Accumulate repeat accumulate codes

An innovative channel coding scheme called "Accumulate Repeat Accumulate codes" (ARA) is proposed. ARA codes can be viewed as a subclass of Low Density Parity Check (LDPC) codes with fast encoder, and they have a projected graph or protograph representation. Using density evolution on their associated protographs, we find examples of rate 1/2 ARA codes with maximum variable node degree 5 for which a minimum bit SNR as low as 0.08 dB from channel capacity can be achieved as the block size goes to infinity. A family of high rate ARA codes with thresholds that stay uniformly close to their respective channel capacity thresholds are constructed. The ensemble weight distribution and ML threshold for rate 1/2 ARA codes were computed. For ARA with repeat 4, the ML threshold approaches within 0.005 dB of the ML threshold of random codes based on the existing tightest closed form bound.