Capacity Theorems for the AWGN Multi-Way Relay Channel

The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and compress-forward are shown to be bounded away from the cut-set upper bound at high signal-to-noise ratios (SNR). It is known that the gap between the compress-forward rate and the capacity upper bound is a constant at high SNR, and that between the complete-decode-forward rate and the upper bound increases with SNR at high SNR. In this paper, a functional-decode-forward coding strategy is proposed. It is shown that for L >= 3, complete-decode-forward achieves the capacity when SNR <= 0 dB, and functional-decode-forward achieves the capacity when SNR >= 0 dB. For L=$, functional-decode-forward achieves the capacity asymptotically as SNR increases.Comment: accepted and to be presented at ISIT 201

Functional-Decode-Forward for the General Discrete Memoryless Two-Way Relay Channel

We consider the general discrete memoryless two-way relay channel, where two users exchange messages via a relay, and propose two functional-decode-forward coding strategies for this channel. Functional-decode-forward involves the relay decoding a function of the users' messages rather than the individual messages themselves. This function is then broadcast back to the users, which can be used in conjunction with the user's own message to decode the other user's message. Via a numerical example, we show that functional-decode-forward with linear codes is capable of achieving strictly larger sum rates than those achievable by other strategies

Optimal Coding Functions for Pairwise Message Sharing on Finite-Field Multi-Way Relay Channels

This paper considers the finite-field multi-way relay channel with pairwise message sharing, where multiple users exchange messages through a single relay and where the users may share parts of their source messages (meaning that some message parts are known/common to more than one user). In this paper, we design an optimal functional-decode-forward coding scheme that takes the shared messages into account. More specifically, we design an optimal function for the relay to decode (from the users on the uplink) and forward (back to the users on the downlink). We then show that this proposed function-decode-forward coding scheme can achieve the capacity region of the finite-field multi-way relay channel with pairwise message sharing. This paper generalizes our previous result for the case of three users to any number of users.Comment: Author's final version (accepted for presentation at the 2014 IEEE International Conference on Communications [ICC 2014]

The Binary-Symmetric Parallel-Relay Network

We present capacity results of the binary-symmetric parallel-relay network, where there is one source, one destination, and K relays in parallel. We show that forwarding relays, where the relays merely transmit their received signals, achieve the capacity in two ways: with coded transmission at the source and a finite number of relays, or uncoded transmission at the source and a sufficiently large number of relays. On the other hand, decoding relays, where the relays decode the source message, re-encode, and forward it to the destination, achieve the capacity when the number of relays is small.Comment: accepted and to be presented at ISIT 201

On Achievable Rate Regions of the Asymmetric AWGN Two-Way Relay Channel

This paper investigates the additive white Gaussian noise two-way relay channel, where two users exchange messages through a relay. Asymmetrical channels are considered where the users can transmit data at different rates and at different power levels. We modify and improve existing coding schemes to obtain three new achievable rate regions. Comparing four downlink-optimal coding schemes, we show that the scheme that gives the best sum-rate performance is (i) complete-decode-forward, when both users transmit at low signal-to-noise ratio (SNR); (ii) functional-decode-forward with nested lattice codes, when both users transmit at high SNR; (iii) functional-decode-forward with rate splitting and time-division multiplexing, when one user transmits at low SNR and another user at medium--high SNR.Comment: to be presented at ISIT 201

The Three-User Finite-Field Multi-Way Relay Channel with Correlated Sources

This paper studies the three-user finite-field multi-way relay channel, where the users exchange messages via a relay. The messages are arbitrarily correlated, and the finite-field channel is linear and is subject to additive noise of arbitrary distribution. The problem is to determine the minimum achievable source-channel rate, defined as channel uses per source symbol needed for reliable communication. We combine Slepian-Wolf source coding and functional-decode-forward channel coding to obtain the solution for two classes of source and channel combinations. Furthermore, for correlated sources that have their common information equal their mutual information, we propose a new coding scheme to achieve the minimum source-channel rate.Comment: Author's final version (accepted and to appear in IEEE Transactions on Communications

The Finite Field Multi-Way Relay Channel with Correlated Sources: The Three-User Case

The three-user finite field multi-way relay channel with correlated sources is considered. The three users generate possibly correlated messages, and each user is to transmit its message to the two other users reliably in the Shannon sense. As there is no direct link among the users, communication is carried out via a relay, and the link from the users to the relay and those from the relay to the users are finite field adder channels with additive noise of arbitrary distribution. The problem is to determine the set of all possible achievable rates, defined as channel uses per source symbol for reliable communication. For two classes of source/channel combinations, the solution is obtained using Slepian-Wolf source coding combined with functional-decode-forward channel coding.Comment: to be presented at ISIT 201