arXiv subjects

Evagoras Stylianou

Publications and source records attributed to Evagoras Stylianou.

10 recordsLinked to original sources

arXiv2026

CSS Quantum LRCs with Intersecting Recovery Sets: Constructions and Bounds

In this work, we study $(r,t,x)$ quantum locally recoverable codes (qLRCs) with locality $r$, $t$ recovery sets per qudit, and intersection parameter $x$. We first show that, assuming the underlying classical codes have dual minimum distance at least two, a CSS code is an $(r,t,x)$-qLRC if and only if the underlying classical codes are $(r,t,x)$ classical LRCs (cLRCs) with common recovery sets. We then use subset-inclusion matrices to construct families of binary dual-containing $(r,t,x)$-cLRCs, which yield binary $(r,t,x)$-qLRCs via the CSS construction. For CSS $(r,t,x)$-qLRCs, we derive upper bounds on the dimension and rate, minimum-distance bounds in the pure case, and a Singleton-like dimension bound in the exact case. Finally, we show that these families attain high rates and nontrivial minimum distances.

cs.IT↗

arXiv2026

Bounds for Pure Disjoint $(r,δ)$-Quantum Locally Recoverable Codes

We study pure disjoint $(r,δ)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill--Laflamme conditions for recovery from up to $δ-1$ erasures within a recovery block, and introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,δ)$-qLRCs under a purity assumption, as well as a linear-programming upper bound on the code dimension. These results provide a non-stabilizer, weight-enumerator-based approach to the study of pure disjoint $(r,δ)$-qLRCs.

cs.IT↗

arXiv2025

Implicit and Explicit Formulas of the Joint RDF for a Tuple of Multivariate Gaussian Sources with Individual Square-Error Distortions

This paper analyzes the joint Rate Distortion Function (RDF) of correlated multivariate Gaussian sources with individual square-error distortions. Leveraging Hotelling's canonical variable form, presented is a closed-form characterization of the joint RDF, that involves {a system of nonlinear equations. Furthermore, for the special case of symmetric distortions (i.e., equal distortions), the joint RDF is explicitly expressed in terms of} two water-filling variables. The results greatly improve our understanding and advance the development of closed-form solutions of the joint RDF for multivariate Gaussian sources with individual square-error distortions.

cs.IT↗

arXiv2024

Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound

We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3} $. For higher rates, our EAQECC also meets the Singleton bound, although with increased entanglement requirements. Additionally, we demonstrate that any classical $[n,k,d]_q$ code can be transformed into an EAQECC with parameters $[[n,k,d;2k]]_q$ using $2k$ pre-shared maximally entangled pairs. The complexity of our encoding protocol for $k$-qudits with $q$ levels is $\mathcal{O}(k \log_{\frac{q}{q-1}}(k))$, excluding the complexity of encoding and decoding the classical MDS code. While this complexity remains linear in $k$ for systems of reasonable size, it increases significantly for larger-levelled systems, highlighting the need for further research into complexity reduction.

quant-ph↗

arXiv2024

Indirect Rate Distortion Functions with Side Information: Structural Properties and Multivariate Gaussian Sources

In this paper, we analyze the indirect source coding problem with side information at both the encoder and decoder, as well as only at the decoder. We first derive structural properties of the two rate distortion functions (RDFs) for general abstract spaces and identify conditions under which the RDFs coincide. For multivariate jointly Gaussian random variables with square-error fidelity, we establish structural properties of the optimal test channels, show that side information at both the encoder and decoder does not reduce compression, and provide water-filling solutions using parallel Gaussian channel realizations. This paper uses a novel realization theory approach to establish achievability of the converse coding theorem lower bounds of the two RDFs.

cs.IT↗

arXiv2024

Minimal Trellises for non-Degenerate and Degenerate Decoding of Quantum Stabilizer Codes

This paper presents a comprehensive guide to designing minimal trellises for both non-degenerate and degenerate decoding of quantum stabilizer codes. For non-degenerate decoding, various strategies are explored, leveraging insights from classical rectangular codes to minimize the complexity associated with the non-degenerate maximum likelihood error estimation using the Viterbi algorithm. Additionally, novel techniques for constructing minimal multi-goal trellises for degenerate decoding are introduced, including a merging algorithm, a Shannon-product approach, and the BCJR-Wolf method. The study establishes essential properties of multi-goal trellises and provides bounds on the decoding complexity using the sum-product Viterbi decoding algorithm. These advancements decrease the decoding complexity by a factor $\mathcal{O}(n)$, where $n$ is the code length. Finally, the paper applies these results to CSS codes and demonstrates a reduction in complexity by independently applying degenerate decoding to $X$ and $Z$ errors.

cs.IT↗

arXiv2022

Equivalence of Insertion/Deletion Correcting Codes for $d$-dimensional Arrays

We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors and arrays, the problem is motivated by several practical applications such as DNA-based storage and racetrack memories. From a theoretical perspective, it is interesting to know whether the same properties of insertion/deletion correcting codes generalize to the $d$-dimensional space. In this work, we show that the equivalence between insertion and deletion correcting codes generalizes to the $d$-dimensional space. As a particular result, we show the following missing equivalence for arrays: a code that can correct $t_\mathrm{r}$ and $t_\mathrm{c}$ row/column deletions can correct any combination of $t_\mathrm{r}^{\mathrm{ins}}+t_\mathrm{r}^{\mathrm{del}}=t_\mathrm{r}$ and $t_\mathrm{c}^{\mathrm{ins}}+t_\mathrm{c}^{\mathrm{del}}=t_\mathrm{c}$ row/column insertions and deletions. The fundamental limit on the redundancy and a construction of insertion/deletion correcting codes in the $d$-dimensional space remain open for future work.

cs.IT↗

arXiv2022

Characterization of the Gray-Wyner Rate Region for Multivariate Gaussian Sources: Optimality of Gaussian Auxiliary RV

Examined in this paper, is the Gray and Wyner achievable lossy rate region for a tuple of correlated multivariate Gaussian random variables (RVs) $X_1 : Ω\rightarrow {\mathbb R}^{p_1}$ and $X_2 : Ω\rightarrow {\mathbb R}^{p_2}$ with respect to square-error distortions at the two decoders. It is shown that among all joint distributions induced by a triple of RVs $(X_1,X_2, W)$, such that $W : Ω\rightarrow {\mathbb W} $ is the auxiliary RV taking continuous, countable, or finite values, the Gray and Wyner achievable rate region is characterized by jointly Gaussian RVs $(X_1,X_2, W)$ such that $W $ is an $n$-dimensional Gaussian RV. It then follows that the achievable rate region is parametrized by the three conditional covariances $Q_{X_1,X_2|W}, Q_{X_1|W}, Q_{X_2|W}$ of the jointly Gaussian RVs. Furthermore, if the RV $W$ makes $X_1$ and $X_2$ conditionally independent, then the corresponding subset of the achievable rate region, is simpler, and parametrized by only the two conditional covariances $Q_{X_1|W}, Q_{X_2|W}$. The paper also includes the characterization of the Pangloss plane of the Gray-Wyner rate region along with the characterizations of the corresponding rate distortion functions, their test-channel distributions, and structural properties of the realizations which induce these distributions.

cs.IT↗

arXiv2021

Joint Rate Distortion Function of a Tuple of Correlated Multivariate Gaussian Sources with Individual Fidelity Criteria

In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs, $X_1 : Ω\rightarrow {\mathbb R}^{p_1}, X_2 : Ω\rightarrow {\mathbb R}^{p_2}$ with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Gray's [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.

cs.IT↗

arXiv2021

Joint Nonanticipative Rate Distortion Function for a Tuple of Random Processes with Individual Fidelity Criteria

The joint nonanticipative rate distortion function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. Further, for the application example of the joint NRDF of a tuple of jointly multivariate Gaussian Markov processes with individual square-error fidelity criteria, a realization of the reproduction processes which induces the optimal test channel distribution is derived, and the corresponding joint NRDF is characterized. The analysis of the simplest example, of a tuple of scalar correlated Markov processes, illustrates many of the challenging aspects of such problems.

cs.IT↗