Random linear network error correction coding

Abstract

Random linear network coding is feasible for noncoherent networks without errors, and its performance analysis is very important in theory and applications. This random method also can be applied to network error correction. That is, each node (maybe the source node) randomly and uniformly picks the local encoding coefficients from the base field for each outgoing channel, which are used to construct extended global encoding kernels and encode the received messages. That is, all local coding coefficients for linear network error correction (LNEC) coding are independently and uniformly distributed random variables taking values in the base field. Further, the LNEC codes constructed by this method are called random LNEC codes. For this random linear network error correction coding, we have to consider two aspects, information transmission and error correction, in order to analyze its performance. In this chapter, we will investigate the performance of random LNEC codes by estimating upper bounds on some failure probabilities.