基于有限域构造的QC LDPC码编码器设计

为了降低准循环低密度奇偶校验（quasi-cyclic low-density parity-check， QC LDPC）码编码的复杂度，提出了一种利用近似满秩（approximate full rank, AFR）矩阵实现QC LDPC码的高效编码方案。基于有限域GF(q)乘群、加群构造出AFR校验矩阵，利用AFR矩阵可以快速得到其系统循环形式的生成矩阵。此方案不但可以实现线性化编码，而且编出的码都为系统码。仿真表明，该编码方案对于列重较小的QC LDPC码具有较好的通用性和实用价值。

Exploit of designing encoder for QC LDPC codes based on finite field approach

To reduce the complexity of encoder for QC LDPC codes, an efficient encoding scheme by using the approximate-full-rank (AFR) parity check matrix is proposed. The AFR matrix is constructed based on finite field approach and can be used to find the systematic generator matrix efficiently. The scheme can be used to encode systematic LDPC codes with linear encoding complexity. Simulations verify its generality and practicality for QC LDPC codes with small column weights.