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

The Finite Field Multi-Way Relay Channel with Correlated Sources: Beyond Three Users

The multi-way relay channel (MWRC) models cooperative communication networks in which many users exchange messages via a relay. In this paper, we consider the finite field MWRC with correlated messages. The problem is to find all achievable rates, defined as the number of channel uses required per reliable exchange of message tuple. For the case of three users, we have previously established that for a special class of source distributions, the set of all achievable rates can be found [Ong et al., ISIT 2010]. The class is specified by an almost balanced conditional mutual information (ABCMI) condition. In this paper, we first generalize the ABCMI condition to the case of more than three users. We then show that if the sources satisfy the ABCMI condition, then the set of all achievable rates is found and can be attained using a separate source-channel coding architecture.Comment: Author's final version (to be presented at ISIT 2012

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 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.

Multi-way relay networks: characterization, performance analysis and transmission scheme design

Multi-way relay networks (MWRNs) are a growing research area in the field of relay based wireless networks. Such networks provide a pathway for solving the ever in- creasing demand for higher data rate and spectral efficiency in a general multi-user scenario. MWRNs have potential applications in video conferencing, file sharing in a social network, as well as satellite networks and sensor networks. Recent research on MWRNs focuses on efficient transmission protocol design by harnessing different network coding schemes, higher dimensional structured codes and advanced relaying protocols. However, the existing research misses out the characterization and analysis of practical issues that influence the performance of MWRNs. Moreover, the existing transmission schemes suffer some significant limitations, that need to be solved for maximizing the benefits of MWRNs. In this thesis, we investigate the practical issues that critically influence the perfor- mance of a MWRN and propose solutions that can outperform existing schemes. To be specific, we characterize error propagation phenomenon for additive white Gaus- sian noise (AWGN) and fading channels with functional decode and forward (FDF) and amplify and forward (AF) relaying protocols, propose a new pairing scheme that out- performs the existing schemes for lattice coded FDF MWRNs in terms of the achievable rate and error performance and finally, analyze the impact of imperfect channel state information (CSI) and optimum power allocation on MWRNs. At first, we analyze the error performance of FDF and AF MWRNs with pair- wise transmission using binary phase shift keying (BPSK) modulation in AWGN and Rayleigh fading channels. We quantify the possible error events in an L-user FDF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) other users. We show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a FDF MWRN. We derive the average BER of a user in a FDF or AF MWRN under high SNR conditions and provide simulation results to verify them. Next, we propose a novel user pairing scheme for lattice coded FDF MWRNs. Lattice codes can achieve the capacity of AWGN channels and are used in digital communica- tions as high-rate signal constellations. Our proposed pairing scheme selects a common user with the best average channel gain and thus, allows it to positively contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. In addition, considering M-ary QAM with square constellation as a special case of lattice codes, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates and error performance, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. Finally, we investigate lattice coded FDF and AF MWRNs with imperfect CSI. Con- sidering lattice codes of sufficiently large dimension, we obtain the bounds on the com- mon rate and sum rate. In addition, considering M-ary quadrature amplitude mod- ulation (QAM) with square constellations, we obtain expressions for the average SER in FDF MWRNs. For AF MWRNs, considering BPSK modulation as the simplest case of lattice codes, we obtain the average BER. Moreover, we obtain the optimum power allocation coefficients to maximize the sum rate in AF MWRN. For both FDF and AF relaying protocols, the average common rate and sum rate are decreasing functions of the estimation error. The analysis shows that the error performance of a FDF MWRN is an increasing function of both the channel estimation error and the number of users, whereas, for AF MWRN, the error performance is an increasing function of only the channel estimation error. Also, we show that to achieve the same sum rate in AF MWRN, optimum power allocation requires 7 − 9 dB less power compared to equal power allocation depending upon users’ channel conditions