Theory of linear and integer programming
Theory of linear and integer programming
Introduction to algorithms
Convex Optimization
Decoding error-correcting codes via linear programming
Decoding error-correcting codes via linear programming
Performance bounds for nonbinary linear block codes over memoryless symmetric channels
IEEE Transactions on Information Theory
Bit-interleaved coded modulation
IEEE Transactions on Information Theory
On the application of LDPC codes to arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
LDPC Codes Over Rings for PSK Modulation
IEEE Transactions on Information Theory
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
A New Linear Programming Approach to Decoding Linear Block Codes
IEEE Transactions on Information Theory
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Hi-index | 754.84 |
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates LP-based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the "maximum-likelihood (ML) certificate" property. It is also shown that the decoder output is the lowest cost. pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. It is also proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. Two alternative polytopes for use with LP decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These polytope representations lead to polynomial-time decoders for a wide variety of classical nonbinary linear codes. LP decoding performance is illustrated for the [11.6] ternary Golay code with ternary phase-shift keying (PSK) modulation over additive white Gaussian noise (AWGN), and in this case it is shown that the performance of the LP decoder is comparable to codeword-error-rate-optimum hard-decision-based decoding. LP decoding is also simulated for medium-length ternary and quaternary low-density parity-check (LDPC) codes with corresponding PSK modulations over AWGN.