The Capacity Region of the Restricted Two-Way Relay Channel with Any Deterministic Uplink

This paper considers the two-way relay channel (TWRC) where two users communicate via a relay. For the restricted TWRC where the uplink from the users to the relay is any deterministic function and the downlink from the relay to the users is any arbitrary channel, the capacity region is obtained. The TWRC considered is restricted in the sense that each user can only transmit a function of its message.Comment: author's final version (accepted and to appear in IEEE Communications Letters

The Capacity Region of Restricted Multi-Way Relay Channels with Deterministic Uplinks

This paper considers the multi-way relay channel (MWRC) where multiple users exchange messages via a single relay. The capacity region is derived for a special class of MWRCs where (i) the uplink and the downlink are separated in the sense that there is no direct user-to-user links, (ii) the channel is restricted in the sense that each user's transmitted channel symbols can depend on only its own message, but not on its received channel symbols, and (iii) the uplink is any deterministic function.Comment: Author's final version (to be presented at ISIT 2012

Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network

The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic network are then used for the Gaussian bidirectional relay network. The strategy in the deterministic channel translates to a specific superposition of lattice codes and random Gaussian codes at the source nodes and successive interference cancelation at the receiving nodes for the Gaussian network. The achievable rate of this scheme with two pairs is analyzed and it is shown that for all channel gains it achieves to within 3 bits/sec/Hz per user of the cut-set upper-bound. Hence, the capacity region of the two-pair bidirectional Gaussian relay network to within 3 bits/sec/Hz per user is characterized.Comment: IEEE Trans. on Information Theory, accepte

Using Network Coding to Achieve the Capacity of Deterministic Relay Networks with Relay Messages

In this paper, we derive the capacity of the deterministic relay networks with relay messages. We consider a network which consists of five nodes, four of which can only communicate via the fifth one. However, the fifth node is not merely a relay as it may exchange private messages with the other network nodes. First, we develop an upper bound on the capacity region based on the notion of a single sided genie. In the course of the achievability proof, we also derive the deterministic capacity of a 4-user relay network (without private messages at the relay). The capacity achieving schemes use a combination of two network coding techniques: the Simple Ordering Scheme (SOS) and Detour Schemes (DS). In the SOS, we order the transmitted bits at each user such that the bi-directional messages will be received at the same channel level at the relay, while the basic idea behind the DS is that some parts of the message follow an indirect path to their respective destinations. This paper, therefore, serves to show that user cooperation and network coding can enhance throughput, even when the users are not directly connected to each other.Comment: 12 pages, 5 figures, submitted to IEEE JSAC Network codin

The Deterministic Capacity of Relay Networks with Relay Private Messages

We study the capacity region of a deterministic 4-node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.Comment: 3 figures, accepted at ITW 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

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]

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