Cooperative Compute-and-Forward

TL;DR

This paper introduces a cooperative lattice coding strategy for compute-and-forward networks, significantly improving computation rates and diversity-multiplexing tradeoffs by enabling transmitters to decode and cooperatively transmit messages.

Contribution

It proposes a novel cooperative lattice coding scheme with block Markov encoding that enhances compute-and-forward performance.

Findings

Cooperation improves achievable computation rates.

The strategy enhances the diversity-multiplexing tradeoff.

Lattice coding with block Markov encoding is effective for cooperation.

Abstract

We examine the benefits of user cooperation under compute-and-forward. Much like in network coding, receivers in a compute-and-forward network recover finite-field linear combinations of transmitters' messages. Recovery is enabled by linear codes: transmitters map messages to a linear codebook, and receivers attempt to decode the incoming superposition of signals to an integer combination of codewords. However, the achievable computation rates are low if channel gains do not correspond to a suitable linear combination. In response to this challenge, we propose a cooperative approach to compute-and-forward. We devise a lattice-coding approach to block Markov encoding with which we construct a decode-and-forward style computation strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information to aid receivers in decoding the integer combinations. Using our strategy, we show that cooperation offers a significant improvement both in the achievable computation rate and in the diversity-multiplexing tradeoff.