相关论文: Public key cryptography and error correcting codes…
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…
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…
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 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…
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 relation between Ising spin systems and public-key cryptography is investigated using methods of statistical physics. The insight gained from the analysis is used for devising a matrix-based cryptosystem whereby the ciphertext comprises…
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…
For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by…
A public-key cryptosystem, digital signature and authentication procedures based on a Gallager-type parity-check error-correcting code are presented. The complexity of the encryption and the decryption processes scale linearly with the size…
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…
The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding,…
We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly…
The problem of error correction for Gallager's low-density parity-check codes is famously equivalent to that of computing marginal Boltzmann probabilities for an Ising-like model with multispin interactions in a non-uniform magnetic field.…
Inspired by compressive sensing principles, we propose novel error control coding techniques for communication systems. The information bits are encoded in the support and the non-zero entries of a sparse signal. By selecting a dictionary…
Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to…