On Quasi-Cyclic Repeat-Accumulate Codes

Repeat-Accumulate (RA) codes, consisting of a simple binary repetition followed by a permutation and an accumulator, are converting into quasi-cyclic codes with multiple cross-linked cycles. The algebraic heuristics are used to design codes with an explicit algebraic permutation yielding desirable graph properties. Recursive graph constructions techniques are given for the construction of very long codes. Simulation results for codes of rate 1/3 and 1/4 demonstrate that these algebraic RA codes can compete with RA codes using pseudo-random permutations and outperform the random codes at high SNR.