Related papers: On PGZ decoding of alternant codes
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed…
Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Let l be an odd prime. For primes, p \equiv 1 (mod l), Gauss (l = 3) and Dickson (l = 5) considered the Diophantine systems in terms of which cyclotomic numbers of order 3 and 5 were obtained. The aim of this paper is to show how to obtain…
We present a general approach to error detection of bosonic quantum error-correction codes via an adaptive quantum phase estimation algorithm assisted by a single ancilla qubit. The approach is applicable to a broad class of bosonic codes…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
The paper is devoted to nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with a periodic potential and repulsive interparticle interactions. It has been recently shown (G. L.…
Twisted generalized Reed-Solomon (TGRS) codes were introduced to extend the algebraic capabilities of classical generalized Reed-Solomon (GRS) codes. This extension holds the potential for constructing new non-GRS maximum distance separable…
It has been shown that graph-cover pseudocodewords can be used to characterize the behavior of sum-product algorithm (SPA) decoding of classical codes. In this paper, we leverage and adapt these results to analyze SPA decoding of quantum…
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Iterative decoding techniques have gain popularity due to their performance and their application in most communications systems. In this paper, we present a new application of our iterative decoder on the GPCB (Generalized Parallel…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
The multiplicity Schwartz-Zippel lemma bounds the total multiplicity of zeroes of a multivariate polynomial on a product set. This lemma motivates the multiplicity codes of Kopparty, Saraf and Yekhanin [J. ACM, 2014], who showed how to use…
In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear…
We consider the problem of determining Gr\"obner bases of binomial ideals associated with linear error correcting codes. Computation of Gr\"obner bases of linear codes have become a topic of interest to many researchers in coding theory…
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…
A modified successive cancellation list (SCL) decoder is proposed for polar-coded probabilistic shaping. The decoder exploits the deterministic encoding rule for shaping bits to rule out candidate code words that the encoder would not…