Construction of finite length irregular repeat accumulate codes

We study the performance of finite length regular and irregular repeat accumulate (RA) codes, whose Tanner graphs are constructed semi-randomly and satisfy one of the following criteria: (a) the graph is free of cycles up to have at least _ external edges (________ and _ are design parameters). We derive an upper bound on the bit error probability of random RA codes under maximum likelihood decoding. For short block lengths, it is found that the performance under belief propagation decoding of the semi-random regular RA ensemble is superior to the performance of the random ensemble under maximum likelihood decoding, and that it is comparable to the best known low density parity check codes, with comparable girth conditioning and block length. As for large block lengths, the performance of the semi-random irregular RA ensemble is superior to the performance of the random ensemble, but remains inferior to that of low density parity check codes with comparable graph conditioning and block length.