Efficient compute-and-forward design with low communication overhead

Abstract

The compute-and-forward scheme for wireless relay networks can achieve higher transmission rates than other existing relaying schemes, such as decode-and-forward. The compute-and-forward (CF) design involves finding an integer-valued coefficient vector at each relay so that the set of coefficient vectors form a full rank matrix allowing the destination to perform decoding. The CF design problem is relevant to an instance of the famous shortest lattice vector problem and has attracted much recent research attention. Two representative CF designs, the so-called local optimization scheme and the Wei-Chen scheme, have been introduced in the literature. However, they either achieve relatively low transmission rate, or require a relatively high communication overhead. In this paper, we propose a new compute-and-forward design that can achieve a significantly higher transmission rate than the local optimization scheme and requires a much lower communication overhead than the Wei-Chen scheme. In particular, the new scheme does not require a list of candidate coefficient vectors and their computation rates to be forwarded from each relay to the destination, and hence avoids the heavy communication overhead incurred. Simulation results for a 2-hop wireless relay network with channel vectors consisting of i.i.d. Gaussian entries are presented to demonstrate the transmission rate improvement of the proposed scheme relative to the local optimization scheme. For example, it is shown that the proposed scheme can achieve about 2.5dB gain at moderate SNR in the case of 8 sources/relays.