Coding Schemes for a Class of Receiver Message Side Information in AWGN Broadcast Channels

This paper considers the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) know some of the messages requested by other receivers as side information. For this setup, all possible side information configurations have been recently classified into eight groups and the capacity of the channel has been established for six groups (Asadi et al., ISIT 2014). We propose inner and outer bounds for the two remaining groups, groups 4 and 7. A distinguishing feature of these two groups is that the weakest receiver knows the requested message of the strongest receiver as side information while the in-between receiver does not. For group 4, the inner and outer bounds coincide at certain regions. For group 7, the inner and outer bounds coincide, thereby establishing the capacity, for four members out of all eight members of the group; for the remaining four members, the proposed bounds reduce the gap between the best known inner and outer bounds.Comment: accepted and to be presented at the 2014 IEEE Information Theory Workshop (ITW

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 Multi-Sender Multicast Index Coding

We focus on the following instance of an index coding problem, where a set of receivers are required to decode multiple messages, whilst each knows one of the messages a priori. In particular, here we consider a generalized setting where they are multiple senders, each sender only knows a subset of messages, and all senders are required to collectively transmit the index code. For a single sender, Ong and Ho (ICC, 2012) have established the optimal index codelength, where the lower bound was obtained using a pruning algorithm. In this paper, the pruning algorithm is simplified, and used in conjunction with an appending technique to give a lower bound to the multi-sender case. An upper bound is derived based on network coding. While the two bounds do not match in general, for the special case where no two senders know any message bit in common, the bounds match, giving the optimal index codelength. The results are derived based on graph theory, and are expressed in terms of strongly connected components.Comment: This is an extended version of the same-titled paper accepted and to be presented at the IEEE International Symposium on Information Theory (ISIT), Istanbul, in July 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

Wireless MIMO Switching: Weighted Sum Mean Square Error and Sum Rate Optimization

This paper addresses joint transceiver and relay design for a wireless multiple-input-multiple-output (MIMO) switching scheme that enables data exchange among multiple users. Here, a multi-antenna relay linearly precodes the received (uplink) signals from multiple users before forwarding the signal in the downlink, where the purpose of precoding is to let each user receive its desired signal with interference from other users suppressed. The problem of optimizing the precoder based on various design criteria is typically non-convex and difficult to solve. The main contribution of this paper is a unified approach to solve the weighted sum mean square error (MSE) minimization and weighted sum rate maximization problems in MIMO switching. Specifically, an iterative algorithm is proposed for jointly optimizing the relay's precoder and the users' receive filters to minimize the weighted sum MSE. It is also shown that the weighted sum rate maximization problem can be reformulated as an iterated weighted sum MSE minimization problem and can therefore be solved similarly to the case of weighted sum MSE minimization. With properly chosen initial values, the proposed iterative algorithms are asymptotically optimal in both high and low signal-to-noise ratio (SNR) regimes for MIMO switching, either with or without self-interference cancellation (a.k.a., physical-layer network coding). Numerical results show that the optimized MIMO switching scheme based on the proposed algorithms significantly outperforms existing approaches in the literature.Comment: This manuscript is under 2nd review of IEEE Transactions on Information Theor

Optimal Coding Schemes for the Three-Receiver AWGN Broadcast Channel with Receiver Message Side Information

This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best known inner and outer bounds. For group 4, our inner and outer bounds tighten the best known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best known inner and outer bounds.Comment: Authors' final version (to appear in IEEE Transactions on Information Theory

Degrees of Freedom for the MIMO Multi-way Relay Channel

This paper investigates the degrees of freedom (DoF) of the L-cluster, K-user MIMO multi-way relay channel, where users in each cluster wish to exchange messages within the cluster, and they can only communicate through the relay. A novel DoF upper bound is derived by providing users with carefully designed genie information. Achievable DoF is identified using signal space alignment and multiple-access transmission. For the two-cluster MIMO multi-way relay channel with two users in each cluster, DoF is established for the general case when users and the relay have arbitrary number of antennas, and it is shown that the DoF upper bound can be achieved using signal space alignment or multiple-access transmission, or a combination of both. The result is then generalized to the three user case. For the L-cluster K-user MIMO multi-way relay channel in the symmetric setting, conditions under which the DoF upper bound can be achieved are established. In addition to being shown to be tight in a variety of scenarios of interests of the multi-way relay channel, the newly derived upperbound also establishes the optimality of several previously established achievable DoF results for multiuser relay channels that are special cases of the multi-way relay channel.Comment: submitted to IEEE Transactions on Information Theor