Related papers: Generalizing Syndrome Decoding problem to the tota…
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, $t$-resilient functions,…
The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation…
We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The…
This paper considers a transmitter, which uses random linear coding (RLC) to encode data packets. The generated coded packets are broadcast to one or more receivers. A receiver can recover the data packets if it gathers a sufficient number…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
Motivated by iterative decoding techniques for the binary erasure channel Hollmann and Tolhuizen introduced and studied the notion of generic erasure correcting sets for linear codes. A generic $(r,s)$--erasure correcting set generates for…
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…
Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very…
Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…
Random jammers that overpower transmitted signals are a practical concern for many wireless communication protocols. As such, wireless receivers must be able to cope with standard channel noise and jamming (intentional or unintentional). To…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
In this paper, we propose a subgradient algorithm with a non-asymptotic convergence guarantee to solve copositive programming problems. The subproblem to be solved at each iteration is a standard quadratic programming problem, which is…
We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…
Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
We propose a new partial decoding algorithm for $h$-interleaved one-point Hermitian codes that can decode-under certain assumptions-an error of relative weight up to $1-(\tfrac{k+g}{n})^{\frac{h}{h+1}}$, where $k$ is the dimension, $n$ the…
This paper addresses the problem of coding a continuous random source correlated with another source which is only available at the decoder. The proposed approach is based on the extension of the channel coding concept of syndrome from the…
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,…