arXiv subjects

Jessica Bariffi

Publications and source records attributed to Jessica Bariffi.

12 recordsLinked to original sources

arXiv2026

Scientific Rigor and Human Warmth: Remembering Vladimir Sidorenko (1949-2025)

During the Foundations of Future Communication Systems (FFCS) conference in Braunschweig, a dedicated memorial session was held in honor of Dr. Vladimir (Volodya) Sidorenko (1949-2025). The session, chaired by Minglai Cai, brought together colleagues, collaborators, and former students to commemorate his scientific achievements and his exceptional human qualities. This report summarizes the biographical tribute, the personal recollections shared by speakers, and the broader impact of Volodya's work in coding theory, cryptography, telecommunications, and quantum error correction. Beyond his more than 150 publications and substantial technical contributions, the session highlighted his intellectual rigor, mentorship, humor, generosity, and lasting influence on the international research community.

cs.IT↗

arXiv2026

A Security Framework for Chemical Functions

In this paper, we introduce chemical functions, a unified framework that models chemical systems as noisy challenge--response primitives, and formalize the associated chemical function infrastructure. Building on the theory of physical functions, we rigorously define robustness, unclonability, and unpredictability for chemical functions in both finite and asymptotic regimes, and specify security games that capture the adversary's power and the security goals. We instantiate the framework with two existing DNA-based constructions (operable random DNA and Genomic Sequence Encryption) and derive quantitative bounds for robustness, unclonability, and unpredictability. Our analysis develops maximum-likelihood verification rules under sequencing noise and partial-edit models, and provides high-precision estimates based on binomial distributions to guide parameter selection. The framework, definitions, and analyses yield a reproducible methodology for designing chemically unclonable authentication mechanisms. We demonstrate applications to in-product authentication and to shared key generation using standard extraction techniques.

cs.CR↗

arXiv2026

Weak Composition Lattices and Ring-Linear Anticodes

Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works connecting lattice theory, anticodes, and coding-theoretic invariants, we investigate ring-linear codes endowed with the Lee metric. We introduce and characterize optimal Lee-metric anticodes over the ring $\mathbb{Z}/p^s\mathbb{Z}$. We show that the family of such anticodes admits a natural partition into subtypes and forms a lattice under inclusion. We establish a bijection between this lattice and a lattice of weak compositions ordered by dominance. As an application, we use this correspondence to introduce new invariants for Lee-metric codes via an anticode approach.

cs.IT↗

arXiv2025

Sequence Reconstruction over Coloring Channels for Protein Identification

This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed subset (the coloring) of the alphabet. By extending this to a coloring profile, a tuple of distinct colorings, we analyze the channel's information rate and capacity. We prove that optimal (i.e., achieving maximum information rate) coloring profiles correspond to 2-covering designs and identify the minimal covering number required for maximum information rate, as well as the minimum number for which any coloring profile is optimal.

cs.IT↗

arXiv2024

Coarsest Fourier-reflexive Partitions for the Lee, Homogeneous and Subfield Metric

MacWilliams identities relate the weight enumerators of a code with those of its dual and are classically formulated with respect to the Hamming weight. For other metrics, however, these identities often fail when considering the weight partition of the ambient space. It is known that MacWilliams identities hold for enumerators associated with Fourier-reflexive partitions, and that orbits of subgroups of the linear isometry group always yield such partitions. This raises the question whether, for metrics beyond the Hamming metric, there exist meaningful partitions that lie strictly between the weight partition and the orbit partition: finer than the latter, yet still coarse enough to retain useful MacWilliams-type identities. In this work, we study this question for finite chain rings endowed with additive metrics. For the Lee metric, we show that the partition induced by the action of the full group of linear isometries is already the coarsest Fourier-reflexive partition refining the weight partition. In particular, no intermediate partition exists that is both finer than the Lee weight partition and Fourier-reflexive. We refer to this partition as the Lee partition and show that it allows the recovery of all additive weight enumerators over the ring. In contrast, for the homogeneous metric and for the subfield metric, we identify new, significantly coarser symmetrized partitions that remain Fourier-reflexive and still allow the recovery of the corresponding weight enumerators. We prove that these partitions are the coarsest such symmetrized partitions for which MacWilliams-type identities hold. As an application, we derive linear programming bounds based on the resulting MacWilliams identities.

math.AC↗

arXiv2024

Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics

This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive improved upper and lower bounds based on the entropy of a distribution related to the Boltzmann distribution, which work for any coordinate-additive metric. Additionally, we derive new closed-form upper and lower bounds specifically for the sum-rank metric that outperform existing closed-form bounds.

cs.IT↗

arXiv2023

Error-Correction Performance of Regular Ring-Linear LDPC Codes over Lee Channels

Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their error-correction performance is studied over two channel models, in the Lee metric. The first channel model is a discrete memoryless channel, whereas in the second channel model an error vector is drawn uniformly at random from all vectors of a fixed Lee weight. It is known that the two channel laws coincide in the asymptotic regime, meaning that their marginal distributions match. For both channel models, we derive upper bounds on the block error probability in terms of a random coding union bound as well as sphere packing bounds that make use of the marginal distribution of the considered channels. We estimate the decoding error probability of regular LDPC code ensembles over the channels using the marginal distribution and determining the expected Lee weight distribution of a random LDPC code over a finite integer ring. By means of density evolution and finite-length simulations, we estimate the error-correction performance of selected LDPC code ensembles under belief propagation decoding and a low-complexity symbol message passing decoding algorithm and compare the performances. The analysis developed in this paper may serve to design regular LDPC codes over integer residue rings for storage and cryptographic application.

cs.IT↗

arXiv2023

Better bounds on the minimal Lee distance

This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear code. In this regard, we introduce three main different support types for codes in the Lee metric and analyze their utility to derive bounds on the minimum Lee distance. Eventually, we propose a new point of view to generalized weights and give an improved bound on the minimum distance of codes in the Lee metric for which we discuss the density of maximum Lee distance codes with respect to this novel Singleton-like bound.

cs.IT↗

arXiv2022

Analysis of Low-Density Parity-Check Codes over Finite Integer Rings for the Lee Channel

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distributions of the two channels coincide, in the limit of large block length. Random coding union bounds on the block error probability are derived for both channels. Moreover, the performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm and it is compared to the derived bounds.

cs.IT↗

arXiv2022

Information Set Decoding for Lee-Metric Codes using Restricted Balls

The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternative for classical code-based cryptography. Unlike in the Hamming metric, an error vector that is chosen uniform at random of a given Lee weight is expected to have only few entries with large Lee weight. Using this expected distribution of entries, we are able to drastically decrease the cost of generic decoders in the Lee metric, by reducing the original problem to a smaller instance, whose solution lives in restricted balls.

cs.IT↗

arXiv2022

On the Properties of Error Patterns in the Constant Lee Weight Channel

The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of particular interest for cryptographic applications, like for example Lee metric code-based cryptosystems, since an attacker may use scalar multiplication to reduce the Lee weight of the error vector and thus to reduce the complexity of the corresponding generic decoder. The scalar multiplication problem is analyzed in the asymptotic regime. Furthermore, the construction of a vector with constant Lee weight using integer partitions is analyzed and an efficient method for drawing vectors of constant Lee weight uniformly at random from the set of all such vectors is given.

cs.IT↗

arXiv2021

Moderate Density Parity-Check Codes from Projective Bundles

A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a parity-check matrix for this family of binary codes as the concatenation of two matrices: the incidence matrix between points and lines of the Desarguesian projective plane and the incidence matrix between points and ovals of a projective bundle. A projective bundle is a special collection of ovals which pairwise meet in a unique point. We determine minimum distance and dimension of these codes, showing that they have a natural quasi-cyclic structure. In addition, we analyze the error-correction performance within one round of a modification of Gallager's bit-flipping decoding algorithm. In this setting, our codes have the best possible error-correction performance for this range of parameters.

cs.IT↗