Coarse Network Coding: A Simple Relay Strategy to Resolve Interference

Reminiscent of the parity function in network coding for the butterfly network, it is shown that forwarding the sign of a linear combination of two source signals recovers 1 bit of information at the two destinations in a noiseless interference channel where interference is treated as noise. Based on this observation, a coding strategy is proposed to improve the rate of both users at the same time using a relay node in a noisy interference channel. In this strategy, the relay observes a linear combination of signals sent by the two sources, and broadcasts a common message to the two destinations over a shared digital link of a constant rate $R_0$ bits per channel use. The relay message consists of the bin index of a structured binning scheme obtained from a $2^{R_0}$-way partition of the squared lattice in the complex plane. The source nodes encode their message using bit-interleaved coded-modulation (BICM), and the destination nodes decode the corresponding source codeword according to log-likelihood ratios enhanced by the extra bits received from the relay. This coding strategy is a practical implementation of the extended hash-and-forward scheme, and is shown to improve the achievable rates of each user by as much as $R_0$ bits, asymptotically at high signal to noise ratios (SNR).