On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel

Abstract

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 zeroerror capacity region of a two-way channel via the asymptotic spectrum of graphs and show that this bound could be achieved for certain cases. * The authors are with the The main objective of this paper is to provide several single-letter outer and inner bounds on the non-adaptive zero-error capacity region of the DM-TWC. The remainder of this paper is organized as follows. In Section 2, we consider the confusion graphs of a DM-TWC, and discuss their performances with respect to the graph homomorphisms and the one-shot zero-error communication. Section 3 is devoted to three general outer bounds of the zero-error capacity region of DM-TWC, which are based on Shannon's vanishing-error non-adaptive capacity region, a two-way analogue of the linear programming bound for point-to-point channels, and the asymptotic spectra of graphs. In Section 4, we provide two general inner bounds using random coding and random linear codes respectively. In Section 5, we establish outer bounds for certain types of DM-TWC via the Shannon capacity of a graph, and also explicitly construct the uniquely decodable codebook pairs achieving the outer bound. Some concluding

On the Non-Adaptive Zero-Error Capacity of the Discrete Memoryless Two-Way Channel

“…To the best of our knowledge, this problem has not been addressed before, except in the special case of the binary multiplying channel, where upper and lower bounds on non-adaptive zero-error sum capacity have been obtained [13][14][15]. Our bounds are partially based on generalizations of these ideas and an earlier short version [16].…”