Transversal GRAND for Network Coded Data

TL;DR

This paper introduces transversal GRAND, a decoding algorithm that leverages error dependence to improve the recovery probability of data packets in network coding, enhancing traditional syndrome decoding methods.

Contribution

It proposes a novel transversal GRAND algorithm that exploits error dependence, providing a significant improvement over existing syndrome decoding techniques.

Findings

Transversal GRAND outperforms syndrome decoding in error recovery probability.

The algorithm effectively exploits statistical dependence in errors.

Simulation results demonstrate improved decoding success rates.

Abstract

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.