Multi-way Relay Networks Research Articles

Space–Time Physical-Layer Network Coding

A space–time physical-layer network coding (ST-PNC) method is presented for information exchange among multiple users over fully connected multiway relay networks. The method involves two steps: 1) side-information learning and 2) space–time relay transmission. In the first step, different sets of users are scheduled to send signals over networks, and the remaining users and relays overhear the transmitted signals, thereby learning the interference patterns. In the second step, multiple relays cooperatively send out linear combinations of signals received in the previous phase using space–time precoding so that all users efficiently exploit their side information in the form of 1) what they sent and 2) what they overheard in decoding. This coding concept is illustrated through two simple network examples. It is shown that ST-PNC improves the sum of degrees of freedom (sum-DoF) of the network compared to existing interference management methods. With ST-PNC, the sum-DoF of a general multiway relay network without channel knowledge at the users is characterized in terms of relevant system parameters, chiefly the number of users, the number of relays, and the number of antennas at relays. A major implication of the derived results is that efficiently harnessing both transmitted and overheard signals as side information brings significant performance improvements to fully connected multiway relay networks.

Rateless Codes for the Multiway Relay Channel

We consider distributed Luby transform (DLT) codes for efficient packet transmission in a multiway relay network, where the links are modeled as erasure channels. Density evolution is applied for asymptotic performance analysis and subsequently used in a linear-programming design framework for optimizing the degree distribution at the relay in terms of overhead. Moreover, a buffer is introduced at the relay to enable efficient downlink transmission even if packets are lost during uplink transmission. Performance losses in terms of delay and/or erasure rates caused by link erasures during uplink transmission are thus alleviated. The proposed DLT codes provide significant improvements in overhead and decoded erasure rates. Numerical results for finite-length codes follow closely the asymptotic analysis. Our results demonstrate that the proposed buffer-based DLT codes outperform its counterparts for lossy uplink transmission.

Multi-Way MIMO Amplify-and-Forward Relay Networks with Zero-Forcing Transmission

Two transmission strategies, namely (i) pairwise zero-forcing transmission and (ii) non-pairwise zero-forcing transmission, for multiple-input multiple-output (MIMO) amplify-and-forward (AF) multi-way relay networks (MWRNs) are analytically studied. To this end, lower and upper bounds of the outage probability, the corresponding high signal-to-noise ratio outage probability approximations, the achievable sum rate, and the fundamental diversity-multiplexing trade-off are derived in closed-form. The proposed pairwise zero-forcing transmission strategy possesses a lower practical implementation complexity as each node requires only the instantaneous respective node-to-relay channel knowledge. Counter intuitively, the non-pairwise zero-forcing transmission strategy achieves higher spatial multiplexing gains over the pairwise counterpart at the expense of higher relay processing complexity and more stringent channel state information requirements. Moreover, numerical results are presented to further validate our analysis and thereby to obtain valuable insights into practical MIMO AF MWRN implementation.

Error performance analysis of decode‐and‐forward and amplify‐and‐forward multi‐way relay networks with binary phase shift keying modulation

In this study, we analyse the error performance of decode and forward (DF) and amplify and forward (AF) multi-way relay networks (MWRNs). The authors consider a MWRN with pair-wise data exchange protocol using binary phase shift keying (BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The authors quantify the possible error events in an L-user DF 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]) users. They 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 DF MWRN. They derive the average BER of a user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high SNR conditions. Simulation results validate the correctness of the derived expressions. The authors results show that at medium to high SNR, DF MWRN provides better error performance than AF MWRN in AWGN channels even with a large number of users (e.g. L = 100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh fading channels even for much smaller number of users (e.g. L > 10).

Multi-Way Relay Networks: Orthogonal Uplink, Source-Channel Separation and Code Design

We consider a multi-way relay network with an orthogonal uplink and correlated sources, and we characterise reliable communication (in the usual Shannon sense) with a single-letter expression. The characterisation is obtained using a joint source-channel random-coding argument, which is based on a combination of Wyner et al.'s "Cascaded Slepian-Wolf Source Coding" and Tuncel's "Slepian-Wolf Coding over Broadcast Channels". We prove a separation theorem for the special case of two nodes; that is, we show that a modular code architecture with separate source and channel coding functions is (asymptotically) optimal. Finally, we propose a practical coding scheme based on low-density parity-check codes, and we analyse its performance using multi-edge density evolution.

Design of Binary Network Codes for Multiuser Multiway Relay Networks

We study multiuser multiway relay networks where N user nodes exchange their information through a single-relay node. We use network coding (NC) in the relay to increase the throughput. Due to the limitation of complexity, we only consider the binary multiuser NC (BMNC) in the relay. We study the BMNC matrix [in GF(2)] and propose several design criteria on the BMNC matrix to improve the symbol error probability (SEP) performance. Closed-form expressions of the SEP of the system are provided. Moreover, an upper bound of the SEP is also proposed to provide further insights into system performance. Then, BMNC matrices are designed to minimize error probabilities.

Performance Analysis of Pairwise Amplify-and-Forward Multi-Way Relay Networks

For the first time, the performance of pairwise amplify-and-forward multi-way relay networks (MWRNs) is studied. To this end, new end-to-end signal-to-noise ratio (e2e SNR) expression at an arbitrary source is first derived in closed-form, and thereby, an insightful statistical characterization is developed. In this context, tight closed-form approximations are derived for the cumulative distribution function, probability density function and moment generating function of the e2e SNR. Specifically, the conditional outage probability and the average bit error rate conditioned on error-free back-propagated successive interference cancellation are also derived in closed-form. Moreover, valuable insights into practical MWRN system-designing is obtained by deriving the fundamental diversity-multiplexing trade-off by employing the high SNR outage probability approximation.

Achieving full diversity and fast ML decoding via simple analog network coding for asynchronous two-way relay networks

In this paper, we propose a simple analog network coding (ANC) scheme for asynchronous two-way relay networks where two sources exchange information through the relay nodes. In our proposed scheme, we consider a wireless scenario with frequency selective fading channels. Orthogonal frequency-division multiplexing (OFDM) is implemented at the two sources and then the OFDM blocks are transmitted to the relay nodes in the first time slot. In the second time slot, at the relay nodes, the ANC that has a few simple operations are implemented on the received mixed signals and then the processed signals are broadcasted to the two sources to finish the information exchange. In this scheme, at each source, when recovering the designed information transmitted from another source, the received signals have the orthogonal space time block code (OSTBC) structure or the quasi-orthogonal space time block code (QOSTBC) structure on each subcarrier. By a proper power allocation, the two sources can achieve full spatial diversity and fast ML decoding without the requirement of symbol level synchronization. By the repetition across the subcarriers, multi-path diversity available in frequency selective fading channels can be also exploited. Moreover, the proposed ANC scheme is also valid for multi-way relay networks where multiple sources exchange information.