# 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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