相关论文: Relations between random coding exponents and the …
The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size…
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 study the channel output distribution induced by a rate-$R$ random code via statistical physics. The partition function is $Z_n(\beta|\mathcal{C}) = \sum_{y^n}[P_{Y^n|\mathcal{C}}(y^n)]^\beta$, where $\mathcal{C}$ is the code and $\beta…
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…
This paper studies the concentration properties of random codes. Specifically, we show that, for discrete memoryless channels, the error exponent of a randomly generated code with pairwise-independent codewords converges in probability to…
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…
Based on the mapping between stabilizer quantum error correcting codes and disordered statistical mechanics models, we define a ratio of partition functions that measures the success probability for maximum partition function decoding,…
Partition functions $Z(x)$ of statistical mechanics are generally approximated by integrals. The approximation fails in small cavities or at very low temperature, when the ratio $x$ between the energy quantum and thermal energy is larger or…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized…
We demonstrate that there is an intimate relationship between the magnetic properties of Derrida's random energy model (REM) of spin glasses and the problem of joint source--channel coding in Information Theory. In particular, typical…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
This paper considers guessing-based decoders with abandonment for discrete memoryless channels in which all codewords have the same composition. This class of decoders rank-orders all input sequences in the codebook's composition class from…
The effect of finite temperature $T$ and finite strain rate $\dot\gamma$ on the statistical physics of plastic deformations in amorphous solids made of $N$ particles is investigated. We recognize three regimes of temperature where the…
We consider the model of random binning and finite-temperature decoding for Slepian-Wolf codes, from a statistical-mechanical perspective. While ordinary random channel coding is intimately related to the random energy model (REM) - a…
We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum…
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…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known…
Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…