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We consider a transmitter that encodes data packets using network coding andbroadcasts coded packets. A receiver employing network decoding recovers thedata packets if a sufficient number of error-free coded packets are gathered.The receiver does not abandon its efforts to recover the data packets ifnetwork decoding is unsuccessful; instead, it employs syndrome decoding (SD) inan effort to repair erroneously received coded packets, and then reattemptsnetwork decoding. Most decoding techniques, including SD, assume that errorsare independently and identically distributed within received coded packets.Motivated by the guessing random additive noise decoding (GRAND) framework, wepropose transversal GRAND (T-GRAND): an algorithm that exploits statisticaldependence in the occurrence of errors, complements network decoding andrecovers all data packets with a higher probability than SD. T-GRAND examineserror vectors in order of their likelihood of occurring and altering thetransmitted packets. Calculation and sorting of the likelihood values of allerror vectors is a simple but computationally expensive process. To reduce thecomplexity of T-GRAND, we take advantage of the properties of the likelihoodfunction and develop an efficient method, which identifies the most likelyerror vectors without computing and ordering their likelihoods.

Guessing Random Additive Noise Decoding of Network Coded Data Transmitted over Burst Error Channels