Sequential Decoding With Adaptive Reordering Of Codeword Trees

Decoding algorithms are investigated in which codeword trees are generated from an ordered list of parity checks. The order is computed from the received message, and low-density parity-check codes are used to help control the growth of the tree. Simulation results are given for the binary erasure and binary symmetric channels. They suggest that for small erasure probability, the method is computationally feasible at rates above the computational cutoff rate. 1 Summary Sequential decoding is a general method for decoding tree codes. The amount of computation depends on the channel noise, and the expected computation per decoded digit is finite only at code rates below &, the computational cutoff rate. In particular, a long burst of noise requires a great deal of computation to resolve. This leads one to consider adaptively reordering the codeword tree, that is, changing the order of the digits used to generate the tree. In this way, one can try to limit the occurrence and duration of bursts of noise. More generally, the goal of reordering the tree is to decrease the computation performed by the sequential decoder. The present scheme is a modification of standard sequential decoding, devised in an attempt to operate at rates greater than Ro.