关于冰酒问题：高斯多址信道上码字线性组合的恢复
On the Ice-Wine Problem: Recovering Linear Combination of Codewords over the Gaussian Multiple Access Channel
摘要：
在本文中，我们考虑冰酒问题：两个发射机发送他们的消息在高斯多址信道（MAC）和接收机的目标是恢复码字的线性组合。对于这个问题，最著名的可达到的速率区域是由于[1]，[2]作为$R_{i}\leq\frac{1}{2}\log\left(\frac{1}{2}+{\rm SNR}\right)$ $(i=1,2)$。在本文中，我们设计了一个新的计划，使用格码，并表明，该问题的速率区域可以得到改善。我们提出的方案与[1]，[2]中已知方案之间的主要区别在于，不是在解码器处恢复码字的总和，而是恢复码字的非整数线性组合。将可达速率区域与外部边界$R_{i}\leq\frac{1}{2}\log\left(1+{\rm SNR}\right)\,\,(i=1,2)$进行比较，我们观察到每个用户的可达速率是部分紧的。最后，通过将我们提出的方案应用于高斯双向中继信道（GTWRC），我们表明，这个问题的最佳速率区域可以得到改善。
英文摘要：
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.
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