Construction of a multi-level Hierarchical Quasi-Cyclic matrix with layered permutation for partially-parallel LDPC decoders

Abstract

Implementation of partially-parallel (Low-Density Parity-Check) LDPC decoders using unstructured random matrices is very complex and requires huge hardware resources. To alleviate the complexity and minimize resource requirements, structured LDPC matrices are used. This paper presents a novel technique for constructing a multi-level Hierarchical Quasi-Cyclic (HQC) structured matrix for LDPC decoders. A unique multi-level structure of the proposed matrix provides flexibility in generating different code lengths and code rates for various applications such as WiMAX, WLAN and DVB-S2. In addition, different combinations of permuted sub-matrices are inserted in layers, to provide virtual randomness in the LDPC matrix. Simulations results show that the HQC matrices generated using the proposed technique have a marginal loss of less than 0.1 dB at a bit error rate (BER) performance of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , compared to unstructured random matrices. The proposed matrix therefore provides BER performance close to random matrices while significantly reducing hardware resource requirements.