  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.
