Multi-level compress and forward coding for half-duplex relays

This paper presents a multi-level compress and forward coding scheme for a three-node relay network in which all transmissions are constrained to be from an M-ary PAM constellation. The proposed framework employs a uniform scalar quantizer followed by Slepian-Wolf coding at the relay. We first obtain a performance benchmark for the proposed scheme by deriving the corresponding information theoretical achievable rate. A practical coding scheme involving multi-level codes is then discussed. At the source node, we use multi-level low-density parity-check codes for error protection. At the relay node, we propose a multi-level distributed joint source-channel coding scheme that uses irregular repeat-accumulate codes, the rates of which are carefully chosen using the chain rule of entropy. For a block length of 2×10⁵ symbols, the proposed scheme operates within 0.56 and 0.63 dB of the theoretical limits at transmission rates of 1.0 and 1.5 bits/sample, respectively.