Related papers: Statistical Mechanics and Capacity-Approaching Err…
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…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
The "turbo codes", recently proposed by Berrou et. al. are written as a disordered spin Hamiltonian. It is shown that there is a threshold Theta such that for signal to noise ratios v^2 / w^2 > Theta, the error probability per bit vanishes…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic…
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…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
Since the discovery of turbo codes 20 years ago and the subsequent re-discovery of low-density parity-check codes a few years later, the field of channel coding has experienced a number of major advances. Up until that time, code designers…
In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-tooptimal decoding results when compared to full belief propagation…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Gallager codes are the best error-correcting codes to-date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be…
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…
Reachability analysis has been a prominent way to provide safety guarantees for neurally controlled autonomous systems, but its direct application to neural perception components is infeasible due to imperfect or intractable perception…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
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…
We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower…