In this paper, we present a novel log-log domain sum-product algorithm (SPA) for decoding low-density parity-check (LDPC) codes in continuous-variable quantum key distribution (CV-QKD) systems. This algorithm reduces the fractional bit width of decoder messages, leading to a smaller memory footprint and a lower resource consumption in hardware implementation. We also provide practical insights for fixed-point arithmetic and compare our algorithm with the conventional SPA in terms of performance and complexity. Our results show that our algorithm achieves comparable or better decoding accuracy than the conventional SPA while saving at least $25\%$ of the fractional bit width.

翻译：本文提出了一种新颖的对数-对数域和积算法（SPA），用于连续变量量子密钥分发（CV-QKD）系统中低密度奇偶校验（LDPC）码的解码。该算法降低了解码器消息的分数位宽，从而在硬件实现中减少内存占用和资源消耗。我们还提供了定点算术的实用见解，并从性能和复杂度两方面将我们的算法与传统SPA进行了比较。结果表明，我们的算法在实现相当或更优解码精度的同时，节省了至少25%的分数位宽。