In this paper, soft-decision (SD) decoders of permutation trellis code (PTC) with $M$-ary frequency shift keying are designed using three optimization algorithms and presented in four decoding schemes. In a concatenated code such as PTC, the Viterbi decoder for the outer convolutional code provides maximum likelihood decoding. Hence, the error correction performance is dependent on the decoding scheme used for the inner code. Due to the structure of the encoder with the modulation scheme, the channel output can be interpreted as an assignment problem. SD decoding can then be designed accordingly, using the presented, low-complexity optimization-based schemes. The bit error rate (BER) performance of the schemes are simulated in an additive white Gaussian noise (AWGN) and powerline communication (PLC) channel. The complexities of the schemes are also presented. The performance of the SD schemes are compared with the existing SD threshold detector, with BER results showing significant coding gain for certain codebooks. From the results, a reasonable trade-off between the complexity and coding gain is observed for a noisy channel such as the PLC channel.

在本文中，带有网格的排列格码（PTC）的软判决（SD）解码器 $\mathrm{中号}$使用三种优化算法设计了四进制频移键控，并以四种解码方案进行了介绍。在诸如PTC的级联代码中，用于外部卷积代码的维特比解码器可提供最大似然解码。因此，纠错性能取决于用于内部码的解码方案。由于采用调制方案的编码器的结构，通道输出可以解释为分配问题。然后，可以使用提出的基于低复杂度优化的方案相应地设计SD解码。在加性高斯白噪声（AWGN）和电力线通信（PLC）通道中模拟了方案的误码率（BER）性能。还介绍了方案的复杂性。将SD方案的性能与现有SD阈值检测器进行了比较，BER结果显示了某些码本的显着编码增益。从结果可以看出，对于嘈杂的通道（例如PLC通道），在复杂度和编码增益之间可以进行合理的权衡。