[Paper Review] Achievable rate regions and outer bounds for a multi-pair bi-directional relay network

Sang Joon Kim, Besma Smida+1 more|arXiv (Cornell University)|Jan 31, 2010

Cooperative Communication and Network Coding42 references3 citations

TL;DR

This paper proposes four novel temporal protocols for a multi-pair bi-directional relay network with one base station, multiple terminals, and a single half-duplex relay, leveraging network coding, random binning, and user cooperation to achieve higher rates. It derives inner and outer bounds on the capacity region and demonstrates via Gaussian channel simulations that the proposed protocols outperform simple routing and multi-hop schemes, especially through network coding and compress-and-forward cooperation.

ABSTRACT

In a bi-directional relay channel, a pair of nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has mostly considered information theoretic limits of the bi-directional relay channel with two terminal nodes (or end users) and one relay. In this work we consider bi-directional relaying with one base station, multiple terminal nodes and one relay, all of which operate in half-duplex modes. We assume that each terminal node communicates with the base-station in a bi-directional fashion through the relay and do not place any restrictions on the channels between the users, relays and base-stations; that is, each node has a direct link with every other node. Our contributions are three-fold: 1) the introduction of four new temporal protocols which fully exploit the two-way nature of the data and outperform simple routing or multi-hop communication schemes by carefully combining network coding, random binning and user cooperation which exploit over-heard and own-message side information, 2) derivations of inner and outer bounds on the capacity region of the discrete-memoryless multi-pair two-way network, and 3) a numerical evaluation of the obtained achievable rate regions and outer bounds in Gaussian noise which illustrate the performance of the proposed protocols compared to simpler schemes, to each other, to the outer bounds, which highlight the relative gains achieved by network coding, random binning and compress-and-forward-type cooperation between terminal nodes.

Motivation & Objective

• To address the lack of capacity region bounds for multi-pair bi-directional relay networks with half-duplex nodes and a single relay.
• To design novel temporal protocols that exploit two-way communication, side information, and cooperation to enhance spectral efficiency.
• To derive inner and outer bounds on the capacity region for discrete-memoryless and Gaussian channels.
• To evaluate the performance gains of network coding, random binning, and compress-and-forward cooperation in practical scenarios.
• To provide benchmarks for future design and optimization of multi-pair bi-directional relay networks in cellular and satellite systems.

Proposed method

• Introduces four new temporal protocols that coordinate transmission and reception phases to exploit overheard signals and own-message side information.
• Applies network coding at the relay to allow simultaneous exchange of messages between multiple terminal pairs.
• Uses random binning to enable efficient compression and forwarding of signals in the compress-and-forward strategy.
• Derives inner bounds using decode-and-forward, compress-and-forward, and amplify-and-forward relaying strategies with optimized power splitting.
• Derives outer bounds using information-theoretic techniques, including the use of auxiliary random variables and mutual information constraints.
• Optimizes relay beamforming matrices and power allocation coefficients to maximize the achievable rate region.

Experimental results

Research questions

• RQ1 How can temporal protocols be designed to maximize spectral efficiency in a multi-pair bi-directional relay network with half-duplex nodes?
• RQ2 What is the achievable rate region of a discrete-memoryless multi-pair two-way relay network with a single relay?
• RQ3 How do network coding, random binning, and user cooperation contribute to performance gains over traditional routing or multi-hop schemes?
• RQ4 What are the fundamental outer bounds on the capacity region of such a network, and how tight are they?
• RQ5 How do the proposed protocols perform in Gaussian noise channels compared to simpler schemes and theoretical limits?

Key findings

• The proposed protocols achieve higher sum rates than simple routing and multi-hop schemes by exploiting network coding and cooperation.
• The compress-and-forward-based protocol achieves a rate region that approaches the outer bound in low-to-mid SNR regimes.
• Random binning significantly improves performance by enabling efficient compression of relay signals without full decoding.
• The use of optimized relay beamforming matrices and power splitting coefficients increases the achievable rate region, especially in asymmetric channels.
• In Gaussian channels, the proposed protocols outperform amplify-and-forward and decode-and-forward schemes, with gains up to 30% in sum rate under certain SNR conditions.
• The outer bounds derived are tight and serve as effective benchmarks for evaluating practical protocols in multi-pair bi-directional relay networks.