Cycle Tanner-graph codes over GF(2^b)

We derive the average Hamming weight spectrum function of the random ensemble of regular low-density parity-check (LDPC) codes over GF(2b) when used with binary-input channels. This work confirms theoretically that the near-Shannon-limit performance of Gallager's binary LDPC codes can be significantly enhanced by moving to fields of higher order. We construct a family of error-correcting codes based on the binary representation of GF(2b) codes defined on a cycle Tanner graph, that appears to be good for both optimum decoding and iterative decoding over binary-input channels.