The ML decoding performance of LDPC ensembles over Z/sub q/

We derive the asymptotic spectra of low-density parity-check (LDPC) ensembles over Z/sub q/. We consider two ensembles of LDPC matrices, one is binary and the other q-ary. We also show that for modulo-additive noise channels, both ensembles achieve the random coding error exponent, for graphs with sufficiently large connectivity.