Improved Bounds on the Decoding Failure Probability of Network Coding Over Multi-Source Multi-Relay Networks

Abstract

This letter considers a multi-source multi-relay network, in which relay nodes employ a coding scheme based on random linear network coding on source packets and generate coded packets. If a destination node collects enough coded packets, it can recover the packets of all source nodes. The links between source-to-relay nodes and relay-to-destination nodes are modeled as packet erasure channels. Improved bounds on the probability of decoding failure are presented, which are markedly close to simulation results and notably better than previous bounds. Examples demonstrate the tightness and usefulness of the new bounds over the old bounds.Index Terms-Network coding, sparse random matrices, probability of decoding failure, linear dependence.

Reliability of Relay Networks Under Random Linear Network Coding

“…Several efforts to analyse the performance RLNC applied to relay networks are present in the literature. Multiple-source, multiple-relay two-hop networks were studied in [11]- [13]. In [11], each source node was designed to transmit a single uncoded packet, while each relay node encoded packets it received into a single linear combination and forwarded it to the destination node.…”

“…More general scenarios involving sparse RLNC [14] were considered in [12], for which lower and upper bounds were proposed. More accurate bounds were subsequently derived in [13]. In both [12], [13] the degree of sparsity was determined by packet loss, which led to poor code performance in certain scenarios.…”

“…In both [12], [13] the degree of sparsity was determined by packet loss, which led to poor code performance in certain scenarios. Furthermore, it should be noted that in all three studies [11]- [13], only a single packet was assumed to be transmitted by any source or relay node, and the number of necessary relay nodes was set to be equal to the number of required coded transmissions. As a result, a large number of relay nodes was required to provide reliability, which is often impractical.…”

“…Another common assumption in [11]- [13] was that the source nodes transmit uncoded packets. Encoding at the source node was considered in [15] for a single-source single-relay network with a direct link between the source and destination nodes.…”

“…• 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. In addition, we generalise the approach of [11]- [13] by allowing each relay node to transmit multiple coded packets, thus resulting in a fewer relays to achieve reliable communication.…”