Performance Analysis of Fountain Codes in Multihop Relay Networks

Fountain codes have been extensively employed in delay-tolerant networks (DTNs) due to their near-capacity performance with very low encoding/decoding complexity. A decode-and-forward-based relaying strategy is ideally suited for fountain codes in such networks due to its ability to recover the source message from any subset of encoded packets with sufficient mutual information. However, the unreliable nature of the channel may lead to the starvation of some subsequent nodes with good channel conditions. By cooperation among the forwarding nodes, the overall latency of such networks can be alleviated. This paper analytically quantifies the latency of both cooperative and conventional fountain-coded delay-tolerant multihop networks by deriving the exact closed-form equations for the channel usage. The overall latency suffered by such networks forces conservation of the end-to-end delay, particularly for real-time applications. However, by constraining the total delay (the number of encoded transmissions), the performance of fountain codes deteriorates due to the lack of encoded packets for retrieving the entire source message. This degradation can be gauged by the average packet loss experienced with partial decoding of fountain codes. The exact closed-form equation for the average packet loss based on the channel usage for such delay-constrained networks (DCNs) is derived in this paper. The tradeoff between average delay and the channel usage required for successful decoding is also analyzed. It is observed that the average packet loss can be minimized by optimizing the total delay based on the performance across each link. Finally, the pros and cons of using DCNs and DTNs employing fountain codes are evaluated, and theoretical grounding to the simulated results is provided.