Design of LDPC codes for the q-ary partial erasure channel

Abstract

In this paper, we discuss practical design of low-density parity-check (LDPC) codes for the q-ary partial erasure channel (QPEC). This channel is an extension of the binary erasure channel (BEC), where partial information on the output is available. We provide a linear programming (LP) optimization for the design of good degree distributions, and compare our code design results to codes obtained using an LP optimization formulated for the BEC. We show superior performance in terms of code rate and complexity, when designing an LDPC code for a desired decoding threshold.