Extended Low Rank Parity Check Codes and Their Efficient Decoding for Multisource Wireless Sensor Networks

In this paper, we consider a multisource network transmitting information through relays to a base station using Network Coding. We design a model for this scenario and use the rank metric to address the problem of packet errors (caused for example by a malicious user or a defective node). We introduce a new family of codes, the extended LRPC codes, that are very well suited to this model and extensively use the fact that the information comes from multiple sources to decode. They therefore improve the communication reliability compared to classical LRPC codes and Gabidulin codes. We provide a theoretical analysis of their decoding failure probability, both in a one source and multisource scenario, as well as simulation results confirming our analysis.