A New Non-Iterative Decoding Algorithm for the Erasure Channel : Comparisons with Enhanced Iterative Methods

This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a Multi-Guess Algorithm extended from the Guess Algorithm and a new algorithm -- the In-place Algorithm. The Multi-Guess Algorithm can push the limit to break the stopping sets. However, the performance of the Guess and the Multi-Guess Algorithm depend on the parity-check matrix of the code. Simulations show that we can decrease the frame error rate by several orders of magnitude using the Guess and the Multi-Guess Algorithms when the parity-check matrix of the code is sparse. The In-place Algorithm can obtain better performance even if the parity check matrix is dense. We consider the application of these algorithms in the implementation of multicast and broadcast techniques on the Internet. Using these algorithms, a user does not have to wait until the entire transmission has been received.