We present two sequences of ensembles of non-systematic irregular
repeat-accumulate codes which asymptotically (as their block length tends to
infinity) achieve capacity on the binary erasure channel (BEC) with bounded
complexity per information bit. This is in contrast to all previous
constructions of capacity-achieving sequences of ensembles whose complexity
grows at least like the log of the inverse of the gap (in rate) to capacity.
The new bounded complexity result is achieved by puncturing bits, and allowing
in this way a sufficient number of state nodes in the Tanner graph representing
the codes. We also derive an information-theoretic lower bound on the decoding
complexity of randomly punctured codes on graphs. The bound holds for every
memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information
Theor