Distributed decoding of convolutional network error correction codes

The decoding problem is addressed in this paper for the scenario that convolutional codes are employed at the source node of the network with linear or convolutional network coding for error correction. Since network errors may disperse or neutralize due to network coding, decoding cannot be done at sink nodes merely based on the minimum Hamming distance between the received and sent sequence. Source decoding is proposed in previous work by multiplying the inverse of the network transfer matrix, where the inverse is hard to compute and sometimes the result is noncausal. Starting from the Maximum A Posteriori (MAP) decoding criterion, we find that it is equivalent to the minimum error weight under our model. Inspired by classical Viterbi algorithm, we propose a Viterbi-like decoding algorithm based on the minimum error weight of combined error vectors, which can be carried out directly at sink nodes and can correct any network errors within the capability of convolutional network error correction codes (CNECC). We then study the distributed decoding of CNECC and give a sufficient condition that is able to realize such a decoding process with the proposed algorithm.