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 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.
Highlights
The problem of reliable communication over a discrete memoryless two-way channel (DMTWC) was originally introduced and investigated by Shannon [1] in a seminal paper that has marked the inception of multi-user information theory
In [1], Shannon provided inner and outer bounds for the vanishing-error capacity region of the DM-TWC, in the general setting where the users are allowed to adapt their transmissions on the fly based on past observations
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
Summary
The problem of reliable communication over a discrete memoryless two-way channel (DMTWC) was originally introduced and investigated by Shannon [1] in a seminal paper that has marked the inception of multi-user information theory. Alice and Bob observe the resulting (random) channel outputs Y1n ∈ Y1n and Y2n ∈ Y2n respectively, and attempt to decode the message sent by their counterpart, without error When this is possible, that is, when there exist decoding functions φ1 : [2nR1 ] × Y1n → [2nR2 ] and φ2 : [2nR2 ] × Y2n → [2nR1 ] such that m2 = φ1 (m1 , Y1n ) and m1 = φ2 (m2 , Y2n ), for all m1 , m2 , with probability one, the codebook pair (or the encoding functions) is called (n, R1 , R2 ) uniquely decodable.
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