[Paper Review] Short Message Noisy Network Coding with Rate Splitting

Ivana Marić, Dennis Hui|arXiv (Cornell University)|Mar 31, 2014

Cooperative Communication and Network Coding6 references3 citations

TL;DR

This paper proposes Short Message Noisy Network Coding with Rate Splitting (SNNC-RS), a novel relaying scheme that enhances performance in multi-relay networks by enabling decode-and-forward (DF) relays to partially cancel interference from noisy network coding (SNNC) relays through superposition coding. By splitting quantization indices and using rate splitting, the scheme reduces inter-relay interference, achieving higher achievable rates than conventional SNNC and mixed strategies, particularly in Gaussian two-relay channels where gains are demonstrated.

ABSTRACT

Short message noisy network coding with rate splitting (SNNC-RS) encoding strategy is presented. It has been shown by Hou and Kramer that mixed cooperative strategies in which relays in favorable positions perform decode-and-forward (DF) and the rest of the relays perform short message noisy network coding (SNNC) can outperform noisy network coding (NNC). Our proposed strategy further improves the rate performance of such mixed SNNC-DF cooperative strategy. In the proposed scheme, superposition coding is incorporated into the SNNC encoding in order to facilitate partial interference cancellation at DF relays, thereby increasing the overall rate. To demonstrate gains of the proposed SNNC-RS strategy, the achievable rate is analyzed for the discrete memoryless two-relay network with one DF relay and one SNNC-RS relay and compared to the case without rate-splitting. The obtained rate is evaluated in the Gaussian two-relay network and gains over the rate achieved without rate splitting are demonstrated.

Motivation & Objective

• To address the performance degradation in mixed cooperative strategies where SNNC relays cause uncancelable interference at DF relays.
• To improve end-to-end transmission rates in multi-relay networks by enabling partial interference cancellation at DF relays.
• To develop a practical encoding strategy that combines short message noisy network coding with rate splitting for enhanced spectral efficiency.
• To derive and evaluate an achievable rate for the proposed SNNC-RS scheme in discrete memoryless and Gaussian two-relay networks.

Proposed method

• Incorporates superposition coding into SNNC encoding by splitting the compression index at SNNC relays into two lower-rate components.
• Uses rate splitting to allow DF relays to decode one part of the quantization index, enabling partial cancellation of interference from SNNC relays.
• Applies backward decoding at the destination and relay nodes, relying on joint typicality and typical set enumeration for reliable message recovery.
• Derives an achievable rate region using standard information-theoretic bounding techniques, including Fourier-Motzkin elimination to eliminate auxiliary rates.
• Models the two-relay network with one relay using DF and the other using SNNC-RS, and derives mutual information constraints for reliable communication.
• Evaluates the scheme in the Gaussian channel case, comparing performance against SNNC and other baseline strategies.

Experimental results

Research questions

• RQ1 Can rate splitting in SNNC reduce inter-relay interference and improve end-to-end rate performance in multi-relay networks?
• RQ2 Does superposition coding at SNNC relays enable DF relays to decode and cancel partial interference, thereby increasing the achievable rate?
• RQ3 How does the achievable rate of SNNC-RS compare to conventional SNNC and mixed DF/SNNC strategies in a two-relay Gaussian channel?
• RQ4 What are the necessary and sufficient conditions on mutual information terms to ensure reliable decoding and rate improvement?
• RQ5 Is the rate gain from rate splitting preserved in practical Gaussian channels, and how significant are the gains?

Key findings

• The SNNC-RS scheme achieves higher achievable rates than conventional SNNC and mixed DF/SNNC strategies in the two-relay Gaussian channel, with demonstrated rate gains.
• Rate splitting does not reduce the SNNC rate in a single-relay channel, confirming that the scheme is compatible with single-hop scenarios.
• The derived achievable rate region for the discrete memoryless two-relay network includes constraints on mutual information terms involving quantized signals and relay decoding.
• In the Gaussian case, the scheme achieves a higher end-to-end rate by enabling partial interference cancellation at DF relays through superposition-coded quantization indices.
• The key rate-limiting condition is the mutual information inequality I(Ŷ₃; Y₃ | X̄X₃₀X₃₁Y₄) < I(X₃₀X₃₁; Y₄ | X̄), which ensures reliable decoding and prevents rate collapse.
• Fourier-Motzkin elimination yields a final rate bound that combines the rates from both relay paths and accounts for interference cancellation, demonstrating the scheme's optimality under the derived constraints.