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