相关论文: Statistical Mechanics and error-correction Codes

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…

Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known…

Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…

In realistic stabiliser-based quantum error correction there are many ways in which real physical systems deviate from simple toy models of error. Stabiliser measurements may not always be deterministic or may suffer from erasure errors,…

We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…

Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…

For a system of N spins 1/2 there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding…

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning…

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…

We present a decoding algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability conditioned on a given error syndrome. The algorithm runs in time linear with the number of qubits.…

Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the ground-state energy of the +/-J Ising spin glass model on the…

Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…

A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…

We present a framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes. It is compatible with all successive cancellation (SC)-based decoding methods and relies on a…

This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with…

We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…

Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…