Abstract
Statistical mechanics of information has been applied to problems in various research topics of information science and technology [1],[2]. Among those research topics, error-correcting code is one of the most developed subjects. In the research field of error-correcting codes, Nicolas Sourlas showed that the so-called convolutional codes can be constructed by spin glass with infinite range p-body interactions and the decoded message should be corresponded to the ground state of the Hamiltonian [3]. Ruján pointed out that the bit error can be suppressed if one uses finite temperature equilibrium states as the decoding result, instead of the ground state [4], and the so-called Bayes-optimal decoding at some specific condition was proved by Nishimori [5] and Nishimori and Wong [6]. Kabashima and Saad succeeded in constructing more practical codes, namely low-density parity check (LDPC) codes by using the infinite range spin glass model with finite connectivities [7]. They used the so-called TAP (Thouless–Anderson–Palmer) equations to decode the original message for a given parity check.
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Acknowledgements
One of the authors (J.I.) acknowledges Kazutaka Takahashi for useful comments on the analysis of the infinite range transverse Ising spin glass model. We thank Arnab Das, Anjan K. Chandra, and Bikas K. Chakrabarti for organizing the international workshop Quantum Phase Transition and Dynamics: Quenching, Annealing and Quantum Computation in Kolkata. We were financially supported by Grant-in-Aid Scientific Research on Priority Areas “Deepening and Expansion of Statistical Mechanical Informatics (DEX-SMI)” of The Ministry of Education, Culture, Sports, Science and Technology (MEXT) No. 18079001.
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Inoue, J., Saika, Y., Okada, M. (2010). Quantum-Mechanical Variant of the Thouless–Anderson–Palmer Equation for Error-Correcting Codes. In: Chandra, A., Das, A., Chakrabarti, B. (eds) Quantum Quenching, Annealing and Computation. Lecture Notes in Physics, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11470-0_14
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