Critical Noise Levels for LDPC decoding

We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator (\cM), rather than on the weight enumerator (\cW) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.Comment: 9 pages, 5 figure

Transient dynamics for sequence processing neural networks

An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analyzing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.Comment: 21 pages, 4 figure

Parallelization of Markov chain generation and its application to the multicanonical method

We develop a simple algorithm to parallelize generation processes of Markov chains. In this algorithm, multiple Markov chains are generated in parallel and jointed together to make a longer Markov chain. The joints between the constituent Markov chains are processed using the detailed balance. We apply the parallelization algorithm to multicanonical calculations of the two-dimensional Ising model and demonstrate accurate estimation of multicanonical weights.Comment: 15 pages, 5 figures, uses elsart.cl

Statistical Physics of Irregular Low-Density Parity-Check Codes

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 simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP

Statistical Mechanics of Broadcast Channels Using Low Density Parity Check Codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple timesharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based timesharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the timesharing limit.Comment: 14 pages, 4 figure

Analysis of common attacks in LDPCC-based public-key cryptosystems

We analyze the security and reliability of a recently proposed class of public-key cryptosystems against attacks by unauthorized parties who have acquired partial knowledge of one or more of the private key components and/or of the plaintext. Phase diagrams are presented, showing critical partial knowledge levels required for unauthorized decryptionComment: 14 pages, 6 figure

Prospects for Supersymmetry at LEP2

Working within the framework of the minimal supergravity model with gauge coupling unification and radiative electroweak symmetry breaking (SUGRA), we map out regions of parameter space explorable by experiments at LEP2, for center of mass energy options of $\sqrt{s}=150,\ 175$, $190$ and 205 GeV. We compute signals from all accessible $2 \rightarrow 2$ SUSY pair production processes using the ISAJET simulation program, and devise cuts that enhance the signal relative to Standard Model backgrounds, and which also serve to differentiate various supersymmetric processes from one another. We delineate regions of SUGRA parameter space where production of neutralino pairs, chargino pairs, slepton pairs and the production of the light Higgs scalar of SUSY is detectable above Standard Model backgrounds and distinguishable from other SUSY processes. In addition, we find small regions of SUGRA parameter space where \te\te, \tz_2\tz_2 and \tnu_L\tnu_L production yields spectacular events with up to four isolated leptons. The combined regions of parameter space explorable by LEP2 are compared with the reach of Tevatron Main Injector era experiments. Finally, we comment on how the reach via the neutralino pair channel is altered when the radiative electroweak symmetry breaking constraint is relaxed.Comment: 22 page REVTEX file + 9 uuencoded figures; a uuencoded PS file with PS figures is available via anonymous ftp at ftp://hep.fsu.edu/preprints/baer/FSUHEP950501.u

Uncertainties in Coupling Constant Unification

The status of coupling constant unification in the standard model and its supersymmetric extension are discussed. Uncertainties associated with the input coupling constants, $m_{t}$, threshold corrections at the low and high scales, and possible nonrenormalizable operators are parametrized and estimated. A simple parametrization of a general supersymmetric new particle spectrum is given. It is shown that an effective scale $M_{SUSY}$ can be defined, but for a realistic spectrum it may differ considerably from the typical new particle masses. The implications of the lower (higher) values of $\alpha_{s}(M_{Z})$ suggested by low-energy ($Z$-pole) experiments are discussed.Comment: LaTex, 51 pages, 6 figures (available upon request), UPR-0513

Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under LDPC network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and the symmetric and asymmetric interference channels. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases.Comment: 25 pages, 7 figure