©¤Âº·Ë¸n¯£·´¥Â¥·¤£¶´ (tail bit) Ê· £´²¬£¯· 2 ¶  ʹ¯¥³©¥Ån§³Æ¬m»¬´²Ê·ª»¤q³Ë £ ¥²© ´¥Ân´¥¬³ ¸ ²Â¬¥É¬£»¥q³Ë ¬ºn´¤ ´¥Â§¹¯´m ¯¶´£·§³´¥m´¤È ¹¯Ån ¶´¥´»©m´¶n¯£»§ÅÊ·£·§Ï´Ån ´m ÅÂ¥¬¶ ¯¥qçʹ¯Âɪ»¤q³Ë £ ʸÅÊ··Ë²Æn©m´Ånn¯¶ 0 ¬¯¶ Ân´ÆÅ©¥É²Ï´Ån©¥Ân´¥³¬§³Æ¬m»¬´² 00 ¯·¥³Ë ʸ¹¯©m´¬¶Ë ¬º ¥²©´¥Ân´¥³¬ Ĥ¶´³©Ã¥²Ånn¯£»§Â¯´q ºÂÉ Y1 = 1 ç² Y2 = 1 Ųʷ ¶ ´©³ ʬ· ¯²Ånn¯£»§Â¯´q º ÂÉ Y1 = 0 ç² Y2 = 1³©¯¤m´´¥Ân´¥³¬Ê·Æn¯¶´¤£´·Ëìť»Ê· 2.3 ʸn´Ï´£´Ã¬Å¥»¯Ã¢´ ´¥Â§Ê·¤ ร ัหสเทอ รโบ¬´²É²£·§³«²´£¥»Ê· 2.4 ¥¹¯n´Ï´£´Ã¬Å¥»¯Ã¢´ Â¥§§¶¬É²£·§³«²´£¥» Ê· 2.5 ʸ ²ÂÉ Æ©n m´¥» Ê· 2.3 – 2.5 Ån §§³ qÂm´³ ¯´·Ë´¥Ân´¥¬³ ¯Ä©§»³¤³¬´£´¥Ï´ÆnĤÅn´¥Ã§ D (D transform) [1] 2Âm ³ ³Ê¹¯¯n £§» ¯´q ºÊÆ· n´©¥Ân´¥³¬¯Ä©§»³ ²£·m´Â´m ³ บทท่ี Yi D Gi DX D (2.3) เลม 3 : การออกแบบวงจรภาครบั ขนั้ สูง 21 Volume III : Advanced Receiver Design
¥» Ê· 2.3 ³Ë ¯´¥Â´n ¥¬³ ¯Ä©§»³ ų©¯¤´m Ê· 2.1 xk / yk1yk2 ¥»Ê· 2.4 â´ ´¥Â§Ê¤· ¬´²Å©³ ¯¤´m Ê· 2.1 £ʹ¯ Yi D k yki Dk ¹¯§´¥Ã§ D ¯n¯£»§Â¯´q º yki ¬Ï´¥³ i \1, 2^ , Gi(D) ¹¯ º´£³©Ï´Â¶¯n¯£»§Â¯´q º yki , ç² X D k xkDk ¹¯§´¥Ã§ D ¯ n¯£»§¯¶ º Âm ´³©¯¤m´Ê· 2.1 (¥»Ê· 2.1 ()) ²Æn©m´ X D 1 D2 D3 ç² Gi D \ ^ÂÉÆ´£¬£´¥ (2.2) ³³Ë¯n £»§Â¯´ q ºÊÆ· n ´´¥Â´n ¥¬³ ³Ë ¬¯º yk1 ,yk2 £· m´Â´m ³22 การประมวลผลสัญญาณสำหรับการจดั เกบ็ ขอ มูลดจิ ทิ ัล Signal Processing for Digital Data Storage
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g2 D 1 1 D3 D 3 g1 D D D2¥» Ê· 2.6 ©¥Ân´¥¬³ ¯Ä©§» ³Ê·£ · º´£©³ ϴ¶ť» ¯Â§´Ã¹¯ (g1, g2) = (17, 11) 1000/0 1/0 0/1 1/1 010 0/0 000 1/1 0/1 1/0 110001 0/1 1/1 1/0 101 111 0/1 0/0 1/0 1/1 0/0 011 ¶¯n £§» ¯¶ º / ¶ ¯n £§» ¯´ q ºÃ¶ n¯£»§¯¶ º ·£Ê ·m´ÂÉ 0ö n¯£»§¯¶ º ·£Ê ·m´ÂÉ 1¥» Ê· 2.7 â´ ¥ʯ¹ ¬´²Ï´³ (FSM) ¯©¥Â´n ¥¬³ ¯Ä©§» ³Å¥» Ê· 2.6´Ï Ån¬´²¯Â¥¬¶ ¯¥qçʹ¯³Ë ££·m´ÂÉ 0 ´³ËÉÏ´´¥n¯n¯£»§Ân´ÆÅ©¥·§²¶ çn©Ï´©´n¯£»§Â¯´q º¯©¥Ân´¥³¬·§²³© £ʹ¯n¯¶n¯£»§¯¶ ºÂn´ÆÅ©¥Ân´¥³¬¥Ã§n© ÉÅnn¯¶´¯·Ï´©Ê¸¥²³ÊÏ´ÅnÂ¥¶¬Â¯¥qçʹ¯³Ë ££·m´ÂÉ 0 £¹¯Â¶£ ´Ï´»n¯²Æn©m´¶´Ê·n¯n¯Ân´ÆÅ©¥Ân´¥³¬¹¯ 111 粧§³ qÊ·Æn´´¥Ân´¥¬³ ¯¹ 1010111000124 การประมวลผลสญั ญาณสำหรบั การจัดเกบ็ ขอมลู ดจิ ทิ ัล Signal Processing for Digital Data Storage
xk\ ^xk 00z 1 k0z 1 zk z 0 , z10z11 , ..., z k \ ^yk z k0z 1 \xkyk ^ k xk / xkyk xk 0 xk 1¥»Ê· 2.8 () ©¥Â´n ¥³¬¯Ä©§»³ ç² () ⴠ¥§§¬¶2.1.2 ´¥¯¥¬³Å´¶³¶n¯£»§·Ê»Ân´¥³¬n©¤¥³¬¯Ä©§»³¬´£´¥Ï´´¥¯¥³¬n¯£»§Ænn©¤©¥¯¥³¬Ê·¬¥n´´¯³§¯¥¶¸£©·Â¯¥q¶ [13] ¥¹¯Ê·Â¥·¤©m´©¥¥©´©·Â¯¥q¶ ÅÊ··Ë²Ã¬©³ ¯¤´m ´¥¯¥¬³ ¯n £»§Ê· »Ân´¥¬³ n©¤¥³¬¯Ä©§»³ ³ m¯Æ·Ë³©¯¤m´Ê· 2.3 ¶´¥´©¥Ân´¥³¬¯Ä©§»³Å¥»Ê· 2.8 () ʸ£·Ã¢´ Â¥§§¶¬´£¥»Ê· ร ัหสเทอ รโบ2.8 () n´¬££º¶©m´§Ï´³n¯£»§ zk ¹¯¬Ê¶Ê·©¥¯¥³¬n¯´¥¯¥³¬n¯£»§ ¯¥³¬§Ï´³n¯£»§ zk = {11 01 10 11 00}©¶· Ï´ ´Ï Ån (u, q) ô¥Â§Ê·¤¬´²´¬´² u Ƭ´² q ç²Â£¥¶¬´´(branch metric) ¥²¤²Ê· k ¶¤´£Ä¤Sk u,q z 0 xk u,q 2 z 1 yk u,q 2 k kĤʷ xk u,q ç² yk u,q ¯¹ ¶ n¯£»§ xk ç² yk ʬ· ¯§n¯³´¥Â§Ê·¤¬´² (u, q) 2¯´·Ë´Ï ÅÂn £¥¶ ¬n´ (path metric) ¬´² q ʷ©§´ k + 1 ²¶¤´£Ä¤ บทที่ เลม 3 : การออกแบบวงจรภาครบั ขัน้ สงู 25 Volume III : Advanced Receiver Design
02 2 2 022 1 20 100 02\zk ^ 11 0020\xˆk ^ 1 01 10 11 ¶ ´ 00 0 11 0¥»Ê· 2.9 ⴠ¥§§¬¶ ì´¥´¥¯¥³¬n¯£§» zk = {11 01 10 11 00} 'k 1 q min \'k u Sk u ,q ^ u³³Ë³Ë ¯´¥¯¥³¬¯©¥¥©´©·Â¯¥q¬¶ ¥º Æn ³·Ë1) ¬´Ï ¥³Ã§m ²¥²¤²Ê· k¬Ï´¥³Ã§m ²¬´² qÏ´©´m´Â£¥¶¬´´ S u ,q ¯º ¬n¬´´Ê·£´¸ ¬´² q k§¹¯Â¬n ¬´´Ê£· ·´m £¥¶ ¬n ´n¯¤¬º¥³ ¥º ´m £¥¶Â¬n´¯¬´² q ʷ©§´ k + 1 ³Ê¹¯ 'k 1 q(Ï´´ÏË ¥º ¬´² q)(´Ï ´ÏË ¥º¥²¤²Ê· k)2) ¯¥¬³ ¯n £»§¯¶ º xk ´Â¬n´Ê£· ·Â£¥¶ ¬n´n¯¤¬º¥» Ê· 2.9 ì³Ë ¯´¥¯¥³¬¯n £§» ´£Ã¢´ Â¥§§¶¬ ʸ ²Ã¬Â ´²Â¬n ´Ê·¤³£··©¶ ¯¤m» (survivor path) Ê·£´¸Ãm§²¬´² Ĥm´Ê·¯¤»m¶³Ãm§²Â¬n¬´´¹¯m´Â£¥¶¬´´Sk u,q ʬ· ¯§¯n ³´¥Â§Ê¤· ¬´² (u, q) ³ËÈ Ã§²³©Â§Ê·¯¤»m¥Ä¯Ãm§²¬´²¹¯m´Â£¥¶ ¬n ´ 'k q ´¥»²Æn©m´©¥¯¥³¬¯Ä©§»³²Ånm´¥²£´¯¶n¯£»§¯¶ º xk ÂÉ xˆk \1, 0,1,1^ ¬Ï´¥³¥´¤§²Â¯·¤³Ë ¯´¥¯¥³¬n¯£»§¯©¥¥©´©Â· ¯¥q ¬¶ ´£´¥ª¸ «´ÆÅn Ê· 4 ¯ [10]26 การประมวลผลสญั ญาณสำหรับการจดั เก็บขอมลู ดิจทิ ัล Signal Processing for Digital Data Storage
¯¤´m Æ¥É ´£n´Ï´¥³¬¯Ä©§»³£´ÅnÂɬm©¥²¯Å¥³¬Â¯¥qÄ É²Æ£m¬´£´¥Ån©¥¥©´©Â· ¯¥q Ŷ ©¥¯¥¬³ ¯¥Äq Æn  ¥´²©¥¯¥¬³ ¯¥Äq Ï´´Ä¤Ånm´©¬´¥Ã¯¡q ¯¶¯n £§» ´m ³Ë (ém ¥¥©´©Â· ¯¥q¶²Ån§§³ qÂÉm´©¬´¥Ã°´¥q¥¹¯m´¥²£´¯¶n¯£»§) ³³Ë©¥¯¥³¬Â¯¥qÄÊ·Ån¯¥³¬n¯£»§Ê·»Ân´¥³¬n©¤¥³¬¯Ä©§» ³ ²n¯ÂÉ©¥¥©´Ê·¬¥´n ´¯³§¯¥¶¸£ BCJR [18] ¥¹¯ SOVA (soft-outputViterbi algorithm) [19] Âm´³Ë ʸ²¯¶´¤¯m ÆÅ©³ n¯Ê· 2.2 ç²Ê· 3 ´£§´Ï ³2.2 ¯§³ ¯¥¶£¸ BCJR ร ัหสเทอ รโบ©¥¥©´©·Â¯¥q¶ [1, 13] ¹¯©¥¥©´Ã©¥²Âɬ»¬º¥¹¯©¥¥©´Ã ML(maximum-likelihood) Ê·ÅnÅ´¥¯¥³¬n¯£»§Ê·»Ân´¥³¬n©¤¥³¬¯Ä©§»³ Ĥn¯£»§Â¯´q ºÊ·Æn²ÂÉ´m ¥²£´¯§Ï´³¯n £§» Ê·¯n ´¥¥©´ ¥¯¹ ¯´§m´©Æn©m´©¥¥©´Ã ML ²´Ï Ånn¯¶ §´¯§Ï´³ n¯£§» £·´m n¯¤¬º ÃÆm £Æm n¥³¥²³©m´¶n¯£»§Ãm§²¶Ê·¯¤»mŧ´Ï ³n¯£»§³ËÂɶn¯£»§Ê··Ê·¬º ³Ê¹¯©¥¥©´Ã ML Æ£mÆn´Ï Ån¶n¯£»§Ã§m ²¶£·n¯¶ §´n¯¤¬º ¯´·Ë©¥¥©´©Â· ¯¥q ¶Æ£¬m ´£´¥Ï´£´ÅnÅ¥²¯¥³¬n¯£»§Ã©Ï´Ë Æn ¥´²¥²·Ë²£·´¥Ã§Â§Ê·¤m´©¬´¥Ã¯¡q¥²©m´©¥¥©´Ã§²©¥¯¥³¬ÃnÆn¯¶ §´ ³³Ë¥²¯¥³¬n¯£»§Ã©Ï´Ë ²n¯Ån©¥¥©´©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶¬»¬º¥¹¯Â¥·¤©m´ “©¥¥©´Ã MAP (maximum a posteriori probability)”Ĥ©¥¥©´Ã MAP ¬´£´¥¥³¥²³Æn©m´¶n¯£»§Ãm§²¶Ê·¥©´ÆnÂɶn¯£»§Ê· ·Ê·¬º (¥¯¹ ¶ ¯n £»§Ãm§²¶ £· ¯n ¶ §´n¯¤¬º ) Ŭm©·Ë²¯¶´¤§³´¥Ï´´¯¯³§¯¥¶¸£ BCJR [18]  ¥´²Âɯ³§¯¥¶¸£Ê·ÅnÅ´¥¬¥´n ©¥¥©´Ã MAP ʸ¯³§¯¥¶¸£·ËÆn»¶nç² ³´Ë¸Ä¤ Bahl, Cock,Jelinek, ç² Raviv  ʹ¯ÅnÅ´¥¥©´m´©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶ (APP: a posterioriprobability) ¬»¬º¯¬³´Ê·m´m¯¬³´Ê·£·´¥Ã¥¬¯¥²©m´¬³§³«q (ISI)ç²£·¬³´¥©Â´¬q¬·´©Ã© (AWGN)2.2.1 ÃÏ´§¯¯m¯¬³´Ã§²Ã¢´ Â¥§§¶¬ 2 ¶´¥´ÃÏ´§¯¯m¯¬³´Å¥»Ê· 2.10 £ʹ¯¬³´Ê·©¥¢´¥³Æn¥³ (¥¹¯¬³´ บทท่ีÊ· ¯n ´¥¯¥¬³ ) §´Ï ³ Ê· k ¹¯ เลม 3 : การออกแบบวงจรภาครบั ข้นั สงู 27Volume III : Advanced Receiver Design
nk N 0,T2 ak H D rk O yk aihki nk i 0 ¥»Ê· 2.10 Ã´Ï §¯m¯¬³´ Zk u u Hk u,q Bk 1 q Zk 1 q B k Ck 1 q Ck u\ ^yl k k 1 \ ^yk L O 1yl 0 yl k yl k 1¥»Ê· 2.11 ´¥Â§Ê¤· ¬´² (u, q) Å¥²¤²Ê· k ¯Ã¢´ Â¥§§¬¶ O (2.4) yk aihki nk i 0£ʹ¯ ak A ¹¯n¯£»§¯¶ º¶Ê·»Â§¹¯£´´Â¯º³©¯³«¥ A (Âm ¥²Æ´¥·²ÆnA = {0, 1} ¥¹¯ {–1, 1}), H (D) O hk Dk ¹¯m¯¬³´Ê·Æ£mm¯Âʹ¯ (discrete k 0channel), hk ¹¯m´¬³£¥²¬¶¶Î ³©Ê· k ¯m¯¬³´, O ¹¯m©¤©´£Ï´¯m¯¬³´,nk ¹¯ AWGN Ê·£·m´Â§Ê·¤Âm´³ª»¤q粩´£Ã¥¥©Âm´³ V2 ¥¹¯Â·¤Ãn©¤ nk a Ư 0,T2 , rk ¹¯n¯£»§Â¯´q º¯m¯¬³´, ç² L ¹¯©´£¤´©¯§Ï´³n¯£»§¯¶ º{ak} Ĥ©³Ê Æn¯£§» ʸ¯¥q²£· L = 4096 ¶ n´¬££º¶©m´©¥¢´¬mÆnÏ´´¥¬m§Ï´³n¯£»§¯¶ º a = <a0 ,...,aL1> Ï´© L ¶ Ĥ¶n¯£»§Ãm§²¶£·m´Ê·ÂÉÆÆn¯¤m»¢´¤Å A ç²Æ£m£·´¥¬mn¯£»§ÅÈ Åm©Â©§´Ê· k < 0 ç² k > L – 1 ³³Ë´¬£´¥ (2.4)¬³´Ê©· ¥¢´¥³Æ¥n ³ ³Ë £Å¥» ¯Â©Â¯¥q¯¹ y \yl ^L O1 ¢ y0 , ..., yL O1 ¯± 0¥»Ê· 2.11 ìⴠ¥§§¶¬¯m¯¬³´ hk £ʹ¯ Zk w <ak1,ak2 ,...,akO >¹¯¬´² (state) ©§´ k (¥¹¯m´Ê·¯¤»mÅÂ¥¶¬Â¯¥qçʹ¯³Ë £ ©§´ k), Q A O28 การประมวลผลสัญญาณสำหรับการจัดเกบ็ ขอมลู ดิจทิ ลั Signal Processing for Digital Data Storage
¹¯Ï´©¬´²³Ë £Ê·ÂÉÆÆn, ¥²¤²Ê· k (k-th stage) ¹¯§mº£¯Â¬n¬´´ (branch) Ê·ÂÉÆÆn³Ë £¥²©m´Â©§´ k ç²Â©§´ k + 1, ç² (u, q) ¹¯¬³§³«qÊ·Ånô¥Â§Ê·¤¬´² (transition) ´¬´² u Ƥ³ ¬´² q ´n Ån¬´²Ãm§²¬´²¯¹ ¬´² 0 ¸¬´²Q – 1 Ĥʷ¬´² 0 ¥¯¹ Zk w <0, 0,..., 0> ²Ånì´²©´m §´m (idle state) ¬´Ï ¥³ k d 0ç² k t L + Q – 1 ³³Ë¯´§m´©Æn©m´¥»Ê· 2.11 쥲¤²Ê· k ¯Ã¢´ Â¥§§¶¬Ê¸¬¯§n¯³¶ n¯£§» ¯¶ º§Ï´³Ê· k (¥¹¯ ak), n¯£»§Â¯´q º¯m¯¬³´§Ï´³Ê· k (¥¹¯rk), 粯n £»§Ê·©¥¢´¥³Æ¥n ³§´Ï ³Ê· k (¥¹¯ yk)2.2.2 ©¥¥©´Â£´²Ê·¬ºÅ´¶³¶©¥¥©´Ã MAP ¹¯©m´ÂÉ©¥¥©´Â£´²Ê·¬º (optimal detector) ¥´²ÂÉ©¥¥©´n¯£»§Ê¬· ´£´¥¥³ ¥²³Æ©n ´m ©´£m´²Âɯn¯¶ §´¯¶n¯£»§Ãm§²¶ £·´m n¯¤¬º ©³ ¯¤m´Âm Å´¥³ ¬¶ Ŷn¯£»§§Ï´³Ê· k (¥¹¯ ak) ©¥¥©´ÃMAP ²Ï´©´m´©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶ (APP) ¥¹¯ Pr<ak | y> ʸ£´¤¸m´©´£m´²Âɯ¶ n¯£»§ ak £ʹ¯Ï´§Ï´³n¯£»§ y £´Ån ¬Ï´¥³Ãm§²¶n¯£»§ ak ´³Ë²Â§¹¯m´ ak Ê· ´Ï Ån Pr<ak | y> £·m´¬»¬º ©¥¥©´Ã MAP ²Ï´Â¶´¥§³«²·ËÆ¥ʹ¯¤È ¥n¯£»§ L ¶ Å´¶³¶m´ Pr<ak | y> Ï´©ÆnĤm´¤ n´¥´m´©´£m´²Âɯ´¥Â§Ê¤· ¬´²Ã¯²Ä ¬Â¯¥¶¯¯¥¶ Pr ¢ Zk u; Zk 1 q | y¯± ¬Ï´¥³º´¥Â§Ê·¤¬´² (u, q) Åⴠ¥§§¬¶ ¯³§¯¥¶¸£ BCJR ¯¹ ÂÉ³Ë ¯©¶·Ê·£·¥²¬¶¶¢´ £´Å´¥´m´©´£m´²Âɯ´¥Â§·Ê¤¬´²Ã¯²Ä ¬Â¯¥¶¯¯¥¶ ʸϴÆnm´¤Ä¤´¥³¥» Pr ¢ Zk u; Zk 1 q | y¯±¬Ï´¥³ ´¥Â§Ê·¤¬´² ©§´ k ¯¯ÂÉ 3 ¬©m ³·Ë1) ¬©m Ê· ʸ¸Ë ¯¤»m³¯n £»§Ê·Æn¥³ ³Ë £Å¯· ³Ê¯¹ yl k \yl ; l k^ \yl ^k012) ¬m©Ê¬· ¯Ë¸¯¤m» ³¯n £§» ÊÆ· ¥n ³ ųº³ ³Ê¯¹ yk3) ¬m©Ê¬· ´£¸Ë¯¤m» ³ ¯n £§» Ê·Æ¥n ³ ³Ë £Å¯´ ³Ê¯¹ yl k \yl ; l k^ \yl ^L O1 k 1 ร ัหสเทอ รโบ ´¯Â¬q (Bayes’ rule) m´ Pr ¢ Zk u; Zk 1 q | y±¯ ³ ¥»Å£Æm nÂÉ Pr ¢ Zk u; Zk 1 q | y¯± p Zk u; Zk 1 q; y / p y 2 p Zk u; Zk 1 q; yl k ; yk ; yl k / p y บทท่ี p yl k |Zk u; Zk 1 q; yl k ;yk p Zk u; Zk 1 q; yl k ;yk / p y (2.5) เลม 3 : การออกแบบวงจรภาครับขน้ั สูง 29 Volume III : Advanced Receiver Design
£ʹ¯ p x ¹¯¡³q³©´£´Ãm©´£m´²ÂÉ (pdf: probability density function) ¯ x´º¬£³¶¯£´¥q¯¡ (Markov property) [4] ¯ÃÏ´§¯Â¥Ê¹¯¬´²Ï´³Ê¸§m´©©m´¬Ï´¥³m¯¬³´ÅÈ m´©¬´¥ÂÊ·¤©³n¯£»§¯¬´²Ê·Â©§´ k + 1 ²Ân´£´ÃÊ·m´©¬´¥Âʤ· ©³n¯£»§¯¬´²Ê· ©§´ k ¥©£³Ë ´m yk ç² yl k ³³Ë¬£´¥ (2.5) §¥» ÆÂn É Pr ¢Zk u; Zk 1 q | y±¯ p yl k |Zk 1 qp Zk u; Zk 1 q; yl k ;yk / p y p yl k |Zk 1 qp Zk 1 q;yk | Zk u; yl k p Zk u; yl k / p y (2.6) ÅÏ´¯Â¤· ©³ ¯´ª³¤º¬£³ ¶ ¯£´¥q ¯¡Â ʹ¯³ ¥» ¬£´¥ (2.6) É ²ÆÂn ÉPr ¢Zk u; Zk 1 q|y¯± p Zk u; yl k p Zk 1 q;yk | Zk up yl k |Zk 1 q p y Bk uqHk u,qqCk 1 q / p y (2.7)ʸ ²ÂÉÆn©´m ´¥´£Â¶ ¯¥q Bk u ¹¯m´©´£m´²Âɬ´Ï ¥³¬´² u ©§´ k ʸ˸¯¤m»³n¯£»§Ê·Æn¥³Å¯· yl k , ´¥´£¶Â¯¥q Ck 1 q ¹¯m´©´£m´²Âɬϴ¥³¬´² q ©§´k + 1 ʸ¸Ë¯¤»m³n¯£»§Ê·Æn¥³Å¯´ rl!k , ç² ´¥´£¶Â¯¥q Hk u,q ¹¯m´©´£m´²Âɯ´¥Â§Ê·¤¬´²´¬´² u ©§´ k Ƥ³¬´² q ©§´ k + 1 ʸ¸Ë¯¤m»³n¯£»§Å³º ³ yk ( » ´¥´£¶Â¯¥qm´È Å¥»Ê· 2.11) Ĥ³©Ê Æ ´¥´£¶Â¯¥q Bk u ç² Ck 1 q Â¥·¤©m´Â£¥¶ ¬´² (state metric) ç² ´¥´£Â¶ ¯¥q Hk u,q Â¥¤· ©´m £¥¶¬´´ (branch metric) n´Ï´Ån Sa ¯¹ ¯´¥Â§Ê·¤¬´² (u, q) Ê·ÂÉÆÆn³Ë £Ê·¬¯§n¯³¶ ¯n £»§ a ³³Ë´m ©´£m´²Âɯ²Ä ¬Â¯¥¯¶ ¯¥¶ Pr<ak a | y> ´Æn ´ Pr<ak a | y> Pr ¢Zk u; Zk 1 q | y¯± u ,q Sa 1 p y u,qSa Bk u Hk u ,q Ck 1 q (2.8)¬£´¥ (2.8) ´Æn m´¤ £ʹ¯¥´´m Bk u , Hk u,q ç² Ck 1 q ¬Ï´¥³º´¥Â§Ê·¤¬´² u,q 粺 ¥²¤²Ê· k30 การประมวลผลสัญญาณสำหรบั การจัดเก็บขอ มลู ดิจทิ ลั Signal Processing for Digital Data Storage
2.2.3 ´¥´Ï ©´´m ´¥´£¶Â¯¥q¯¯³§¯¥¶£¸ BCJR ´¥´£¶Â¯¥q¯¯³§¯¥¶¸£ BCJR ´£¬£´¥ (2.8) ³Ê¹¯ Hk u,q , Bk u , Ck 1 q ç²p y ¬´£´¥´Ï ©´Æn³·Ë´¥´´m £¥¶¬´´ Hk u,q ¬´Ï ¥³ m¯¬³´ AWGN¯³§¯¥¶¸£ BCJR ²Ãm´´¯³§¯¥¶¸£©·Â¯¥q¶ [13] ¥Ê·©m´¯³§¯¥¶¸£ BCJR ²Ï´´¥´Ï ©¬¯Â¬n ´¹¯1) ¬n´´n n´ (forward pass) Ĥ¥ʶ£Ï´©m´m´È ³Ë Ãmn¯£»§Ê·Æn¥³³©Ã¥Æn´n´ ¸¯n £»§³©¬º´n ¤2) ¬n´¤n¯§³ (backward pass) Ĥ¥¶Ê£Ï´©m´m´È ³Ë Ãmn¯£»§Ê·Æn¥³³©¬ºn´¤ ¤n¯§³£´¸ n¯£§» ³©Ã¥ ¯´·Ë£¥¶ ¬´´¯¯§³ ¯¥¶£¸ BCJR ´Ï ©Æn ´Hk u,q p Zk 1 q; yk | Zk u p yk | Zk u; Zk 1 qp Zk 1 q | Zk u (2.9) ¬Ï´¥³m¯¬³´Ã AWGN ¬³´·ÊÆn¥³¹¯ yk rk nk £ʹ¯ nk ~ Ư 0,T2 ¹¯¬³´¥©Â´¬q¬·´©Ã© n´Ï´Ån aˆ u,q ç² rˆ u,q ¹¯¶n¯£»§¯¶ ºÃ§²n¯£»§Â¯´q º¯m¯¬³´Ê·¬¯§n¯³´¥Â§Ê·¤¬´² u,q ´£§Ï´³ ³³Ë qÃ¥´©´£¹¯¯¬£´¥ (2.9) £·m´Âm´³p yk | Zk u; Zk 1 q 1 exp ¦¥£¦¦¤ 1 yk rˆ u,q 2»¦¦¦¼² (2.10) 2QT2 2T2£ʯ¹ exp(.) ¹¯¡³q³Â§·Ë Ï´§³ (exponential function) ç² qÊ·¬¯´©´£¹¯¯¬£´¥ ร ัหสเทอ รโบ(2.9) ¹¯ 2 p Zk 1 q | Zk u p ak aˆ u,q; Zk u / p Zk u บทที่ p Zk u | ak aˆ u,qp ak aˆ u,q / p Zk u เลม 3 : การออกแบบวงจรภาครับข้ันสงู 31 Volume III : Advanced Receiver Design
p Zk up ak aˆ u,q / p Zk u (2.11) p ak aˆ u,qÅ´¶³¶m´©´£m´²ÂÉŬ£´¥ (2.11) ²Â¥·¤©m´©´£m´²Âɯ² ¶¥¶¯¯¥¶ (a prioriprobability) ¯¶n¯£»§ ak ´³ËÃm´¬£´¥ (2.10) ç² (2.11) §Å¬£´¥ (2.9) ²Æn©´m £¥¶¬´´¯¯§³ ¯¥¶¸£ BCJR £·m´Âm´³ Hk u,q 1 exp ¦¦¤¥¦£ 1 yk rˆ u,q 2¦¦²¼»¦qp ak aˆ u,q (2.12) 2QT2 2T2ʸ² ©m´Â£¥¶¬´´¯¯³§¯¥¶¸£ BCJR £· q p ak aˆ u,q  ʶ£Ë¸£´´Â£¥¶¬´´¯¯³§¯¥¶¸£©·Â¯¥q¶ [4] Å¥·Ê·¶n¯£»§ ak º³©£·Ä¯´¬Â¶¸ËÂm´³ m´©´£m´²Âɯ² ¶¥¶¯¯¥¶ p ak a ²ÂÉm´©³ Ê·Æ£m˸ ³´m a ³ ³ËÅ¥··Ë£¥¶ ¬´´¯¯§³ ¯¥¶ £¸BCJR ²£·m´Âm´³Â£¥¶¬´´¯¯³§¯¥¶¸£©·Â¯¥q¶ ¯¤m´Æ¥É´£Å¥·Ê·¶n¯£»§ ak Ãm§²³©£·Ä¯´¬Â¶¸ËÆ£mÂm´³  ¥´²²³Ë´n ¥´¯n £»§ÂÊ·¤©³ ak çm ²©³ §©m n´ ɲm©¤´Ï Ån ´¥¯¥³¬n¯£§» £· ©´£» ¯n £´¤Ê¶Ë¸´¥´´m £¥¶¬´² Bk u ç² Ck 1 q£¥¶¬´² Bk u ç² Ck 1 q Ŭ£´¥ (2.7) Ï´©´Ænm´¤Ä¤¯´ª³¤º¬£³¶¯£´¥q¯¡Ã§²Â¶Â©·¤Â¶ (recursive) ³ ·Ë ´¬£´¥ (2.7) ²Æn©´m Bk u p Zk u; yl k (2.13)³³Ë Bk 1 q p Zk 1 q; yl k 1 p Zk 1 q; yk ; yl k Q1 p Zk 1 q; yk ; Zk u; yl k u 0 Q1 p Zk 1 q; yk | Zk u; yl k p Zk u; yl k u 032 การประมวลผลสญั ญาณสำหรบั การจัดเก็บขอมูลดจิ ิทลั Signal Processing for Digital Data Storage
Q1 (2.14) p Zk 1 q; yk | Zk up Zk u; yl k u 0 Q1 Hk u,qBk u u 0 Å´Ï ¯Â¤· ©³ ´¬£´¥ (2.7) ²Æn©´m Ck 1 q p yl k | Zk 1 q (2.15)³ ³Ë Ck u p yl k1 | Zk u p yl k ; yk | Zk u Q1 p yl k ; yk ; Zk 1 q | Zk u q 0 Q1 p yl k |yk ; Zk 1 q; Zk up yk ; Zk 1 q | Zk u q 0 Q1 p yl k | Zk 1 qp yk ; Zk 1 q | Zk u q 0 Q1 (2.16) Ck 1 qHk u,q q 0´¥Ï´Âʯ¹ Æ¥ʶ£n ¯ Bk u ç² Ck 1 q ร ัหสเทอ รโบ¯³§¯¥¶¸£ BCJR Ê·¯¶´¤Å³©n¯·Ë²¬££º¶©m´¬£´¥ (2.15) ç² (2.16) ¥ʶ£Ï´´¥Ï´©Ä¤ÅÂn ʹ¯Æ¥ʣ¶ n (initial condition) ¯Â£¥¶¬´² Bk u ç² Ck 1 q ³ ·Ë B0 u ¥£¦¦¤¦¦10,, u 0 ç² CL O q £¦¦¥¦¤¦10,, q 0 (2.17) 2 else else บทที่ เลม 3 : การออกแบบวงจรภาครบั ขั้นสงู 33 Volume III : Advanced Receiver Design
ʸÅn³¥·Ê·ºÂ¬n¬´´ (branch) Åⴠ¥§§¶¬Â¥Ê¶£nÊ·¬´² Z0 0 ç²£·´¥³ ³Ån º ¬n¬´´Åⴠ¥§§¶¬¬¶Ë ¬ºÊ·¬´² ZL O 0 ³Ê¹¯ºÂ¬n¬´´Åm©´¥Â©·¤Â¶ ôn n´ (forward recursion) n¯¬¶Ë ¬ºÊ·¬´² ZL O 0 粺¬n¬´´Å©m ´¥Â©·¤Â¶ än¯§³ (backward recursion) n¯¬¶Ë ¬ºÊ¬· ´² Z0 0 ¯¤m´Æ¥É ´£Å ¥· Ê·Æ£m£· ´¥ ³ ³ Å n º ¬n ¬ ´ ´Å à ¢ ´  ¥§ §¶¬ ¬¶Ë ¬º Ê·¬´² ZL O 0 ɶ¤£Ï´Ånm´Â¥Ê¶£n¯Â£¥¶¬´² CL O q £·m´Âm´³Â£¥¶¬´² BL O q ³Ê¯¹ CL O q BL O q (2.18)¬Ï´¥³º¬´² q {0, 1, …, Q – 1}  ¥´²¯³§¯¥¶¸£ BCJR Æ£m£·©´£¥n»ÂÊ·¤©³n¯£»§©´£m´²Âɯçm ²¬´² ©§´ L O´¥´´m p yÅ´¶³¶m´ p y Ê·ÅnÅ´¥Ï´©´m´©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶ Pr<ak | y> ´£¬£´¥ (2.8) ¬´£´¥§²¶Ë Æn Âʹ¯´ p y £·m´Ê·¬Ï´¥³ºÂ©§´ k ³³Ë¥²©´¥´m´¬»¬º¯ Pr<ak | y> ¸¤³ Ån §§ ³ q´m £¶ ¯¤´m ƥɴ£ÅÊ··Ë²Ã¬©¶·´m´ p y³·Ë Âʹ¯´§¥©£¯©´£m´²ÂÉã·Âʹ¯Æ¯ºÂº´¥qn¯£·m´Âm´³Ê¸Â¬£¯ ³³Ë´¬£´¥ (2.7) ²Æ©n m´ Q1Q1 ¢Zk q|y¯± Q1 Q1 Bk u Hk u,q Ck 1 q ¬® q 0 u 0 q 0 p y u 0 Pr u; Zk 1 1 (2.19)³Ê¯¹ p y Q1 Q1 Bk uHk u,qCk 1 q (2.20) u 0 q 0´¬£´¥ (2.16) ²Æ©n m´ Q1 (2.21) p y Bk uCk u u 034 การประมวลผลสญั ญาณสำหรบั การจดั เกบ็ ขอมูลดจิ ทิ ลั Signal Processing for Digital Data Storage
¬£´¥ (2.21) ìÅÂn É©m´§»¯m´ Bk u ç² Ck u ¯º¬´² u ¢´¤Åⴠ¥§§¬¶ ²£·´m Âm´³ºÂ©§´ k ʸ £· m´Âm´³ m´ p y  ¥´²²³Ë´¬£´¥ (2.17) Ï´ÅnÆn©´£¬£³ ³ q©m´ p y C0 0 BL O 0 (2.22)2.2.4 ¯³§¯¥¶£¸ BCJR ¬Ï´¥³¶ n¯£§» ÃÆ´¥·Å¥·Ê·¶n¯£»§¯¶ ºÂÉÃÆ´¥· ³Ê¹¯ ak \1,1^ m´©´£m´²Âɯ²Ä ¬Â¯¥¶¯¯¥¶Pr<ak a | y> Ŭ£´¥ (2.8) ²» Ï´n©¤´m Pr<ak 1 | y> 1 Pr<ak 1 | y> ¥¹¯´m ¯³ ¥´¬m© Pr<ak 1 | y> / Pr<ak 1 | y> ʸÅÄ£§¯´¥¶ ¸£ (logarithm domain) ·¤ÆÂn É M p ak ln Pr<ak 1 | y> >¬® (2.23) Pr<ak 1 |y£ʯ¹ Mp ak ¯¹ m´ LLR ï²Ä ¬Â¯¥¶¯¯¥¶¯¶ n¯£»§ ak ³³Ë´¬£´¥ (2.8) ²Æn©m´ Mp ak ln uu,q,qSS11BBkk uuHHkk uu,,qqCCkk 11 qq¬® (2.24) ¯³§¯¥¶ £¸ BCJR ¬Ï´¥³¶n¯£§» ÃÆ´¥·²Ån¬£´¥ (2.24) Å´¥Ï´©´m´LLR ¬Ï´¥³ çm ²¶¯n £»§Ê¬· m £´´©¥¢´¬m ʸm´ Mp ak ²»Ï´£´ÅnÅ´¥³¬¶Å´´m ¥²£´¯¶ ¯n £»§ ak Ê· Ï´Ån ©´£m´²Âɯn¯¶ §´£·m´n¯¤¬º Ĥ¯´ª³¤´¥³¬¶ ų ·Ë aˆk ¦£¥¦¦¦¤1, 1, if Mp ak p 0 (2.25) ร ัหสเทอ รโบ if Mp ak 0 ¯´·Ëm´©´£m´²Âɯ² ¶¥¯¶ ¯¥¶ p ak a ¬´Ï ¥³ a \o1^ ¤³£·©´£¬³£ ³q³¡³q ³ ©¥²ÂÉ篴¥¶ £¸ ³·Ë (»¬£´¥ (1.6)) p ak a exp Ma exp aMa ak / 2 ak / 2 (2.26) 2 ak / 2 exp Ma บทที่ เลม 3 : การออกแบบวงจรภาครับข้นั สงู 35 Volume III : Advanced Receiver Design
£ʯ¹ Ma ak lnpp a akk 11¬® (2.27)¯¹ m´ LLR ï² ¥¶ ¯¶ ¯¥¶ ¯¶n¯£»§ ak ¯¤´m ƥɴ£Âʹ¯´©³ ¬m©Å¬£´¥ (2.26) £·m´Â´m ³ ¬Ï´¥³º ´¥Â§Ê¤· ¬´² (u, q) Åⴠ¥§§¶¬ ³³Ë¸¬´£´¥Ånm´©´£m´²Âɯ² ¶¥¶¯¯¥¶ p ak a expaMa2 ak ®¬ (2.28)Å´¥´´m £¥¶¬´´¯¯³§¯¥¶ £¸ BCJR Ŭ£´¥ (2.12) Æn ³Ê¹¯ Hk u,q 1 exp ¦£¤¦¦¥ 1 yk rˆ u ,q 2 ²¦¦»¦¼qexp aˆ u,q Ma ak ¬® (2.29) 2QT2 2T2 22.2.5 ¬¥º ³Ë ¯´¥Ï´´¯¯§³ ¯¥¶ £¸ BCJR§³´¥Ï´´¯¯³§¯¥¶ ¸£ BCJR ¬¥º ÂÉ³Ë ¯m´È Æn´£¥» Ê· 2.122.2.6 n¯¬³ ¯¯§³ ¯¥¶ £¸ BCJR´¥Ï´¯³§¯¥¶¸£ BCJR Ê·¯¶´¤Å¥»Ê· 2.12 ÆÅn´¥¶Å´¶³¶ Ï´Âɲn¯Ï´´¥¯¥q£¯§Æ§Â³ (normalization) [22] m´Â£¥¶¬´² Bk u ç² Ck u ¬Ï´¥³º¬´²u 粺©§´ k  ʹ¯§·Â§Ê·¤³´Â¥Ê¹¯n¯¤Â¶Âɶ³©Â§ (numerical underflow) Åĥ壯£ ¶©Â¯¥q §m´©¹¯ÅÃm§²Â©§´ k Ê·Ï´´¥Ï´©´m´ Bk u ç² Ck u £ʹ¯Æn m´ Bk u ç² Ck u ´£¬£´¥ (2.14) ç² (2.16) ¬Ï´¥³º¬´² u çn© ÉÅnÏ´´¥¯¥£q ¯§Æ§Â³ m´Â£¥¶¬´²³Ë ¬¯´£©´£¬³£ ³ q³ ·Ë Bk u Bk u Ck u Ck u (2.30) i Bk i ç² i Ck i ʯ¹ Ån §¥©£¯ Bk u ¬´Ï ¥³º u £· ´m ´m ³ ʸ ç²Ån §¥©£¯ Ck u ¬´Ï ¥³ º u£· m´Âm´³ ʸ ´³Ë¸Â¥Ê£¶ Ï´©´´m Bk u ç² Ck u Å©§´ k ³ Æ36 การประมวลผลสัญญาณสำหรับการจัดเก็บขอมูลดจิ ิทัล Signal Processing for Digital Data Storage
¯§³ ¯¥¶¸£ BCJR1. ´Ï ´m ¥ʣ¶ n £¥¶ ¬´² ¢ B0 0,B0 1,!,B0 Q 1¯± <1, 0,!, 0>2. ´¥Â©·¤Â¶ Ãn´n´ (forward recursion) ¬Ï´¥³ k 0,1,!, L O 1 ¬Ï´¥³ q 0,1,!,Q 1 Ï´©´m´ Hk u,q ´£¬£´¥ (2.29) ¬Ï´¥³ º u Ê·´Ï Ån (u, q) ÂÉ¥¶ Ï´©´m´ Bk 1 q ´£¬£´¥ (2.14) (¬¶Ë ¬º ´¥©Ï´Ë ¯ q) (¬¶Ë ¬º´¥©´ÏË ¯ k)3. Ï´m´Â¥Ê¶£n£¥¶ ¬´²6 ¢ CL O 0, CL O 1,!, CL O Q 1±¯ <1, 0,!, 0>4. ´¥Â©·¤Â¶ än¯§³ (backward recursion) ¬´Ï ¥³ k L O 1, L O 2,!, 0 ¬Ï´¥³ u 0,1,!,Q 1 Ï´©7´m´ Hk u,q ´£¬£´¥ (2.29) ¬´Ï ¥³ º q Ê·´Ï Ån (u, q) ÂÉ¥¶ ´Ï ©´m´ Ck u ´£¬£´¥ (2.16) (¬¶Ë ¬º´¥©´ÏË ¯ u) ´Ï ©´m´ Mp ak ´£¬£´¥ (2.24) ³¬¶ Å´m´ ak ´£¬£´¥ (2.25) (¬¶Ë ¬º´¥©Ï´Ë ¯ k)¥»Ê· 2.12 ³Ë ¯´¥Ï´´¯¯³§¯¥¶ ¸£ BCJR ¸Ã£n©m´©¥¥©´Ã MAP Ê·Ån¯³§¯¥¶¸£ BCJR ²ÂÉ©¥¥©´Â£´²Ê·¬º ร ัหสเทอ รโบ ¥´²¬´£´¥¥³¥²³Æn©m´¶n¯£»§Ãm§²¶²£·n¯¶ §´n¯¤¬º ¯¤m´Æ¥É´£Å´¶³¶6 £ʹ¯¬££¶©´m £·´¥³ ³ÅnºÂ¬n ¬´´Åⴠ¥§§¶¬¬¶Ë ¬ºÊ¬· ´² ZL O 0 £¶ ²³Ëç©n n¯Ï´ 2 ´m ¥ʶ£n¯ CL O q ´£¬£´¥ (2.18) บทที่7 ´m £¥¶¬´´ Hk u,q Ê· Ï´©ÆÅn m©´¥Â©¤· ¶än¯§³ ²£· m´Âm´³ m´Â£¥¶ ¬´´Ê· ´Ï ©ÆnÅ m©´¥Â©·¤Â¶ ôn n´ ÃmÊ·Ï´´¥Ï´©m´Â£¥¶¬´´Å£¯m · ¥³Ë Åm©´¥Â©·¤Â¶Ã¤n¯§³ É ʹ¯ §Ï´©m©¤©´£´Ï (memory) Ê·¯n ÅÅn ´¥ÂÉm´Â£¥¶¬´´Åm©´¥Â©·¤Â¶Ã´n n´ เลม 3 : การออกแบบวงจรภาครับขั้นสูง 37Volume III : Advanced Receiver Design
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