Performance analysis of random linear network coding in two-source single-relay networks

Abstract

This paper considers the multiple-access relay channel in a setting where two source nodes transmit packets to a destination node, both directly and via a relay node, over packet erasure channels. Intra-session network coding is used at the source nodes and inter-session network coding is employed at the relay node to combine the recovered source packets of both source nodes. In this work, we investigate the performance of the network-coded system in terms of the probability that the destination node will successfully recover the source packets of the two source nodes. We build our analysis on fundamental probability expressions for random matrices over finite fields and we derive upper bounds on the system performance for the case of systematic and non-systematic network coding. Simulation results show that the upper bounds are very tight and accurately predict the decoding probability at the destination node. Our analysis also exposes the clear benefits of systematic network coding at the source nodes compared to non-systematic transmission.Index Terms-Network coding, fountain coding, multiple access relay channel, decoding probability, block angular matrix.

Reliability of Relay Networks Under Random Linear Network Coding

“…We now compare the throughput of the proposed scheme with other RLNC-based coding and relaying strategies. We consider three schemes: RF, analysed in this work, DF, briefly described in Section I and analysed in [18], [19] for a single-relay network, and the RF strategy in which coding is performed only at the relay nodes, which will be referred to as Code-and-Forward (CF). The decoding probability of the CF scheme can be approximated by the same simplified bound (27) as for the RF scheme by letting N S = K and assuming no coding at S, thus resulting in the following bound:…”

“…The analysis, however, was performed assuming an infinitely large field size, which in practice is limited [16], [17]. A finite field size was considered in [18], where the relay node attempts the decoding of the source message, followed by recoding. Using the terminology of relay networks, such scheme can be referred to as Decode-and-Forward (DF).…”

“…Using the terminology of relay networks, such scheme can be referred to as Decode-and-Forward (DF). However, the analysis in [18] was based on the assumption that the relay and destination nodes receive uncorrelated subsets of packets from the source. As a result, the derived performance bounds were accurate only under certain network scenarios.…”

“…• We generalise the single-relay scenario considered previously in [18], [19] to an arbitrary number of relays. In contrast to [11]- [13], we enable encoding at the source node to further mitigate packet loss.…”

“…We also propose an approximation of the bound, which is accurate for networks with a sufficiently large number of relays. • Compared with the DF scheme employed in [18], [19], we consider a different relaying strategy, whereby the relay nodes do not attempt to decode, but simply recode the packets they receive from the source. Once again employing the terminology of relay networks, we call such scheme Recode-and-Forward (RF).…”