Bilayer LDPC Codes for the Relay Channel

This paper describes a methodology for efficient implementation of binning and block-Markov coding for the relay channel using powerful features of low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated random linear paritybits in a specially designed bilayer graphical code structure. Bilayer density evolution is devised as a novel extension of the standard density evolution algorithm to analyze the performance of the proposed bilayer LDPC code. Based on this bilayer density evolution technique, an EXIT-chart-based code design method using linear programming is developed. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC code is capable of working at two different channel parameters, the signal-to-noise ratio (SNR) at the relay and the SNR at the destination. In this paper, for specific channel parameters, it is demonstrated that a bilayer LDPC code can approach the theoretical decode-and-forward rate of the relay channel within a 0.19 dB gap to the source-relay channel capacity and a 0.34 dB gap to the relay-destination channel capacity.