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

Abstract

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.

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

“…Using (22), the exact probability of two error events in an AF MWRN can be expressed as (see (23)) where m is the decoding order difference between the two users that are incorrectly decoded. (23) represents the probability that a user incorrectly decodes the message of exactly 2 users in an L-user AF MWRN.…”

A Multiway Relay Channel With Balanced Sources

“…In other words, R(p) is the Slepian-Wolf rate region without the total sum-rate constraint. Intuitively, the additional sumrate constraint in (7) does not play a role in R(p) and Theorem 2 because user always has its own source data W as side information. The omission of this constraint is an important characteristic of the rate region R(p) that shapes much of the following discussion.…”

“…We call a cell (K i , s ) positive if s ∈ K i and negative otherwise. 7 Lemma 10: In each and every column in Table I, Proof: The table has |S| columns and Lemma 10 holds for every column.…”

“…In Section II, we present lower and upper bounds on the optimal source-channel rate that hold for any source and L ≥ 2 users. The upper bound (i.e., achievability) is proved using a standalone distributed source code proposed by Timo et al [7] together with a standalone functional-decode-forward channel code by Ong et al [2].…”

“…positive and negative cells respectively.Proof: Consider an arbitrary column s ∈ S. Recall that there are L−1 k−1 ways of selecting (k − 1) unordered elements from the set [1, L]\{s }. The union of each such selection with {s } forms a subset K i such that |K| = k and K i s ,7 The terms positive and negative refer to the sign of the coefficient fraction in Js (K i ), and not to the sign of I K i . so it follows that the column has L−1 k−1 positive cells.…”