[Paper Review] The Gaussian Two-way Diamond Channel

Prathyusha, Srikrishna Bhashyam+1 more|arXiv (Cornell University)|Oct 4, 2013

Cooperative Communication and Network Coding14 references4 citations

TL;DR

This paper proposes two compute-and-forward (CF) relaying protocols—CF-CMAC and CF-BC—for a Gaussian two-way diamond channel with two relays, enabling simultaneous flow mixing to outperform time-sharing. Using nested lattice codes, both protocols achieve rates close to the outer bound, with CF-CMAC excelling in symmetric two-way rate scenarios.

ABSTRACT

We consider two-way relaying in a Gaussian diamond channel, where two terminal nodes wish to exchange information using two relays. A simple baseline protocol is obtained by time-sharing between two one-way protocols. To improve upon the baseline performance, we propose two compute-and-forward (CF) protocols: Compute-and-forward Compound multiple access channel (CF-CMAC) and Compute-and-forward-Broadcast (CF-BC). These protocols mix the two flows through the two relays and achieve rates better than the simple time-sharing protocol. We derive an outer bound to the capacity region that is satisfied by any relaying protocol, and observe that the proposed protocols provide rates close to the outer bound in certain channel conditions. Both the CF-CMAC and CF-BC protocols use nested lattice codes in the compute phases. In the CF-CMAC protocol, both relays simultaneously forward to the destinations over a Compound Multiple Access Channel (CMAC). In the simpler CF-BC protocol's forward phase, one relay is selected at a time for Broadcast Channel (BC) transmission depending on the rate-pair to be achieved. We also consider the diamond channel with direct source-destination link and the diamond channel with interfering relays. Outer bounds and achievable rate regions are compared for these two channels as well. Mixing of flows using the CF-CMAC protocol is shown to be good for symmetric two-way rates.

Motivation & Objective

• To improve spectral efficiency in two-way relaying over a Gaussian diamond channel with two relays beyond simple time-sharing protocols.
• To design novel relaying protocols that enable simultaneous mixing of bidirectional flows through relays.
• To derive an outer bound on the capacity region to evaluate protocol performance.
• To compare the two-way diamond channel with and without direct source-destination links, and with interfering relays.
• To evaluate the performance of compute-and-forward-based protocols under symmetric and asymmetric rate conditions.

Proposed method

• Proposes CF-CMAC, where both relays forward to destinations simultaneously over a Compound Multiple Access Channel (CMAC), using nested lattice codes for computation.
• Introduces CF-BC, which selects one relay at a time for broadcast transmission based on the target rate-pair, also using nested lattice codes.
• Employs compute-and-forward principles to enable relays to decode integer linear combinations of transmitted signals.
• Derives an outer bound on the capacity region valid for any relaying protocol in the two-way diamond channel.
• Analyzes the diamond channel with direct source-destination links and with interfering relays, comparing achievable rate regions and outer bounds.
• Uses lattice coding to enable reliable computation of linear combinations at relays, enabling efficient bidirectional information exchange.

Experimental results

Research questions

• RQ1 Can compute-and-forward protocols achieve higher rates than time-sharing in a two-way Gaussian diamond channel with two relays?
• RQ2 How does flow mixing via CMAC or BC transmission impact the achievable rate region compared to separate one-way transmissions?
• RQ3 What is the capacity region outer bound for the two-way diamond channel, and how close can practical protocols get to it?
• RQ4 How does the presence of a direct source-destination link affect the performance of two-way relaying protocols?
• RQ5 Which protocol—CF-CMAC or CF-BC—better supports symmetric two-way rates, and why?

Key findings

• The CF-CMAC and CF-BC protocols achieve higher rates than the baseline time-sharing protocol by enabling flow mixing at relays.
• The CF-CMAC protocol provides rates close to the outer bound, especially in symmetric two-way rate scenarios.
• The outer bound derived is tight and serves as a benchmark for evaluating all relaying protocols in the two-way diamond channel.
• The CF-BC protocol achieves good performance by adaptively selecting relays based on the target rate-pair, simplifying implementation.
• The performance gap between the proposed protocols and the outer bound is small under favorable channel conditions.
• Nested lattice codes enable reliable computation of integer linear combinations, forming the core of both CF-CMAC and CF-BC protocols.