Fast Linear-Programming decoding of LDPC codes over GF(2m)

Junya Honda, Hirosuke Yamamoto

Abstract: Recently Linear Programming (LP) decoding is attracting much attention as an alternative to Belief Propagation (BP) decoding for LDPC codes. It is well known for the BP decoding that nonbinary LDPC codes can improve the decoding error probability considerably. On the other hand, Flanagan et al. proposed an LP decoding scheme for LDPC codes over finite rings. Although their scheme is applicable to LDPC codes over finite fields, the number of variables in the LP grows rapidly and hence, its implementation becomes harder as the field size increases. To overcome this defect we propose a new LP decoding scheme for GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ), in which the number of variables increases linearly in the field size. Although our scheme relaxes a maximum likelihood decoding problem more loosely to an LP problem than their scheme, the deterioration of the decoding error probability is small.