[Paper Review] Network Coded Transmission of Fountain Codes over Cooperative Relay Networks

Ernest Kurniawan, Sumei Sun+2 more|arXiv (Cornell University)|May 14, 2010

Cooperative Communication and Network Coding9 references4 citations

TL;DR

This paper proposes a network-coded fountain code transmission scheme for cooperative relay networks that improves throughput by enabling the source to send partial information about the next message block during current transmission. By applying digital or analog network coding over erasure and Rayleigh fading channels, the scheme reduces required transmissions—especially in low SNR regimes—demonstrating superior performance over direct and naive relaying methods.

ABSTRACT

In this paper, a transmission strategy of fountain codes over cooperative relay networks is proposed. When more than one relay nodes are available, we apply network coding to fountain-coded packets. By doing this, partial information is made available to the destination node about the upcoming message block. It is therefore able to reduce the required number of transmissions over erasure channels, hence increasing the effective throughput. Its application to wireless channels with Rayleigh fading and AWGN noise is also analysed, whereby the role of analogue network coding and optimal weight selection is demonstrated.

Motivation & Objective

• To address the increased complexity in fountain code transmission over multiple relay networks.
• To reduce the number of required transmissions in erasure and fading channels by exploiting partial information about upcoming blocks.
• To develop a scalable transmission strategy that integrates network coding with fountain codes for cooperative relay systems.
• To analyze performance in both erasure and wireless Rayleigh fading channels with practical power allocation.
• To demonstrate improved effective throughput through numerical evaluation under realistic channel conditions.

Proposed method

• Applies digital network coding to fountain-encoded packets of two consecutive message blocks in erasure channels, allowing the source to transmit combined information.
• Uses random linear fountain coding with degree distribution ρ(d) ≈ C_d^K / 2^K for generating encoded packets over GF(2).
• Employs analog network coding with optimal power allocation in wireless Rayleigh fading channels, modeling channel gains as independent Rayleigh-distributed variables.
• Introduces a two-phase transmission model: phase one for current block, phase two for relaying partial information about the next block.
• Derives the probability of successful decoding as a function of received packets using the CDF F(N) = ∏_{i=0}^{K-1} (1 - 2^{i-N}) for N ≥ K.
• Analyzes the capacity region of the scheme by varying the transmission rate ratio α between current and next block phases, identifying optimal operating points on the boundary.

Experimental results

Research questions

• RQ1 How can network coding be integrated with fountain codes to reduce the number of transmissions in cooperative relay networks?
• RQ2 What is the impact of partial information exchange about the next message block on the effective throughput of fountain-coded transmissions?
• RQ3 How does the proposed scheme perform in Rayleigh fading channels compared to conventional relaying and direct transmission?
• RQ4 What is the optimal power allocation and transmission rate ratio (α) that maximizes throughput in analog network coding-based implementation?
• RQ5 Can the scheme achieve better performance than naive relaying in low SNR regimes, and why?

Key findings

• The proposed network-coded scheme reduces the average number of required transmissions compared to direct transmission and naive relaying, particularly in low SNR regimes.
• The scheme achieves a positive probability of decoding in fewer than K transmissions due to partial information from previous blocks.
• In Rayleigh fading channels, the scheme outperforms both direct and naive relaying, with the performance gap widening in low SNR conditions.
• The sum rate capacity increases with the transmission rate ratio α, and optimal performance is achieved when operating on the boundary of the capacity region.
• The variance in required transmissions is higher than in baseline schemes, indicating suitability for non-delay-constrained applications.
• Numerical results confirm that the scheme improves effective throughput by enabling early delivery of partial information about the next message block through network coding.