Recent Results on Capacity-Achieving Codes for the Erasure Channel with Bounded Complexity

The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with bounded complexity (per information bit). It also introduces symmetry properties which play a central role in the construction of various capacity-achieving ensembles for the BEC. The results improve on the tradeoff between performance and complexity provided by the first capacity-achieving ensembles of irregular repeat-accumulate (IRA) codes with bounded complexity (constructed by Pfister, Sason and Urbanke). The superiority of ARA codes with moderate to large block lengths is exemplified by computer simulations comparing their performance with those of previously reported capacity-achieving ensembles of LDPC and IRA codes. ARA codes also have the advantage of being systematic.