Linear Programming Decoding of Binary Linear Codes for Symbol-Pair Read Channel

Mathematical Programming Approaches for Decoding of Binary Linear Codes

An optimum symbol-by-symbol decoding rule for linear codes

A decoding rule is presented which minimizes the probability of symbol error over a time-discrete memoryless channel for any linear error-correcting code when the code words are equiprobable. The complexity of this rule varies inversely with code rate, making the technique particularly attractive for high rate codes. Examples are given for both block and convolutional 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...

Optimal Decoding of Linear Codes for Minimizing Symbol

The previous are identical to the expressions (2) and (3). Thus the n 1 columns do consist of two repetitions of 2”-r-level Gray code. Now if we combine the first two columns again, we reduce each 2”-‘-level Gray code into two 2n-2-level Gray codes, or, the complete array into four 2”-2-level Gray codes. This can continue until we have only m columns, which would be 2n-m repetitions of 2”‘-leve...

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...