Gu Yujie, Shayevitz Ofer
Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka 819-0395, Japan.
Department of EE-Systems, Tel Aviv University, Tel Aviv 69978, Israel.
Entropy (Basel). 2021 Nov 15;23(11):1518. doi: 10.3390/e23111518.
We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon's vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which, in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs, and show that this bound can be achieved in certain cases.
我们研究了在零错误概率准则下，使用非自适应方案在离散无记忆双向信道上进行通信的问题。我们基于随机编码、线性规划、线性码和图的渐近谱，推导出了零错误容量区域的单字母内界和外界。其中，我们基于香农的消失错误容量区域与点对点信道线性规划界的双向类似物的组合，提供了一个单字母外界，与单向情况不同的是，该外界通常比两者都要好。此外，我们通过图的渐近谱建立了双向信道零错误容量区域的外界，并表明在某些情况下可以达到这个界。
