相关论文: The glassy phase of Gallager codes
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed…
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average…
The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
In a previous work it was shown that the best measure for the efficiency of a single burst-correcting code is obtained using the Gallager bound as opposed to the Reiger bound. In this paper, an efficient algorithm that searches for the best…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
We explore the relation between the techniques of statistical mechanics and information theory for assessing the performance of channel coding. We base our study on a framework developed by Gallager in {\em IEEE Trans. Inform. Theory} {\bf…
The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation…
The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or…
Gallager-type error-correcting codes that nearly saturate Shannon's bound are constructed using insight gained from mapping the problem onto that of an Ising spin system. The performance of the suggested codes is evaluated for different…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two…
We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very…