Linear block codes

1. Computing the weight distribution
2. Bounds on error performance over AWGN, flat Rayleigh fading and BSC channels

1. Hamming codes
2. Binary Golay (23,12,7) code and extended Golay (24,12,8) code
3. First order RM codes

1. Error-trapping decoding of cyclic codes
2. Berlekamp-Massey, Euclidean and PGZ algorithms
3. Chien search and error correction
4. Errors-and-erasures decoding
5. Error performance evaluation

1. Berlekamp-Massey, Euclidean and PGZ algorithms
2. Errors-and-erasures decoding
3. Error performance evaluation

1. Weight enumeration sequences and error performance evaluation
2. Viterbi algorithm with Hamming metrics
3. Viterbi algorithm with Euclidean metrics
4. Punctured convolutional codes

1. Decoding binary linear block codes with a trellis
2. Chase type-II algorithm
3. Ordered statistics decoding (OSD)
4. GMD decoding

1. MAP and log-MAP
2. Max-log-MAP
3. SOVA
4. SO-OSD and SO-Chase

1. Parallel concatenation (turbo codes)
2. Serial concatenation (product codes)
3. Block product codes
4. Low-density parity-check (LDPC) codes
• Bit-flip hard-decision algorithm
• Belief-propagation (sum-product) algorithm

1. Trellis coded modulation (TCM)
2. Pragmatic TCM
3. Multilevel coded modulation (MCM)
• Unequal error protection
4. Bit-interleaved coded modulation (BICM)
5. Turbo TCM

Basic performance analysis tools

1. Bounds and approximations on block and bit error rates
2. Program to compute the weight distribution of short codes
3. Data files with weight distrbutions of extended BCH codes of length up to 128

1. Syndrome and look-up table based
2. Berlekamp-Massey
3. Euclidean
4. Direct-solution (PGZ)
5. Viterbi decoder
6. Gallager's iterative bit-flip decoder

1. Viterbi decoder
• Binary convolutional codes
• Binary linear block codes
2. Chase type-II
3. Ordered-statistics
4. Generalized minimum distance

1. Optimal MAP (BCJR)
2. Log-MAP (log-BCJR)
3. Max-log-MAP
4. Soft-output ordered-statistics
5. Soft-output Chase type-II
6. Iterative belief-propagation

1. Parallel concatenated or turbo (partial-product) codes
2. Serial concatenated (product) codes
3. Low-density parity-check (LDPC) codes

1. TCM decoding
2. Pragmatic TCM decoding
3. Multistage decoding of MCM
• Conventional schemes
• Unequal error protection schemes
4. BICM decoding
5. Turbo TCM decoding
• Symbol interleaving (Robertson)

Bit interleaving (Benedeto et al)

This page was last updated on July 16, 2006, by Robert H. Morelos-Zaragoza.