Transversal GRAND for Network Coded Data

This paper considers a transmitter, which uses random linear coding (RLC) to encode data packets. The generated coded packets are broadcast to one or more receivers. A receiver can recover the data packets if it gathers a sufficient number of coded packets. We assume that the receiver does not abandon its efforts to recover the data packets if RLC decoding has been unsuccessful; instead, it employs syndrome decoding in an effort to repair erroneously received coded packets before it attempts RLC decoding again. A key assumption of most decoding techniques, including syndrome decoding, is that errors are independently and identically distributed within the received coded packets. Motivated by the ‘guessing random additive noise decoding’ (GRAND) framework, we develop transversal GRAND: an algorithm that exploits statistical dependence in the occurrence of errors, complements RLC decoding and achieves a gain over syndrome decoding, in terms of the probability that the receiver will recover the original data packets.