The statistical physics properties of low-density parity-cheek codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity meth...The statistical physics properties of low-density parity-cheek codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check （bit） nodes have higher decoding thresholds compared to regular counterparts with homo- geneous degree distribution. We also show that the instability of the mean-field caiculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed （searching for the ground state）, we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is dose to the dynamicai transition where all local search heuristics fail to identify the true message （codeword or the ferromagnetic state）. After the dynamical transition, the number of metastable states with larger energy density （than the ferromagnetic state） becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentiaily numerous codewords sharing the identical ferromagnetic energy.展开更多
基金Supported by the JSPS Fellowship for Foreign Researchers under Grant No.24.02049
文摘The statistical physics properties of low-density parity-cheek codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check （bit） nodes have higher decoding thresholds compared to regular counterparts with homo- geneous degree distribution. We also show that the instability of the mean-field caiculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed （searching for the ground state）, we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is dose to the dynamicai transition where all local search heuristics fail to identify the true message （codeword or the ferromagnetic state）. After the dynamical transition, the number of metastable states with larger energy density （than the ferromagnetic state） becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentiaily numerous codewords sharing the identical ferromagnetic energy.
