Capacity of Two-Way Channels With Symmetry Properties

Abstract

In this paper, we make use of channel symmetry properties to determine the capacity region of three types of two-way networks: (a) two-user memoryless two-way channels (TWCs), (b) two-user TWCs with memory, and (c) three-user multiaccess/degraded broadcast (MA/DB) TWCs. For each network, symmetry conditions under which Shannon's random coding inner bound is tight are given.For two-user memoryless TWCs, prior results are substantially generalized by viewing a TWC as two interacting state-dependent one-way channels. The capacity of symmetric TWCs with memory, whose outputs are functions of the inputs and independent stationary and ergodic noise processes, is also obtained. Moreover, various channel symmetry properties under which Shannon's inner bound is tight are identified for three-user MA/DB TWCs. The results not only enlarge the class of symmetric TWCs whose capacity region can be exactly determined but also imply that adaptive coding, not improving capacity, is unnecessary for such channels. Index TermsNetwork information theory, two-way channels, capacity region, inner and outer bounds, channel symmetry, multiple access and broadcast channels, channels with memory, adaptive coding.

Classes of Full-Duplex Channels With Capacity Achieved Without Adaptation

“…Since the first presentation of some of our results [1], [2], more general characterizations of two-way channel capacity regions have been established [16]. Notwithstanding, the purpose of this paper is to show that such informationtheoretic results are insightful for the design of full-duplex communication schemes over realistic channel models arising from important communication systems.…”

“…whereZ i is Gaussian distributed and models the echo-channel estimation error [33]. Interestingly, the capacity region of this model is still open: It does not belong to the ISD TWC or any capacity-known TWC classes, e.g., [16]. Characterizing the capacity region or investigating whether adaptation is useful in this TWC model is an interesting topic for future research.…”

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

“…1−λ (6) and the maximum in (5) is taken over all the input probability distributions P X 1 and P X 2 , and the maximum in (6) is taken over all the dual clique pairs (S,…”

“…The non-adaptive DM-TWC is also sometimes called the restricted DM-TWC [2]. Shannon's inner and outer bounds have later been improved by utilizing auxiliary random variable techniques [3][4][5], and sufficient conditions under which his bounds coincide have been obtained [6,7]. However, despite much effort, the capacity region of a general DM-TWC under the vanishing-error criterion remains elusive.…”

On the Common Randomness Capacity of a Special Class of Two-way Channels

“…The CR capacity of decoupling two-way settings, namely those with general transition function factored as p(y 1 , y 2 |x 1 , x 2 ) = p(y 1 |x 2 )p(y 2 |x 1 ), has been solved by Venkatesan and Anantharam [2]. Recently, two-way channel transmission capacities have been studied [3], [4], [5]. We would like to study the CR capacity of intertwined two-way settings, namely those with p(y 1 , y 2 |x 1 , x 2 ) = p(y 1 |x 1 , x 2 )p(y 2 |x 1 , x 2 ).…”