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.

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