Low Density Parity Check Codes over GF(q)

Matthew C. Davey and David J. C. MacKay

Binary Low Density Parity Check (LDPC) codes have been shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. The analogous codes defined over finite fields GF(q) of order q>2 show significantly improved performance. We present the results of Monte Carlo simulations of the decoding of infinite LDPC Codes which can be used to obtain good constructions for finite Codes. We also present empirical results for the Gaussian channel including a rate 1/4 code with bit error probability of 0.0001 at E_b/N_0=-0.05dB.

Status: Published in the Proceedings of the 1998 IEEE Information Theory Workshop, Killarney, June 1998.

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