1 research outputs found
Block Network Error Control Codes and Syndrome-based Complete Maximum Likelihood Decoding
In this paper, network error control coding is studied for robust and
efficient multicast in a directed acyclic network with imperfect links. The
block network error control coding framework, BNEC, is presented and the
capability of the scheme to correct a mixture of symbol errors and packet
erasures and to detect symbol errors is studied. The idea of syndrome-based
decoding and error detection is introduced for BNEC, which removes the effect
of input data and hence decreases the complexity. Next, an efficient
three-stage syndrome-based BNEC decoding scheme for network error correction is
proposed, in which prior to finding the error values, the position of the edge
errors are identified based on the error spaces at the receivers. In addition
to bounded-distance decoding schemes for error correction up to the refined
Singleton bound, a complete decoding scheme for BNEC is also introduced.
Specifically, it is shown that using the proposed syndrome-based complete
decoding, a network error correcting code with redundancy order d for receiver
t, can correct d-1 random additive errors with a probability sufficiently close
to 1, if the field size is sufficiently large. Also, a complete maximum
likelihood decoding scheme for BNEC is proposed. As the probability of error in
different network edges is not equal in general, and given the equivalency of
certain edge errors within the network at a particular receiver, the number of
edge errors, assessed in the refined Singleton bound, is not a sufficient
statistic for ML decoding