Related papers: Turbo Analog Error Correcting Codes Decodable By L…
We refine an old idea for performing fault-tolerant error correction in topological codes by simulating confining interactions between excitations. We implement confinement using an array of local classical processors that measure…
In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in…
We introduce Noise Recycling, a method that enhances decoding performance of channels subject to correlated noise without joint decoding. The method can be used with any combination of codes, code-rates and decoding techniques. In the…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
We develop an approach through geometric functional analysis to error correcting codes and to reconstruction of signals from few linear measurements. An error correcting code encodes an n-letter word x into an m-letter word y in such a way…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
It has been an open question in deep learning if fault-tolerant computation is possible: can arbitrarily reliable computation be achieved using only unreliable neurons? In the grid cells of the mammalian cortex, analog error correction…
Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
A channel with continuous phase modulation and 1-bit ADC with oversampling is considered. Due to oversampling, higher-order modulations yield a higher achievable rate and this work presents a method to approach this with sophisticated…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
Iterative decoding is essential in modern communication systems, especially optical communications, where error-correcting codes such as turbo product codes (TPC) and staircase codes are widely employed. A key factor in achieving high error…
In this paper, we propose a framework to enhance the robustness of the neural models by mitigating the effects of process-induced and aging-related variations of analog computing components on the accuracy of the analog neural networks. We…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…