The Capacity Region of Multiway Relay Channels Over Finite Fields with Full Data Exchange

Abstract

The multi-way relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multi-way relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multi-way relay channels.

References in corpus (4)

• Interference Alignment and the Degrees of Freedom for the K User Interference Channel
• A Deterministic Approach to Wireless Relay Networks
• Approximate capacity of the two-way relay channel: A deterministic approach
• Lossy Broadcasting in Two-Way Relay Networks with Common Reconstructions

Cited by in corpus (5)

• On the Equal-Rate Capacity of the AWGN Multiway Relay Channel
• Multi-Way Information Exchange Over Completely-Connected Interference Networks with a Multi-Antenna Relay
• Capacity Results for Two Classes of Three-Way Channels
• The Finite Field Multi-Way Relay Channel with Correlated Sources: Beyond Three Users
• The Capacity Region of Restricted Multi-Way Relay Channels with Deterministic Uplinks