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

Abstract

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.

Degrees of freedom for the MIMO multi-way relay channel

“…The exact capacity characterization for the multi-way relay channel has been considered in references [4] and [10]- [14]. Specifically, reference [4] has proposed the general multi-way relay channel model, and characterized the upperbounds on the capacity region and established achievable rates based on decode-and-forward (DF), compress-and-forward (CF), amplify-and-forward (AF), and using nested lattice codes.…”

“…Specifically, reference [4] has proposed the general multi-way relay channel model, and characterized the upperbounds on the capacity region and established achievable rates based on decode-and-forward (DF), compress-and-forward (CF), amplify-and-forward (AF), and using nested lattice codes. Reference [10] has considered the special case when there is one cluster of users, and each user wishes to exchange information with the rest of the users. The capacity region is characterized for a finite field channel.…”

Resource allocation for asymmetric multi-way relay communication over orthogonal channels

“…In [11] a scheme called functional decode-and-forward was proposed for the multi-way relay channel, where the relay decodes and forwards a function of the messages of the source nodes. The same authors extended their work also in [12,13]. Another work on multi-way relaying was done in [14,15] where the authors consider non-regenerative relaying with beamforming.…”

On the Gaussian multiway relay channel with intra-cluster links

“…The achievable equal rate point for DF, CF, AF, and CoF is given for the so-called restricted model, in which the nodes' channel inputs depend only on their own messages, not on past symbols. The finite field multiway relay channel has been studied in [18].…”