We present a modification of belief propagation that enables us to decode LDPC codes defined on high order Galois fields with a complexity that scales as p log/sub 2/ (p), p being the field order. With this low complexity algorithm, we are able to decode GF(2/sup q/) LDPC codes up to a field order value of 256. We show by simulation that ultra-sparse regular LDPC codes in GF(64) and GF(256) exhibit very good performance.