Sourlas码系统的腔方法
Cavity approach to the Sourlas code system
摘要：
本文采用腔方法研究了规则和不规则Sourlas码的统计物理性质。在有限温度下，导出了这些编码系统的自由能量密度，并与复制法所得结果进行了比较。在零温度限制下，香农的界限恢复的情况下，无限体相互作用，而码率仍然是有限的。然而，由复制理论得到的解码性能没有考虑零温熵效应。腔方法能够考虑基态熵。它导致了一组渐逝腔场的传播方程，进一步提高解码性能，证实了我们的数值模拟的单个实例。对于非规则Sourlas码，我们发现它在良好的动态性能和高的译码性能之间取得了平衡。与从算法的角度发现的结果一致，解码表现出一阶相变中发生的规则代码系统与三体相互作用。Sourlas码系统的腔方法可以扩展到考虑第一步复制对称破缺。
英文摘要：
The statistical physics properties of regular and irregular Sourlas codes are investigated in this paper by the cavity method. At finite temperatures, the free energy density of these coding systems is derived and compared with the result obtained by the replica method. In the zero temperature limit, the Shannon's bound is recovered in the case of infinite-body interactions while the code rate is still finite. However, the decoding performance as obtained by the replica theory has not considered the zero-temperature entropic effect. The cavity approach is able to consider the ground-state entropy. It leads to a set of evanescent cavity fields propagation equations which further improve the decoding performance, as confirmed by our numerical simulations on single instances. For the irregular Sourlas code, we find that it takes the trade-off between good dynamical property and high performance of decoding. In agreement with the results found from the algorithmic point of view, the decoding exhibits a first order phase transition as occurs in the regular code system with three-body interactions. The cavity approach for the Sourlas code system can be extended to consider first-step replica-symmetry-breaking.
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