Abstract: LDPC-SPC codes is introduced. LDPC-SPC codes choose LDPC codes as horizontal codes and single parity check (SPC) codes as vertical codes. Some decoding algorithms are also given, including algorithms based on hard decision and soft decision. By these algorithms, each bit of every LDPC code can get extrinsic messages from other LDPC code words to help LDPC decoder decode successfully. Based on the LDPC code which is half rate and 8064 bits long, a LDPC-SPC code is constructed. Simulation results show that the LDPC-SPC codes can lower the error floor of the LDPC codes and have better BER (Bit Error Ratio) performance. When BER is 10-7, the performance of the LDPC-SPC codes is 0.3 dB better than the LDPC codes.

Key words: low density parity check codes, single parity check codes, product codes, error floor

摘要： 提出了一种LDPC-SPC乘积码。该乘积码以低密度奇偶校验（low density parity check，LDPC）码为水平码，单奇偶校验（single parity check，SPC）码为垂直码。给出了LDPC-SPC乘积码的硬判决译码算法和软判决译码算法。利用这些译码算法，LDPC-SPC乘积码能够在不同的LDPC码字之间交换比特置信度信息，完成译码。仿真结果表明，以长度8064 bit，码率1/2的LDPC码为基础构造的LDPC-SPC乘积码，能够有效地降低该LDPC码的误码平层，并且在误码率为10-7时，乘积码取得了超过LDPC码0.3 dB的性能优势。

关键词: 低密度奇偶校验码, 单奇偶校验码, 乘积码, 误码平层