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Abstract|Gallager's low density binary parity c heck c o d e s have b e e n shown to have near Shannon limit performance when decoded using a probabilistic decoding algorithm. We report the empirical results of error-correction using the analogous codes over GF(q) for q > 2, with Binary Symmetric channels and Binary Gaussian Channels. We nd a signi cant improvement o ver the performance of the binary codes, including a rate 1/4 code with bit error probability < 10 ;5 at E b =N 0 = 0 :2dB.doi:10.1109/4234.681360 fatcat:qdf5a4gqyrfb3g4n52pubdseay