Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary linear forward error correction codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of queries made by Guessing Random Additive Noise Decoding (GRAND), for binary linear codes that include one full single parity-check (SPC) bit, we show that it is possible to reduce the number of queries made by GCD by a factor of up to 2 without impacting decoding precision. The greatest guesswork reduction is realized at lower SNRs, where the decoder output is usually correct but guesswork is most burdensome. Codes without a SPC can be modified to include one by swapping a column of the generator matrix for an all-ones column to obtain a decoding complexity advantage, and we demonstrate that this can often be done without losing decoding precision. To practically avail of the complexity advantage, a noise effect pattern generator capable of producing sequences for given Hamming weights, such as the one underlying ORBGRAND, is necessary.

翻译：猜测码字解码（GCD）是近期提出的一种适用于任意线性前向纠错码的软输入前向纠错解码器。受近期利用二进制线性码本结构减少猜测随机加性噪声解码（GRAND）查询次数方案的启发，针对包含完整单奇偶校验（SPC）位的二进制线性码，我们证明可将GCD的查询次数降低至多2倍而不影响解码精度。最大的猜测工作量缩减在较低信噪比下实现，此时解码器输出通常正确但猜测负担最重。对于不含SPC的码，可通过将生成矩阵的某一列替换为全1列来引入SPC以获得解码复杂度优势，我们证明这一操作通常不会损失解码精度。为实际利用该复杂度优势，需要配备能够按给定汉明权重生成噪声效应模式的生成器（例如ORBGRAND所采用的生成器）。