Bilayer protograph codes for half-duplex relay channels

This paper presents a high-performing LDPC code for the relay channel that addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly optimized for a given channel quality and are not easily adapted, without extensive re-optimization, for various channel conditions. This paper presents a code for the relay channel that combines structured design and easy encoding with rate compatibility to allow adaptation to the three links involved in the relay channel, and furthermore offers very good performance. The proposed code is constructed by synthesizing a bilayer structure with a protograph. In addition to the contribution to relay encoding, we also produce an improved family of protograph codes for the point-to-point AWGN channel whose high-rate members enjoy thresholds that are within 0.07 dB of capacity.