Sufficient Conditions for the Tightness of Shannon's Capacity Bounds for Two-Way Channels

Abstract

New sufficient conditions for determining in closed form the capacity region of point-to-point memoryless two-way channels (TWCs) are derived. The proposed conditions not only relax Shannon's condition which can identify only TWCs with a certain symmetry property but also generalize other existing results. Examples are given to demonstrate the advantages of the proposed conditions. Index Terms-Network information theory, two-way channels, capacity region, inner and outer bounds, channel symmetry. † The authors are with the

Capacity of Generalized Discrete-Memoryless Push-to-Talk Two-Way Channels

“…Viewing the generalized DM-PTT-TWC as two sets of one-way channels, we further observed that one-way channel components with (relatively) low capacity should be abandoned for efficient transmissions. Future research directions include finding a more general tightness condition for DM-TWCs, identifying the connections between different channel symmetry properties (in particular between the channel symmetry property introduced in this paper and the ones in [10] and [12]), and investigating the transmission of correlated sources over the generalized DM-PTT-TWCs.…”

“…We also illustrate the possible different shapes of the capacity region and discuss efficient transmission strategies via examples. It is worth mentioning that a by-product of our derivation is a new way to show the tightness of Shannon's capacity inner bound [1] which is complementary to prior methods in [7], [10], [12]. In fact, we find that none of these prior results imply that Shannon's inner bound is tight for Shannon's PTT-TWC (and for our general model under the symmetry property).…”

“…Quantifying the trade-off is often the most involved part of determining the capacity region of general TWCs. The prior approach to tackle the problem is to exploit (when they exist) channel symmetry or invariance properties so that for any P X 1 ,X 2 = P X 2 · P X 1 |X 2 , one can always find aP X 1 such that [10], [12]. However, this approach fails here since suchP X 1 may not exist for each P X 1 ,X 2 .…”

“…However, how each user can effectively maximize its individual transmission rate over the shared channel and concurrently provide sufficient feedback to help the other user's transmission is quite a challenging problem. Although in the past two decades increased attention has been given to two-way channels (TWCs) [2][3][4][5][6][7][8][9][10][11][12][13][14], a single-letter characterization of the capacity region for general TWCs remains open. The aim of this report is to establish a capacity result for a generalized push-to-talk (PTT) TWC.…”

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

“…The non-adaptive DM-TWC is also called the restricted DM-TWC in [19]. Shannon's inner and outer bounds have later been improved by utilizing auxiliary random variables techniques [9], [11], [26], and sufficient conditions under which his bounds coincide have been obtained [23,24]. However, despite much effort, the capacity region of a general DM-TWC under the vanishing-error criterion remains elusive.…”