Verification-Based Decoding with MAP Erasure Recovery

Verification-based decoding (VBD) is a simple yet powerful iterative (IT) decoding technique for codes operating on packets (vector-symbols) and channels that introduce packetwise errors. An example is given by the q-ary symmetric channel (qSC) for which a simple improvement of the VBD algorithm is proposed. It consists of performing a Gaussian elimination (GE)-based erasure decoding stage whenever VBD fails, i.e., whenever beta > 0 packets remain unverified. The modified decoder may recover the beta unverified packets with a complexity of O(beta(exp 3)) by making use of the inherent code structure. Numerical results on low-density parity-check (LDPC) codes and analytical expressions for the block error probability of linear random block codes show the benefit of the proposed algorithm.