Constructing LDPC codes from simple loop-free encoding modules

Inspired by recently proposed accumulate-repeat-accumulate (ARA) codes, in this paper we propose a construction method for LDPC codes using simple loop-free encoding modules. Such codes can be viewed as serial/parallel concatenations of simple modules such as accumulators, repetition codes, differentiators, and punctured single parity check codes. Examples are accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-accumulate-accumulate (ARAA) codes and accumulate-repeat-check-accumulate codes, and other variations. These codes constitute a subclass of LDPC codes with very fast encoder structure. They also have a projected graph or protograph representation that allows for high-speed decoder implementation. Based on density evolution, we show through some examples that low iterative decoding thresholds close to the channel capacity limits can be achieved with low maximum variable node degrees, as the block size goes to infinity. The decoding threshold in many examples outperforms that of the best known unstructured irregular LDPC codes constrained to have the same maximum node degree. Furthermore, by puncturing the accumulator modules, any desired higher rate codes can be obtained with thresholds that stay close to their respective channel capacity thresholds uniformly.