Accumulate Repeat Accumulate Check Accumulate Codes

In this paper, a novel accumulate-repeat-accumulate-check-accumulate (ARACA) code is proposed as a subclass of protograph-based low-density parity-check (LDPC) codes. The key feature of the proposed ARACA code is represented by the outer connection doping in the protograph. This feature can provide the linear minimum distance growth (LMDG) property at a good iterative decoding threshold while maintaining an efficient encoder structure. The effect of the outer connection doping on the typical minimum distance, the iterative decoding threshold, and the LMDG property is discussed and analyzed by comparing case examples and using the asymptotic protograph ensemble weight enumerator. Some good ARACA code protographs are provided for a wide range of code rates. In addition, an efficient and universal encoding procedure and the corresponding encoder structure are provided for them. The performance of the proposed ARACA code is evaluated and compared with well-known good LDPC codes. The simulation results confirm the superiority of the proposed ARACA codes in terms of encoding complexity and frame error rate performance, especially at low-rates in an ultra-reliable regime.