On the Ice-Wine Problem: Recovering Linear Combination of Codewords over the Gaussian Multiple Access Channel

TL;DR

This paper introduces a novel lattice coding scheme for the Ice-Wine problem over Gaussian MAC, enabling recovery of non-integer linear combinations of codewords and improving achievable rate regions.

Contribution

The paper proposes a new lattice coding scheme that recovers non-integer linear combinations of codewords, enhancing the rate region over previous methods.

Findings

Achievable rate region is improved compared to prior schemes.

The scheme partially approaches the outer bound for user rates.

Application to Gaussian Two Way Relay Channel yields better rate regions.

Abstract

In this paper, we consider the Ice-Wine problem: Two transmitters send their messages over the Gaussian Multiple-Access Channel (MAC) and a receiver aims to recover a linear combination of codewords. The best known achievable rate-region for this problem is due to [1],[2] as $R_{i}\leq\frac{1}{2}\log\left(\frac{1}{2}+{\rm SNR}\right)$ $(i=1,2)$. In this paper, we design a novel scheme using lattice codes and show that the rate region of this problem can be improved. The main difference between our proposed scheme with known schemes in [1],[2] is that instead of recovering the sum of codewords at the decoder, a non-integer linear combination of codewords is recovered. Comparing the achievable rate-region with the outer bound, $R_{i}\leq\frac{1}{2}\log\left(1+{\rm SNR}\right)\,\,(i=1,2)$, we observe that the achievable rate for each user is partially tight. Finally, by applying our proposed scheme to the Gaussian Two Way Relay Channel (GTWRC), we show that the best rate region for this problem can be improved.