The ML decoding performance of LDPC ensembles over Zq

In this work we derive the asymptotic spectrum of two ensembles of q-ary LDPC codes, one consisting of (almost entirely) binary matrices, the other of q-ary matrices, and show that both ensembles are good as the graph connectivity increases, in the sense that their spectrum approaches that of the random linear ensemble over Z_q and that they allow to approach the random coding error exponent of modulo additive noise channels. This suggests that q-ary LDPC codes may conceivably provide an alternative to multilevel binary LDPC codes for the AWGN channel.