Error Bounds for Repeat-Accumulate Codes Decoded via Linear Programming

TL;DR

This paper derives an upper bound on the decoding error probability for repeat-accumulate codes with even repetition degrees, using linear programming decoding, applicable to any MBIOS channel, extending previous bounds for specific cases.

Contribution

It generalizes existing error bounds to a broader class of RA codes with even repetition degrees and arbitrary MBIOS channels using LP decoding.

Findings

Error probability bound is inverse polynomial in block length.

Bound applies to regular and irregular RA codes with even repetition.

Extends previous bounds from regular RA(2) codes to more general cases.

Abstract

We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a linear-programming based decoder which is an inverse polynomial in the block length. Our bound is valid for any memoryless, binary-input, output-symmetric (MBIOS) channel. This result generalizes the bound derived by Feldman et al., which was for regular RA(2) codes.