Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical Programming Approaches for Decoding of Binary Linear Codes

Metaheuristic Algorithms for Decoding Binary Linear Codes

This paper introduces two decoders for binary linear codes based on Metaheuristics. The first one uses a genetic algorithm and the second is based on a combination genetic algorithm with a feed forward neural network. The decoder based on the genetic algorithms (DAG) applied to BCH and convolutional codes give good performances compared to Chase-2 and Viterbi algorithm respectively and reach th...

On two probabilistic decoding algorithms for binary linear codes

A generalization of Sullivan inequality on the ratio of the probability of a linear code to that of any of its cosets is proved. Starting from this inequality, a sufficient condition for successful decoding of linear codes by a probabilistic method is derived. A probabilistic decoding algorithm for “low–density parity–check codes” is also analyzed. The results obtained allow one to estimate exp...

Looping linear programming decoding of LDPC codes

Considering the Linear Programming (LP) decoding of Low-Density-Parity-Check (LDPC) code [1], we describe an efficient algorithm for finding pseudo codewords with the smallest effective distance. The algorithm, coined LP-loop, starts from choosing randomly initial configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two sub-steps. F...

Decoding Turbo-Like Codes via Linear Programming

We introduce a novel algorithm for decoding turbo-like codes based on linear programming. We prove that for the case of Repeat-Accumulate (RA) codes, under the binary symmetric channel with a certain constant threshold bound on the noise, the error probability of our algorithm is bounded by an inverse polynomial in the code length. Our linear program (LP) minimizes the distance between the rece...