伯努利生成矩阵码中的统计力学性质

孟凡辉; 马啸

doi:10.12263/DZXB.20230319

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伯努利生成矩阵码中的统计力学性质

学术论文 | 更新时间：2025-12-11

- 伯努利生成矩阵码中的统计力学性质
- Statistical Mechanics Properties of Bernoulli Generator Matrix Codes
- 电子学报 2024年52卷第6期页码：1869-1877
- 作者机构：
  
  1.中山大学系统科学与工程学院,广东广州 510006
  2.中山大学计算机学院,广东广州 510006
  3.广东省信息安全技术重点实验室,广东广州 510006
- 作者简介：
  
  [ "孟凡辉男，1993年生，山东聊城人.中山大学博士研究生.主要研究方向为复杂网络、自旋玻璃、信道编码等." ]
  [ "马　啸　男，1968年生，河南焦作人.博士.中山大学教授、博士生导师.主要研究方向为信息与编码理论、编码调制技术、无线通信、光通信等.中国电子学会会员编号：E190005835M." ]
- 基金信息：
  
  国家重点研发计划(2021YFA1000500)
- DOI：10.12263/DZXB.20230319
  中图分类号： TN911.22
- 收稿：2023-04-11，
  
  修回：2023-08-06，
  
  纸质出版：2024-06-25
- 稿件说明：
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孟凡辉,马啸.伯努利生成矩阵码中的统计力学性质[J].电子学报,2024,52(06):1869-1877.

MENG Fan-hui, MA Xiao.Statistical Mechanics Properties of Bernoulli Generator Matrix Codes[J].Acta Electronica Sinica, 2024, 52(06): 1869-1877.
孟凡辉,马啸.伯努利生成矩阵码中的统计力学性质[J].电子学报,2024,52(06):1869-1877. DOI：10.12263/DZXB.20230319

MENG Fan-hui, MA Xiao.Statistical Mechanics Properties of Bernoulli Generator Matrix Codes[J].Acta Electronica Sinica, 2024, 52(06): 1869-1877. DOI：10.12263/DZXB.20230319

摘要

从统计物理的角度，结合自旋玻璃理论与复杂网络理论，系统地研究了伯努利系统低密度生成矩阵码的统计力学性质.首先给出系统低密度生成矩阵码的伯努利构造、编译码框架，并讨论节点度分布以及正规图与Erdös-Rényi（ER）随机图的联系.然后研究自旋玻璃理论框架下的编译码模型、码本与微观构型的关系、空腔方法与消息传递方程，提出针对系统码的种群动力学算法来高效分析其渐近性能.最后提出正规图配置模型（Normal Graph Configuration Model，NGCM）生成具有连接偏好性的正规图，研究异配性对置信传播（Belief Propagation，BP）译码算法性能的影响，并进一步分析其机理.仿真结果表明，种群动力学算法与BP译码算法本质上相同，但前者不局限于某个具体的码，因此在分析码集的渐近性能时更具优势.此外，适当的异配性能够显著提升BP算法在瀑布区的译码性能，获得更低误码率（Bit Error Rate，BER）并且降低译码迭代次数（复杂度）.

Abstract

From the perspective of statistical physics

with the theory of spin glasses and complex networks

this paper systematically studies the statistical mechanics properties of Bernoulli systematic low-density generator matrix codes. First

we introduce Bernoulli construction of the systematic low-density generator matrix codes

encoding and decoding framework

and discuss the distribution of degree as well as the connection between normal graph and Erdös-Rényi (ER) random graphs. Then

we study the encoding and decoding model under the spin glasses theory

the association between codebook and configuration

cavity method and message-passing equation

and propose the population dynamics algorithm for systematic codes to perform asymptotic performance analysis efficiently. Finally

we propose the normal graph configuration model (NGCM) to generate normal graph with connection preference

study the effect of disassortativity on BP decoding performance and analyze the mechanism. The simulation results show that

although the population dynamics is essentially the same as the BP algorithm

the former is not limited to a concrete code

thus having an advantage in asymptotic analysis for code ensemble. In addition

appropriate disassortativity can significantly improve the BP decoding performance in the waterfall region

achieving lower bit error rate (BER) and reducing the iteration number of decoding (hence the complexity).

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references

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