Statistical Mechanics Properties of Bernoulli Generator Matrix Codes
From the perspective of statistical physics,with the theory of spin glasses and complex networks,this pa-per 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 co-debook 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 configura-tion model (NGCM) to generate normal graph with connection preference,study the effect of disassortativity on BP decod-ing performance and analyze the mechanism. The simulation results show that,although the population dynamics is essen-tially 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 com-plexity).
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