Statistical Mechanics of Linear Compression Codes in Network Communication

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We analyze the performance of a linear code used for a data compression of Slepian-Wolf type. In our framework, two correlated data are separately compressed into codewords employing Gallager-type codes and casted into a communication network through two independent input terminals. At the output terminal, the received codewords are jointly decoded by a practical algorithm based on the Thouless-Anderson-Palmer approach. Our analysis shows that the achievable rate region presented in the data compression theorem by Slepian and Wolf is described as first-order phase transitions among several phases. The typical performance of the practical decoder is also well evaluated by the replica method.