Error Correction for Rateless Codes

Rateless codes for erasure channels were recently proposed by Luby with very efficient coding and decoding schemes. However, designing an efficient decoding rateless code for binary error channel (BEC), still remains a difficult problem. In this work we propose a rateless decoding algorithm for the BEC using a coding matrix G with a high level of sparsity. The distribution used to generate the elements of G can be designed to give with high probability a sub-matrix B of G with a sparse inverse leading to an efficient way of computing the syndrome. We show that our method is able to update the syndrome from a previous evaluation. However to obtain the error signal we still have to solve a linear programming problem in R.