Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2409.10979

A Symbol-Pair Decoder for CSS Codes

Vatsal Pramod Jha·Udaya Parampalli·Abhay Kumar Singh
View original source ↗Read source document ↗Export metadata ↓

Abstract

The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work allows us to lift decoders for classical codes over the Hamming metric to decoders for stabilizer quantum codes. A natural question to consider: Can we do something similar with decoders for classical codes considered over other metrics? i.e., Can we lift decoders for classical codes over other metrics to obtain decoders for stabilizer quantum codes? In our current work, we answer this question in the affirmative by considering classical codes over the symbol-pair metric. In particular, we present a relation between the symplectic weight and the symbol-pair weight and use it to improve the error correction capability of CSS-codes (a well-studied class of stabilizer codes) obtained from cyclic codes.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vatsal Pramod Jha, Udaya Parampalli, Abhay Kumar Singh. 2024-09-17. A Symbol-Pair Decoder for CSS Codes. https://arxiv.org/abs/2409.10979

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

cs.IT↗
arXiv2026

Sequence Reconstruction over the Deletion Channel

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $ n \geq t+\ell-1$ and $t \geq 1$.

cs.IT↗
arXiv2026

A generalization of the map $χ$

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

cs.IT↗