相关论文: Bacon-Shor Board Games

Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such…

We recast move generators for solving board games as operations on compressed sets of strings. We aim for compressed representations with space sublinear in the number of game positions for interesting sets of positions, move generation in…

We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have…

We consider the problem of slotted asynchronous coded communication, where in each time frame (slot), the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide…

Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…

Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes is based on Bounded Minimum Distance (BMD) decoders with an erasure option. Such decoders have error/erasure tradeoff factor L=2, which means that an error is…

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We…

We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…

We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…

Compressive Sensing (CS) theory states that real-world signals can often be recovered from much fewer measurements than those suggested by the Shannon sampling theorem. Nevertheless, recoverability does not only depend on the signal, but…

An approximation algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying a $(1 - f(\epsilon))$-fraction of the constraints on any $(1-\epsilon)$-satisfiable instance, where the loss function…

We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the…

A lower bound on the minimum required code length of binary codes is obtained. The bound is obtained based on observing a close relation between the Ulam's liar game and channel coding. In fact, Spencer's optimal solution to the game is…

Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the…

Although conformal prediction provides robust marginal coverage guarantees, achieving reliable conditional coverage for specific inputs remains challenging. While exact distribution-free conditional coverage is impossible with finite…

A real time coding system with lookahead consists of a memoryless source, a memoryless channel, an encoder, which encodes the source symbols sequentially with knowledge of future source symbols upto a fixed finite lookahead, d, with or…

An analog source is to be transmitted across a Gaussian channel in more than one channel use per source symbol. This paper derives a lower bound on the asymptotic mean squared error for a strategy that consists of repeatedly quantizing the…