Accumulate–Repeat–Accumulate Codes: Capacity-Achieving Ensembles of Systematic Codes for the Erasure Channel With Bounded Complexity

This paper introduces ensembles of systematic accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with bounded complexity, per information bit, of encoding and decoding. It also introduces symmetry properties which play a central role in the construction of new capacity-achieving ensembles for the BEC. The results here improve on the tradeoff between performance and complexity provided by previous constructions of capacity-achieving code ensembles defined on graphs. The superiority of ARA codes with moderate to large block length is exemplified by computer simulations which compare their performance with those of previously reported capacity-achieving ensembles of low-density parity-check (LDPC) and irregular repeat-accumulate (IRA) codes. ARA codes also have the advantage of being systematic.