Block network error control codes and syndrome-based maximum likelihood decoding

The block network error control coding, BNEC, is presented to combat error and erasure for multicast in directed acyclic networks. Aiming at reducing complexity, BNEC syndrome-based decoding and detection is introduced. Next, we propose a three-stage syndrome-based BNEC decoding, comprising error detection, finding error positions and error values. Besides considering bounded-distance decoding for error correction up to refined Singleton bound, we present BNEC complete decoding and show that, a code with redundancy order delta_t for receiver t, corrects delta_t-1 errors with a probability approaching 1, for a sufficiently large field size. Also, complete maximum likelihood BNEC decoding is proposed. As probability of error in different network edges is not equal in general, the number of edge errors, assessed in Singleton bound, is not a sufficient statistic for ML decoding.