In this paper we combine the determinism of the chaotic maps with stochastic components to propose a hybrid algorithm for cryptography. This makes the cipher probabilistic in the sense that each plain text corresponds...
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In this paper we combine the determinism of the chaotic maps with stochastic components to propose a hybrid algorithm for cryptography. This makes the cipher probabilistic in the sense that each plain text corresponds to many distinct encoded texts, raising the security against known plain text attacks. In particular, the proposed cipher allows an efficient encryption even if a low entropy key is chosen. Also, the algorithm can be efficiently used as a 'many-times pad' cipher.
We present rigorous results on some open questions on NSRPS, the non-sequential recursive pairs substitution method. In particular, starting from the action of NSRPS on finite strings we de. ne a corresponding natural...
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We present rigorous results on some open questions on NSRPS, the non-sequential recursive pairs substitution method. In particular, starting from the action of NSRPS on finite strings we de. ne a corresponding natural action on measures and we prove that the iterated measure becomes asymptotically Markov. This certifies the effectiveness of NSRPS as a tool for data compression and entropy estimation.
In a recent paper we derived an expression for the replicated free energy of a liquid of hard spheres based on the hypernetted chain ( HNC) free energy functional. An approximate equation of state for the glass and an...
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In a recent paper we derived an expression for the replicated free energy of a liquid of hard spheres based on the hypernetted chain ( HNC) free energy functional. An approximate equation of state for the glass and an estimate of the random close packing density were obtained for d = 3. Here we show that the HNC approximation is not needed: the same expression can be obtained from the full diagrammatic expansion of the replicated free energy. Then, we consider the asymptotics of this expression when the space dimension d is very large. In this limit, the entropy of the hard sphere liquid has been computed exactly. Using this solution, we derive asymptotic expressions for the glass transition density and for the random close packing density for hard spheres for large space dimension.
The Parity source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that t...
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The Parity source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturates the Shannon limit at large K. We also find that the first corrections to the leading behaviour are exponentially small, with the result that the behaviour at finite K is very close to the optimal one.
In this paper we exploit concepts of information theory to address the fundamental problem of identifying and de. ning the most suitable tools for extracting, in a automatic and agnostic way, information from a generi...
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In this paper we exploit concepts of information theory to address the fundamental problem of identifying and de. ning the most suitable tools for extracting, in a automatic and agnostic way, information from a generic string of characters. We introduce in particular a class of methods which use in a crucial way data compression techniques in order to de. ne a measure of remoteness and distance between pairs of sequences of characters ( e. g. texts) based on their relative information content. We also discuss in detail how specific features of data compression techniques could be used to introduce the notion of dictionary of a given sequence and of artificial text and we show how these new tools can be used for information extraction purposes. We point out the versatility and generality of our method that applies to any kind of corpora of character strings independently of the type of coding behind them. We consider as a case study linguistic motivated problems and we present results for automatic language recognition, authorship attribution and self-consistent classification.
It has been shown experimentally that a decimation algorithm based on survey propagation (SP) equations allows one to solve efficiently some combinatorial problems over random graphs. We show that these equations can ...
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It has been shown experimentally that a decimation algorithm based on survey propagation (SP) equations allows one to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum - product equations for the computation of marginals in an extended space where the variables are allowed to take an additional value - - when they are not forced by the combinatorial constraints. An appropriate 'local equilibrium condition' cost/energy function is introduced and its entropy is shown to coincide with the expected logarithm of the number of clusters of solutions as computed by SP. These results may help to clarify the geometrical notion of clusters assumed by SP for random K-SAT or random graph colouring ( where it is conjectured to be exact) and help to explain which kind of clustering operation or approximation is enforced in general/small sized models in which it is known to be inexact.
We consider the progressive transmission of a lossy source across a power constrained Gaussian channel using binary phase-shift keying modulation. Under the theoretical assumptions of infinite bandwidth, arbitrarily c...
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We consider the progressive transmission of a lossy source across a power constrained Gaussian channel using binary phase-shift keying modulation. Under the theoretical assumptions of infinite bandwidth, arbitrarily complex channelcoding, and lossless transmission, we derive the optimal channel code rate and the optimal energy allocation per transmitted bit. Under the practical assumptions of a low complexity class of algebraic channel codes and progressive image coding, we numerically optimize the choice of channel code rate and the energy, per bit allocation. This model provides an additional degree of freedom with respect to previously proposed schemes, and can achieve a higher performance for sources such as images. It also allows one to control bandwidth expansion or reduction.
Turbo codes are a practical solution for achieving large coding gains. In this letter we present a new turbo coding scheme where the component codes are convolutional codes (CC's) over the ring of integers module ...
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Turbo codes are a practical solution for achieving large coding gains. In this letter we present a new turbo coding scheme where the component codes are convolutional codes (CC's) over the ring of integers module M, with M being the alphabet size of the source encoder. The a priori knowledge of the source statistics is used during the iterative decoding procedure for improved decoder performance. As an example of application, we examine differential pulse code modulation (DPCM)-encoded image transmission.
Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. it is known that for the cascade of asymptotically good channel code...
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Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. it is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing a channel code rate that is independent of the overall transmission rate. We show that for certain families of practical channel codes and binary lattice vector quantizers, the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate. This is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows. Explicit channel code rate schedules are obtained for several well-known families of channel codes.
We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vladut-Zink bounds. Formulas giving the high resolution vector quanti...
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We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vladut-Zink bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below channel capacity the transmission rate should be for a given delay constraint. The bounds obtained depend on the relationship between channel code rate and relative minimum distance guaranteed by the Gilbert-Varshamov bound, and do not require sophisticated decoding beyond the error correction limit. We demonstrate that the end-to-end mean-squared error decays' exponentially fast as a function of the overall transmission rate, which need not be the case for certain well-known structured codes such as Hamming codes.
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