[Paper Review] Decode-Forward Transmission for the Two-Way Relay Channels

Ahmad Abu Al Haija, Peng Zhong+1 more|arXiv (Cornell University)|Apr 28, 2015

Cooperative Communication and Network Coding10 references3 citations

TL;DR

This paper proposes a composite decode-forward (DF) relaying scheme for two-way relay channels in both full- and half-duplex modes, combining coherent relaying, independent relaying, and partial relaying to maximize the achievable rate region. The key contribution is identifying closed-form link regimes where the composite scheme strictly outperforms time-sharing between constituent techniques, enabling adaptive, optimal resource allocation based on channel conditions.

ABSTRACT

We propose composite decode-forward (DF) schemes for the two-way relay channel in both the full- and half-duplex modes by combining coherent relaying, independent relaying and partial relaying strategies. For the full-duplex mode, the relay partially decodes each user's information in each block and forwards this partial information coherently with the source user to the destination user in the next block as in block Markov coding. In addition, the relay independently broadcasts a binning index of both users' decoded information parts in the next block as in independent network coding. Each technique has a different impact on the relay power usage and the rate region. We further analyze in detail the independent partial DF scheme and derive in closed-form link regimes when this scheme achieves a strictly larger rate region than just time-sharing between its constituent techniques, direct transmission and independent DF relaying, and when it reduces to a simpler scheme. For the half-duplex mode, we propose a 6-phase time-division scheme that incorporates all considered relaying techniques and uses joint decoding simultaneously over all receiving phases. Numerical results show significant rate gains over existing DF schemes, obtained by performing link adaptation of the composite scheme based on the identified link regimes.

Motivation & Objective

• To design a composite decode-forward relaying strategy that unifies coherent, independent, and partial relaying techniques for two-way relay channels.
• To identify closed-form conditions under which the composite scheme achieves a strictly larger rate region than time-sharing between constituent schemes.
• To enable adaptive, link-condition-based resource allocation by determining when certain relaying techniques can be deactivated without performance loss.
• To extend the framework to both full-duplex and half-duplex modes, including a 6-phase time-division scheme for half-duplex with joint decoding.
• To provide a theoretical foundation for practical relay selection and power allocation by mapping performance gains to specific channel regimes.

Proposed method

• In full-duplex mode, the relay performs partial decoding of each user's signal in a block, forwards the decoded part coherently with the source in the next block using block Markov coding.
• The relay independently broadcasts a binning index of both users' decoded parts in the next block, leveraging independent network coding principles.
• A 6-phase time-division scheme is proposed for half-duplex mode, incorporating all relaying techniques and enabling joint decoding across all receiving phases.
• The achievable rate region is derived using mutual information expressions and power allocation variables γ₁ and γ₂, representing power allocated to coherent and independent relaying.
• Closed-form expressions for critical thresholds (e.g., γ₂^max) are derived to determine when the composite scheme outperforms time-sharing or reduces to simpler schemes.
• Theoretical analysis maps performance gains to link strength regimes, identifying conditions under which partial DF or independent DF provides strict improvements.

Experimental results

Research questions

• RQ1 Under what channel strength regimes does the composite decode-forward scheme strictly outperform time-sharing between direct transmission and independent DF relaying?
• RQ2 When does the independent partial DF scheme reduce to a simpler scheme, such as full DF or direct transmission?
• RQ3 How can the relay optimally allocate power between coherent, independent, and partial relaying to maximize the rate region?
• RQ4 What is the impact of interference management through partial decoding on the overall performance of the two-way relay channel?
• RQ5 How does joint decoding over multiple phases in a 6-phase half-duplex scheme improve the rate region compared to conventional 4-phase schemes?

Key findings

• The composite scheme achieves a strictly larger rate region than time-sharing between direct transmission and independent DF relaying in specific link regimes defined by channel gains and power constraints.
• The independent partial DF scheme reduces to a simpler scheme when the relay's channel to one user is sufficiently weak, making full DF or direct transmission optimal.
• For full-duplex mode, the optimal power allocation is γ₁ = 0 and γ₂ = γ₂^max, where γ₂^max is derived in closed form based on channel gains and power ratios.
• In half-duplex mode, the 6-phase scheme with joint decoding achieves significant rate gains over existing DF schemes, particularly in regimes where partial decoding reduces interference.
• The rate region is maximized when γ₁^* = 0 and γ₂^* = 0 for certain channel conditions, indicating that full DF or direct transmission alone is optimal.
• The paper identifies that the composite scheme outperforms time-sharing when C(g_r1²P₁ + g_r2²P₂) < C(g_21²P₁) + C(g_12²P₂), a condition tied to the relative strength of relay-to-user links.