Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear 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 a full-message 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 with the greatest guesswork reduction realized at lower SNRs, without impacting decoding precision. Codes without a full-message SPC can be modified to include one by changing a column of the generator matrix 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 landslide algorithm developed for 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二进制线性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）查询次数的方案启发，针对包含全信息单奇偶校验（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，且最大猜测工作量缩减在较低信噪比下实现，同时不影响解码精度。不含全信息SPC的码可通过修改生成矩阵的列来加入SPC位以获得解码复杂度优势，我们证明这通常可在不损失解码精度的情况下实现。为实际利用该复杂度优势，需要能够为给定汉明权重生成噪声效应模式的生成器，例如为ORBGRAND开发的滑坡算法。