arXiv subjects

Antonia Wachter-Zeh

Publications and source records attributed to Antonia Wachter-Zeh.

At least 19 recordsLinked to original sources

arXiv2026

On the Average List Size of VT Codes under Two Insertions or Two Deletions

Levenshtein's classical theorem shows that any code that can uniquely decode from $t$ deletions can also uniquely decode from $t$ insertions. This symmetry, however, does not generally hold in the list-decoding regime. Several prior results on the capacity and radii of list-decoding from insertions and deletions suggest that insertions are easier to handle than deletions. In an effort to better understand this asymmetry between insertions and deletions under list-decoding, we study an analogous version of McEliece's \emph{average list size problem}. More precisely, given a binary code $\mathcal{C}$ of length $n$ that uniquely corrects $t'$ insertions (or deletions), we are interested in the average number of codewords returned by a $t$-insertion (or deletion) list decoder, where $t' < t$. Focusing on the case of $t'=1$ and $t=2$, we find that under two insertions, this quantity is at most $(n+12)/4$ for any VT code of length $n$, whereas under two deletions it is at least $n/2 - 10$ when averaged over all length-$n$ VT codes. The nearly factor-of-two gap between these upper and lower bounds serves to confirm the relative ease of list-decoding of insertions compared to deletions from an average-case perspective.

cs.IT↗

arXiv2026

Orthogonal SC-LDPC Codes for the IDS Channel

We propose a coding scheme for the insertion, deletion and substitution (IDS) channel tailored to the short strands of DNA-based data storage. Instead of an inner synchronisation code, a spatially coupled LDPC (SC-LDPC) code is placed across the strands, with its coupling axis aligned to the position along the strands. Every decoded position thus becomes an anchor to synchronise the neighbouring strands. The decoding waves of the SC-LDPC code carry these anchors from both ends of the strands towards the middle. We bound the achievable rate from above by the information rate of a single strand and from below by that of a separated receiver. For strands of 100 nucleotides (the relevant regime for DNA-based data storage), our scheme outperforms a rate-matched concatenated construction.

cs.IT↗

arXiv2026

Secure Over-the-Air Computation Against Multiple Eavesdroppers using Correlated Artificial Noise

Over-the-air (OtA) computation enables scalable analog aggregation by exploiting the superposition property of wireless channels, making it an attractive joint communication and computation paradigm for distributed sensing and learning. However, the uncoded nature of analog transmission exposes the computation result to eavesdropping, and the fundamental security limits of OtA computation against multiple cooperating adversaries remain poorly understood. In this paper, we develop an estimation-theoretic framework for analyzing the security of analog OtA computation in the presence of multiple distributed eavesdroppers that may jointly process their observations. We first derive the optimal estimator for cooperating eavesdroppers and bounds on the achievable estimation accuracy of both the legitimate receiver and the adversaries. Our analysis reveals a key insight: while random channel phase misalignment provides significant inherent MSE-security against individual eavesdroppers, this protection largely disappears once multiple eavesdroppers cooperate. Motivated by this observation, we propose a correlated artificial noise design based on zero-forcing that preserves the aggregation accuracy at the legitimate receiver while maximizing the estimation error at the cooperative eavesdroppers. Numerical results demonstrate that the proposed design substantially reduces the security advantage gained through eavesdropper cooperation and achieves security close to uncorrelated artificial-noise schemes without sacrificing computation accuracy. These results provide both a theoretical characterization of the security limits of analog OtA computation and a practical design guideline for its secure deployment in real-world wireless systems.

eess.SP↗

arXiv2026

Probabilistic GC-Constraints for Composite DNA

This paper addresses the challenge of encoding biochemical GC-content constraints in composite DNA-based data storage. Previous deterministic models impose high rate penalties by avoiding any possibility for a strand to fall outside the allowed range. To account for the stochastic nature of composite DNA, we introduce an $ε$-probabilistic constraint framework, and derive capacity bounds for global constraints using composition types and for local sliding-window constraints via finite-state Markov chains. Furthermore, we propose a capacity-achieving multi-type enumerative encoder.

cs.IT↗

arXiv2026

Coding Schemes for the Noisy Torn Paper Channel

To make DNA a suitable medium for archival data storage, it is essential to consider the decay process of the strands observed in DNA storage systems. This paper studies the decay process as a probabilistic noisy torn paper channel (TPC), which first corrupts the bits of the transmitted sequence in a probabilistic manner by substitutions, then breaks the sequence into a set of noisy unordered substrings. The present work devises coding schemes for the noisy TPC by embedding markers in the transmitted sequence. We investigate the use of static markers and markers connected to the data in the form of hash functions. These two tools have also been recently exploited to tackle the noiseless TPC. Simulations show that static markers excel at higher substitution probabilities, while data-dependent markers are superior at lower noise levels. Both approaches achieve reconstruction rates exceeding 99% with no false decodings observed, primarily limited by computational resources.

cs.IT↗

arXiv2026

A Security Framework for Chemical Functions

In this paper, we provide a unified security framework with the goal of being able to evaluate and compare different (known and new) approaches for authentication and encryption using, for example, DNA-based schemes. Therefore, we introduce and rigorously define chemical functions which model 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 the data from two existing DNA-based constructions ("operable random DNA" and "Genomic Sequence Encryption") and derive quantitative bounds for robustness, unclonability, and unpredictability. These results place DNA-based chemical functions on a rigorous cryptographic footing, enabling principled design and comparison of chemically grounded authentication mechanisms. We demonstrate applications to in-product authentication and to shared key generation using standard extraction techniques, showing the significance of this work regarding real-world applications.

cs.CR↗

arXiv2026

Private Information Retrieval for Large-Scale DNA-Based Data Storage

We investigate Private Information Retrieval (PIR) in the context of synthetic DNA-based data storage. While PIR is a well-studied primitive for digital databases, extending it to DNA-based databases presents unique challenges arising from biochemical query mechanisms and their complexity. We propose two approaches for adapting two-server PIR protocols to DNA-based storage, balancing privacy, efficiency, and feasibility. These approaches illustrate how information-theoretic privacy trade-offs manifest in DNA-based storage systems.

cs.IR↗

arXiv2026

SynDe: Syndrome-guided Decoding of Raw Nanopore Reads

Nanopore sequencing technology remains highly error-prone, making efficient error correction essential in DNA-based data storage. Prior work addressed high error rates using convolutional codes with their decoder coupled with the basecaller, but such approaches only accommodate a limited number of code classes and incur significant decoding complexity. To overcome these limitations, we propose two algorithms: PrimerSeeker, which efficiently detects primer sequences in raw nanopore sequencing reads, and SynDe, a decoder that operates on the same raw reads and supports any linear error correction code with a low-complexity graphical representation. PrimerSeeker provides primer location estimates close to those of existing approaches while being better suited for real-time primer detection during sequencing. SynDe performs well with convolutional codes augmented with periodic markers, often approaching or exceeding the performance of existing algorithms with a lower time complexity. Remarkably, the confidence scores produced by SynDe reliably identify which of its outputs should be discarded.

cs.IT↗

arXiv2026

Coding Schemes for Document Exchange under Multiple Substring Edits

We study the document exchange problem under multiple substring edits. A substring edit in a string $\mathbf{x}$ occurs when a substring $\mathbf{u}$ of $\mathbf{x}$ is replaced by an arbitrary string $\mathbf{v}$. The lengths of $\mathbf{u}$ and $\mathbf{v}$ are bounded from above by a fixed constant. Let $\mathbf{x}$ and $\mathbf{y}$ be two binary strings that differ by multiple substring edits. The aim of document exchange schemes is to construct an encoding of $\mathbf{x}$ with small length such that $\mathbf{x}$ can be recovered using $\mathbf{y}$ and the encoding. We construct a low-complexity document exchange scheme with encoding length of $4t\log n+o(\log n)$ bits, where $n$ is the length of the string $\mathbf{x}$. The best known scheme achieves an encoding length of $4t \log n+O(\log\log n)$ bits, but at a much higher computational complexity. Then, we investigate the average length of valid encodings for document exchange schemes with uniform strings $\mathbf{x}$ and develop a scheme with an expected encoding length of $(4t-1) \log n+o(\log n)$ bits. In this setting, prior works have only constructed schemes for a single substring edit.

cs.IT↗

arXiv2026

On the Extension of Private Distributed Matrix Multiplication Schemes to the Grid Partition

We consider polynomial codes for private distributed matrix multiplication (PDMM/SDMM). Existing codes for PDMM are either specialized for the outer product partitioning (OPP), or inner product partitioning (IPP), or are valid for the more general grid partitioning (GP). We design extension operations that can be applied to a large class of OPP code designs to extend them to the GP case. Applying them to existing codes improves upon the state-of-the-art for certain parameters. Additionally, we show that the GP schemes resulting from extension fulfill additional combinatorial constraints, potentially limiting their performance. We illustrate this point by presenting a new GP scheme that does not adhere to these constraints and outperforms the state-of-the-art for a range of parameters.

cs.IT↗

arXiv2026

TCitH- and VOLEitH-based Signatures from Restricted Decoding

Threshold-Computation-in-the-Head (TCitH) and VOLE-in-the-Head (VOLEitH), two recent developments of the MPC-in-the-Head (MPCitH) paradigm, have significantly improved the performance of digital signature schemes. This work embeds the restricted decoding problem within these frameworks: we propose a structurally simple modeling that achieves competitive signature sizes. Specifically, by instantiating the restricted decoding problem with the same hardness assumption underlying CROSS, we reduce sizes by more than a factor of two compared to the NIST submission. Moreover, we observe that ternary full-weight decoding, closely related to the hardness assumption underlying WAVE, is a restricted decoding problem. Using ternary full-weight decoding, we obtain signature sizes comparable to the smallest MPCitH-based candidates in the NIST competition.

cs.CR↗

arXiv2026

Post-Quantum Secure Aggregation via Code-Based Homomorphic Encryption

Secure aggregation enables aggregation of inputs from multiple parties without revealing individual contributions to the server or other clients. Existing post-quantum approaches based on homomorphic encryption offer practical efficiency but predominantly rely on lattice-based hardness assumptions. We present a code-based alternative for secure aggregation by instantiating a general framework based on key- and message-additive homomorphic encryption under the Learning Parity with Noise (LPN) assumption. Our construction employs a committee-based decryptor realized via secret sharing and incorporates a Chinese Remainder Theorem (CRT)-based optimization to reduce the communication costs of LPN-based instantiations. We analyze the security of the proposed scheme under a new Hint-LPN assumption and show that it is equivalent to standard LPN for suitable parameters. Finally, we evaluate performance and identify regimes in which our approach outperforms information-theoretically secure aggregation protocols.

cs.CR↗

arXiv2025

Correcting Multiple Substitutions in Nanopore-Sequencing Reads

Despite their significant advantages over competing technologies, nanopore sequencers are plagued by high error rates, due to physical characteristics of the nanopore and inherent noise in the biological processes. It is thus paramount not only to formulate efficient error-correcting constructions for these channels, but also to establish bounds on the minimum redundancy required by such coding schemes. In this context, we adopt a simplified model of nanopore sequencing inspired by the work of Mao \emph{et al.}, accounting for the effects of intersymbol interference and measurement noise. For an input sequence of length $n$, the vector that is produced, designated as the \emph{read vector}, may additionally suffer at most $t$ substitution errors. We employ the well-known graph-theoretic clique-cover technique to establish that at least $t\log n -O(1)$ bits of redundancy are required to correct multiple ($t \geq 2$) substitutions. While this is surprising in comparison to the case of a single substitution, that necessitates at most $\log \log n - O(1)$ bits of redundancy, a suitable error-correcting code that is optimal up to a constant follows immediately from the properties of read vectors.

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↗

arXiv2025

CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication

We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic-addition degree tables (CATs). By using roots of unity as evaluation points, we enable modulo-addition in the table. Based on CATs, we present an explicit construction, called CATx, that requires fewer workers than existing schemes in the low-privacy regime. Additionally, we present new families of schemes based on conventional degree tables, called GASPrs and DOGrs, that outperform the state-of-the-art for a wide range of parameters.

cs.IT↗

arXiv2025

Source Anonymity for Private Random Walk Decentralized Learning

This paper considers random walk-based decentralized learning, where at each iteration of the learning process, one user updates the model and sends it to a randomly chosen neighbor until a convergence criterion is met. Preserving data privacy is a central concern and open problem in decentralized learning. We propose a privacy-preserving algorithm based on public-key cryptography and anonymization. In this algorithm, the user updates the model and encrypts the result using a distant user's public key. The encrypted result is then transmitted through the network with the goal of reaching that specific user. The key idea is to hide the source's identity so that, when the destination user decrypts the result, it does not know who the source was. The challenge is to design a network-dependent probability distribution (at the source) over the potential destinations such that, from the receiver's perspective, all users have a similar likelihood of being the source. We introduce the problem and construct a scheme that provides anonymity with theoretical guarantees. We focus on random regular graphs to establish rigorous guarantees.

cs.CR↗

arXiv2025

Multi-Terminal Remote Generation and Estimation Over a Broadcast Channel With Correlated Priors

We study the multi-terminal remote estimation problem under a rate constraint, in which the goal of the encoder is to help each decoder estimate a function over a certain distribution -- while the distribution is known only to the encoder, the function to be estimated is known only to the decoders, and can also be different for each decoder. The decoders can observe correlated samples from prior distributions, instantiated through shared randomness with the encoder. To achieve this, we employ remote generation, where the encoder helps decoders generate samples from the underlying distribution by using the samples from the prior through importance sampling. While methods such as minimal random coding can be used to efficiently transmit samples to each decoder individually using their importance scores, it is unknown if the correlation among the samples from the priors can reduce the communication cost using the availability of a broadcast link. We propose a hierarchical importance sampling strategy that facilitates, in the case of non-zero Gács-Körner common information among the priors of the decoders, a common sampling step leveraging the availability of a broadcast channel. This is followed by a refinement step for the individual decoders. We present upper bounds on the bias and the estimation error for unicast transmission, which is of independent interest. We then introduce a method that splits into two phases, dedicated to broadcast and unicast transmission, respectively, and show the reduction in communication cost.

cs.IT↗

arXiv2025

Decoding Insertions/Deletions via List Recovery

In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and deletions to that of decoding substitution and erasures. Our new approach, presented in this paper, reduces the problem of decoding insertions and deletions to that of list recovery. Specifically, any $(ρ, 2ρn + 1, L)$-list-recoverable code is a $(ρ, L)$-list decodable insdel code. As an example, we apply this technique to Reed-Solomon (RS) codes, which are known to have efficient list-recovery algorithms up to the Johnson bound. In the adversarial insdel model, this provides efficient (list) decoding from $t$ insdel errors, assuming that $t\cdot k = O(n)$. This is the first efficient insdel decoder for $[n, k]$ RS codes for $k>2$. Additionally, we explore random insdel models, such as the Davey-MacKay channel, and show that for certain choices of $ρ$, a $(ρ, n^{1/2+0.001}, L)$-list-recoverable code of length $n$ can, with high probability, efficiently list decode the channel output, ensuring that the transmitted codeword is in the output list. In the context of RS codes, this leads to a better rate-error tradeoff for these channels compared to the adversarial case. We also adapt the Koetter-Vardy algorithm, a famous soft-decision list decoding technique for RS codes, to correct insertions and deletions induced by the Davey-MacKay channel.

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