Knowledge (XXG)

BCJR algorithm

Source 📝

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Bahl, L.; Cocke, J.; Jelinek, F.; Raviv, J. (March 1974). "Optimal Decoding of Linear Codes for minimizing symbol error rate".
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and Raviv. This algorithm is critical to modern iteratively-decoded error-correcting codes, including
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The online textbook: Information Theory, Inference, and Learning Algorithms
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The implementation of BCJR algorithm in Susa signal processing framework
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Compute smoothed probabilities based on other information (i.e.
152: 43:). The algorithm is named after its inventors: Bahl, Cocke, 386: 169: 196: 99: 77: 145:Berrou, Glavieux and Thitimajshima simplification. 105: 83: 310:Robertson, P.; Hoeher, P.; Villebrun, E. (1997). 406: 352:, discusses the BCJR algorithm in chapter 25. 8: 275:EURASIP Journal on Applied Signal Processing 316:European Transactions on Telecommunications 413: 399: 269:Wang, Sichun; Patenaude, François (2006). 327: 294: 98: 76: 21:Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm 199:framework implements BCJR algorithm for 244:IEEE Transactions on Information Theory 234: 203:codes and channel equalization in C++. 219:Maximum a posteriori (MAP) estimation 7: 437:Algorithms and data structures stubs 363: 361: 385:. You can help Knowledge (XXG) by 14: 365: 156: 93:Compute backward probabilities 432:Error detection and correction 71:Compute forward probabilities 53:low-density parity-check codes 1: 453: 360: 214:Forward-backward algorithm 16:Error correction algorithm 125:bit crossover probability 256:10.1109/TIT.1974.1055186 201:forward error correction 129:binary symmetric channel 84:{\displaystyle \alpha } 381:-related article is a 329:10.1002/ett.4460080202 296:10.1155/ASP/2006/95360 107: 106:{\displaystyle \beta } 85: 33:error correcting codes 108: 86: 97: 75: 29:maximum a posteriori 287:2006EJASP2006..242W 224:Hidden Markov model 41:convolutional codes 168:. You can help by 103: 81: 394: 393: 350:David J.C. MacKay 186: 185: 444: 415: 408: 401: 369: 362: 334: 333: 331: 307: 301: 300: 298: 266: 260: 259: 239: 181: 178: 160: 153: 112: 110: 109: 104: 90: 88: 87: 82: 452: 451: 447: 446: 445: 443: 442: 441: 422: 421: 420: 419: 379:data structures 342: 337: 309: 308: 304: 268: 267: 263: 241: 240: 236: 232: 210: 193: 191:Implementations 182: 176: 173: 166:needs expansion 151: 143: 138: 95: 94: 73: 72: 61: 17: 12: 11: 5: 450: 448: 440: 439: 434: 424: 423: 418: 417: 410: 403: 395: 392: 391: 370: 359: 358: 353: 341: 340:External links 338: 336: 335: 322:(2): 119–125. 302: 261: 233: 231: 228: 227: 226: 221: 216: 209: 206: 205: 204: 192: 189: 184: 183: 177:September 2022 163: 161: 150: 147: 142: 139: 137: 134: 133: 132: 117:noise variance 113: 102: 91: 80: 60: 59:Steps involved 57: 15: 13: 10: 9: 6: 4: 3: 2: 449: 438: 435: 433: 430: 429: 427: 416: 411: 409: 404: 402: 397: 396: 390: 388: 384: 380: 376: 371: 368: 364: 357: 354: 351: 347: 344: 343: 339: 330: 325: 321: 317: 313: 306: 303: 297: 292: 288: 284: 280: 276: 272: 265: 262: 257: 253: 249: 245: 238: 235: 229: 225: 222: 220: 217: 215: 212: 211: 207: 202: 198: 195: 194: 190: 188: 180: 171: 167: 164:This section 162: 159: 155: 154: 148: 146: 140: 135: 130: 126: 122: 118: 114: 100: 92: 78: 70: 69: 68: 66: 63:Based on the 58: 56: 54: 50: 46: 42: 39:(principally 38: 34: 30: 26: 22: 387:expanding it 372: 319: 315: 305: 278: 274: 264: 250:(2): 284–7. 247: 243: 237: 187: 174: 170:adding to it 165: 149:Log-Map BCJR 144: 62: 31:decoding of 20: 18: 49:turbo codes 35:defined on 426:Categories 375:algorithms 230:References 136:Variations 281:: 95360. 141:SBGT BCJR 101:β 79:α 37:trellises 25:algorithm 208:See also 283:Bibcode 65:trellis 45:Jelinek 23:is an 373:This 348:, by 383:stub 279:2006 197:Susa 127:for 121:AWGN 119:for 51:and 27:for 19:The 377:or 324:doi 291:doi 252:doi 172:. 428:: 318:. 314:. 289:. 277:. 273:. 248:20 246:. 123:, 67:: 55:. 414:e 407:t 400:v 389:. 332:. 326:: 320:8 299:. 293:: 285:: 258:. 254:: 179:) 175:( 131:)

Index

algorithm
maximum a posteriori
error correcting codes
trellises
convolutional codes
Jelinek
turbo codes
low-density parity-check codes
trellis
noise variance
AWGN
bit crossover probability
binary symmetric channel

adding to it
Susa
forward error correction
Forward-backward algorithm
Maximum a posteriori (MAP) estimation
Hidden Markov model
doi
10.1109/TIT.1974.1055186
"A Systematic Approach to Modified BCJR MAP Algorithms for Convolutional Codes"
Bibcode
2006EJASP2006..242W
doi
10.1155/ASP/2006/95360
"Optimal and Sub-Optimal Maximum A Posteriori Algorithms Suitable for Turbo Decoding"
doi
10.1002/ett.4460080202

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