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里德-所罗门码（硬判决译码）与内码单奇偶校验码（Chase/Wagner软判决译码）的级联前向纠错方案。针对加性高斯白噪声信道下的二进制相移键控（BPSK）与四进制幅移键控（4-ASK）传输，考虑了符号交织器与量化信道输出的情况，推导了端到端误帧率与误比特率的解析表达式。将BPSK误码率与两种内码方案进行了比较：采用SPC分量码的二维乘积码和扩展汉明码。同时给出了单位记忆码间干扰信道下4-ASK的仿真结果。结果表明，各编码方案实现了相近的误码率，但单奇偶校验码具有最低复杂度并支持灵活速率适配。