| Preface |
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xi | |
| Acknowledgement |
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| 1 Introduction |
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1 | (48) |
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1 | (7) |
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8 | (13) |
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21 | (7) |
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1.4 A first encounter with convolutional codes |
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28 | (7) |
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1.5 Block codes versus convolutional codes |
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35 | (1) |
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1.6 Capacity limits and potential coding gain revisited |
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36 | (3) |
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39 | (2) |
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41 | (8) |
| 2 Convolutional encoders-Structural properties |
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49 | (112) |
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2.1 Convolutional codes and their encoders |
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49 | (9) |
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2.2 The Smith form of polynomial convolutional generator matrices |
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58 | (9) |
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67 | (9) |
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2.4 Encoder and code equivalences |
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76 | (3) |
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2.5 Basic encoding matrices |
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79 | (3) |
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2.6 Minimal-basic encoding matrices |
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82 | (8) |
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2.7 Minimal encoding matrices and minimal encoders |
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90 | (19) |
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2.8 Canonical encoding matrices |
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109 | (18) |
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2.9 Minimality via the invariant-factor theorem |
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127 | (4) |
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2.10 Syndrome formers and dual encoders |
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131 | (8) |
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2.11 Systematic convolutional encoders |
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139 | (11) |
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2.12 Some properties of generator matrices-an overview |
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150 | (1) |
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150 | (2) |
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152 | (9) |
| 3 Distance properties of convolutional codes |
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161 | (64) |
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3.1 Distance measures-a first encounter |
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161 | (10) |
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171 | (8) |
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3.3 Properties of convolutional codes via the active distances |
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179 | (2) |
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3.4 Lower bound on the distance profile |
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181 | (5) |
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3.5 Upper bounds on the free distance |
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186 | (5) |
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3.6 Time-varying convolutional codes |
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191 | (4) |
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3.7 Lower bound on the free distance |
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195 | (5) |
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3.8 Lower bounds on the active distances |
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200 | (7) |
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3.9 Distances of cascaded concatenated codes |
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207 | (6) |
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213 | (7) |
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220 | (1) |
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221 | (4) |
| 4 Decoding of convolutional codes |
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225 | (108) |
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4.1 The Viterbi algorithm revisited |
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226 | (9) |
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4.2 Error bounds for time-invariant convolutional codes |
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235 | (15) |
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4.3 Tighter error bounds for time-invariant convolutional codes |
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250 | (5) |
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4.4 Exact bit error probability for Viterbi decoding |
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255 | (16) |
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4.5 The BCJR algorithm for APP decoding |
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271 | (12) |
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4.6 The one-way algorithm for APP decoding |
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283 | (5) |
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4.7 A simple upper bound on the bit error probability for extremely noisy channels |
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288 | (5) |
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293 | (9) |
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4.9 Decoding of tailbiting codes |
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302 | (6) |
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4.10 BEAST decoding of tailbiting codes |
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308 | (15) |
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323 | (1) |
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324 | (9) |
| 5 Random ensemble bounds for decoding error probability |
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333 | (54) |
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5.1 Upper bounds on the output error burst lengths |
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333 | (12) |
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5.2 Bounds for periodically time-varying convolutional codes |
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345 | (10) |
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5.3 Lower error probability bounds for convolutional codes |
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355 | (8) |
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5.4 General bounds for time-varying convolutional codes |
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363 | (12) |
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5.5 Bounds for finite back-search limits |
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375 | (4) |
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5.6 Quantization of channel outputs |
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379 | (5) |
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384 | (1) |
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384 | (3) |
| 6 List decoding |
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387 | (38) |
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6.1 List decoding algorithms |
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388 | (3) |
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6.2 List decoding-performance |
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391 | (6) |
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6.3 The list minimum weight |
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397 | (10) |
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6.4 Upper bounds on the probability of correct path loss |
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407 | (9) |
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6.5 Lower bound on the probability of correct path loss |
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416 | (2) |
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6.6 Correct path loss for time-invariant convolutional codes |
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418 | (4) |
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422 | (1) |
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423 | (2) |
| 7 Sequential decoding |
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425 | (60) |
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426 | (5) |
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431 | (2) |
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433 | (3) |
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7.4 The Creeper algorithm |
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436 | (12) |
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448 | (2) |
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7.6 Computational analysis of the stack algorithm |
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450 | (10) |
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7.7 Error probability analysis of the stack algorithm |
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460 | (11) |
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7.8 Analysis of the Fano algorithm |
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471 | (6) |
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477 | (3) |
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480 | (1) |
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481 | (4) |
| 8 Low-density parity-check codes |
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485 | (82) |
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486 | (10) |
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8.2 LDPC convolutional codes |
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496 | (12) |
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8.3 Block and convolutional permutors |
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508 | (9) |
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8.4 Lower bounds on distances of LDPC codes |
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517 | (12) |
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8.5 Iterative decoding of LDPC codes |
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529 | (9) |
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8.6 Iterative limits and thresholds |
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538 | (15) |
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553 | (9) |
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562 | (1) |
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562 | (5) |
| 9 Turbo coding |
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567 | (26) |
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9.1 Parallel concatenation of two convolutional codes |
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567 | (3) |
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9.2 Distance bounds of turbo codes |
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570 | (3) |
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9.3 Parallel concatenation of three and more convolution codes |
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573 | (9) |
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9.4 Iterative decoding of turbo codes |
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582 | (4) |
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9.5 Braided convolutional codes |
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586 | (5) |
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591 | (1) |
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591 | (2) |
| 10 Convolutional codes with good distance properties |
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593 | (34) |
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10.1 Computing the Viterbi spectrum using FAST |
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594 | (4) |
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10.2 The magnificient BEAST |
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598 | (6) |
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10.3 Some classes of rate R =- 1/2 convolutional codes |
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604 | (4) |
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10.4 Low rate convolutional codes |
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608 | (13) |
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10.5 High rate convolutional codes |
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621 | (1) |
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10.6 Tailbiting trellis encoders |
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622 | (1) |
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622 | (5) |
| Appendix A: Minimal encoders |
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627 | (8) |
| Appendix B: Wald's identity |
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635 | (12) |
| References |
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647 | (12) |
| Index |
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659 | |
Lisainfo e-raamatute kohta