Symbol-asynchronous compute-and-forward

The impact of symbol-asynchronism on compute-and-forward strategy in relay networks is considered. The lattice-based coding and decoding scheme presented recently by Nazer and Gastpar is applied over asynchronous distributed networks. While the key idea in compute-and-forward is to decode a linear combination of the transmitted codewords, due to distributed nature of the network, the relays receive random asynchronous versions of the combinations. It is shown that by using a simple equalizer as a part of the signaling scheme, one can transform the system to a synchronous one albeit with a smaller channel gain. The effect of asynchronism on the achievable rates is also studied, which implies a loss compared to the synchronous case. However, the resulting gap vanishes as the signal-to-noise-ratio (SNR) increases.