Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation.

翻译：研究了采用外码KP4 Reed-Solomon码（硬判决译码）与内码单奇偶校验（SPC）码（Chase/Wagner软判决译码）的级联前向纠错技术。针对加性高斯白噪声信道，分别推导了采用二进制相移键控（BPSK）与四进制幅移键控（4-ASK）调制，并结合符号交织器与量化信道输出时的端到端误帧率与误比特率的解析表达式。将BPSK下的误码率与两种其他内码方案（采用SPC分量码的二维乘积码与扩展汉明码）进行了对比。同时给出了单位记忆码间干扰信道下4-ASK调制的仿真结果。结果表明，各编码方案实现了相近的误码率，但SPC码具有最低的复杂度，且支持灵活码率适配。