Related papers: Turbo Analog Error Correcting Codes Decodable By L…
We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of…
This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes over the BEC can be…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both…
Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…
In this article, we present a denoising algorithm to improve the interpretation and quality of scanning tunneling microscopy (STM) images. Given the high level of self-similarity of STM images, we propose a denoising algorithm by…
Turbo code is a great achievement in the field of communication system. It can be created by connecting a turbo encoder and a decoder serially. A Turbo encoder is build with parallel concatenation of two simple convolutional codes. By…
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…