arXiv subjects

Serge Kas Hanna

Publications and source records attributed to Serge Kas Hanna.

18 recordsLinked to original sources

arXiv2026

Marker-Delimited Codes for Short-Blocklength, High-Rate Coding over Multi-Read Edit Channels

The read process of DNA-based data storage systems generates multiple noisy copies of the stored DNA sequences, affected by edit errors consisting of substitutions, deletions, and insertions. Motivated by the challenge of ensuring reliable data retrieval in the presence of edit errors, we present a concatenated coding scheme that accounts for practical design constraints in DNA storage. We introduce and apply the marker-delimited code (MDC) as the inner code, which enables fast and reliable computation of symbolwise a posteriori probabilities (APPs). We combine MDC with an outer LDPC code. The LDPC is decoded via belief propagation using the soft information generated by MDC. Our results show that, in comparison with prior work, this construction provides more efficient error correction over multi-read edit channels in the short-blocklength and high-rate regime.

cs.IT↗

arXiv2026

DNA-MGC+: A versatile codec for reliable and resource-efficient data storage on synthetic DNA

The biochemical processes underlying DNA data storage, including synthesis, amplification, and sequencing, are inherently noisy. Consequently, base-level insertion, deletion, and substitution (IDS) errors, as well as sequence-level dropouts, occur and pose major challenges for reliable data retrieval. Here we introduce DNA-MGC+, a DNA storage codec designed to enable reliable and resource-efficient data retrieval under diverse operating conditions. We evaluate DNA-MGC+ across a wide range of in silico and in vitro settings, including experiments with both Illumina and Nanopore sequencing, and show that it consistently outperforms several representative codecs from the literature. In particular, DNA-MGC+ achieves simultaneous gains in sequencing depth requirements, read cost, decoding time, storage density, and error-correction capability under explicit reliability constraints. These gains persist and become more pronounced for larger files, with DNA-MGC+ remaining reliable and efficient well beyond the practical scalability limits of the benchmarked codecs. Notable performance results include reliable decoding under IDS error rates of up to 24% in synthetic scenarios, and reliable retrieval at sequencing depths below 3x with read costs below 3.5 nts/bit under electrochemical synthesis for both Illumina and Nanopore sequencing.

cs.IT↗

arXiv2026

The Synthesis-Sequencing Channel for DNA-based Data Storage

We introduce and study the synthesis-sequencing channel, a two-stage model for DNA-based data storage that jointly captures synthesis and sequencing effects. The synthesis-sequencing channel provides a more nuanced and realistic model of the DNA storage process compared to prior work, as it distinguishes between physical coverage after synthesis and sequencing coverage after readout, relaxes the assumption of independent errors across reads, and naturally induces coverage bias through the composition of synthesis and sequencing stages. We establish the information-theoretic capacity of this channel by deriving matching converse and achievability bounds for the case where synthesis and sequencing errors are modeled by binary symmetric channels with possibly different error probabilities, under mild assumptions on the channel parameters. Our results reveal multiple trade-offs between physical coverage, synthesis errors, sequencing coverage, and sequencing errors that influence the maximum achievable rate for reliable data storage.

cs.IT↗

arXiv2026

On the Reliability of Information Retrieval From MDS Coded Data in DNA Storage

This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed (i.i.d.) substitution errors, focusing on a common code design strategy that combines inner and outer MDS codes. Our analysis demonstrates how this probability depends on factors such as the total number of sequencing reads, their distribution across strands, the rates of the inner and outer codes, and the substitution error probabilities. These results provide actionable insights into optimizing DNA storage systems under reliability constraints, including determining the minimum number of sequencing reads needed for reliable data retrieval and identifying the optimal balance between the rates of inner and outer MDS codes.

cs.IT↗

arXiv2025

GC+ Code: A Systematic Short Blocklength Code for Correcting Random Edit Errors in DNA Storage

Storing digital data in synthetic DNA faces challenges in ensuring data reliability in the presence of edit errors--deletions, insertions, and substitutions--that occur randomly during various stages of the storage process. Current limitations in DNA synthesis technology also impose the use of short DNA sequences, highlighting the particular need for short edit-correcting codes. Motivated by these factors, we introduce a systematic code designed to correct random edits while adhering to typical length constraints in DNA storage. We evaluate its performance both theoretically and through simulations, and assess its integration within a DNA storage framework, revealing promising results.

cs.IT↗

arXiv2024

Approximate Gradient Coding for Privacy-Flexible Federated Learning with Non-IID Data

This work focuses on the challenges of non-IID data and stragglers/dropouts in federated learning. We introduce and explore a privacy-flexible paradigm that models parts of the clients' local data as non-private, offering a more versatile and business-oriented perspective on privacy. Within this framework, we propose a data-driven strategy for mitigating the effects of label heterogeneity and client straggling on federated learning. Our solution combines both offline data sharing and approximate gradient coding techniques. Through numerical simulations using the MNIST dataset, we demonstrate that our approach enables achieving a deliberate trade-off between privacy and utility, leading to improved model convergence and accuracy while using an adaptable portion of non-private data.

cs.LG↗

arXiv2023

Optimal Codes Detecting Deletions in Concatenated Binary Strings Applied to Trace Reconstruction

Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $δ$ deletions occur in each of the concatenated strings. Since deletions alter the lengths of the strings, a fundamental question to ask is: how much redundancy do we need to introduce in $\mathbf{x}$ in order to recover the boundaries of $\mathbf{x}^1,\mathbf{x}^2,\ldots$? This boundary problem is equivalent to the problem of designing codes that can detect the exact number of deletions in each concatenated string. In this work, we answer the question above by first deriving converse results that give lower bounds on the redundancy of deletion-detecting codes. Then, we present a marker-based code construction whose redundancy is asymptotically optimal in $δ$ among all families of deletion-detecting codes, and exactly optimal among all block-by-block decodable codes. To exemplify the usefulness of such deletion-detecting codes, we apply our code to trace reconstruction and design an efficient coded reconstruction scheme that requires a constant number of traces.

cs.IT↗

arXiv2023

Fast and Straggler-Tolerant Distributed SGD with Reduced Computation Load

In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the effect of unresponsive or slow workers called stragglers, that otherwise degrade the benefit of outsourcing the computation. This can be done by only waiting for a subset of the workers to finish their computation at each iteration of the algorithm. Previous works proposed to adapt the number of workers to wait for as the algorithm evolves to optimize the speed of convergence. In contrast, we model the communication and computation times using independent random variables. Considering this model, we construct a novel scheme that adapts both the number of workers and the computation load throughout the run-time of the algorithm. Consequently, we improve the convergence speed of distributed SGD while significantly reducing the computation load, at the expense of a slight increase in communication load.

cs.DC↗

arXiv2023

Codes Correcting Burst and Arbitrary Erasures for Reliable and Low-Latency Communication

Motivated by modern network communication applications which require low latency, we study codes that correct erasures with low decoding delay. We provide a simple explicit construction that yields convolutional codes that can correct both burst and arbitrary erasures under a maximum decoding delay constraint $T$. Our proposed code has efficient encoding/decoding algorithms and requires a field size that is linear in $T$. We study the performance of our code over the Gilbert-Elliot channel; our simulation results show significant performance gains over low-delay codes existing in the literature.

cs.IT↗

arXiv2022

Adaptive Stochastic Gradient Descent for Fast and Communication-Efficient Distributed Learning

We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or unresponsive workers who cause delays. One solution studied in the literature is to wait at each iteration for the responses of the fastest $k<n$ workers before updating the model, where $k$ is a fixed parameter. The choice of the value of $k$ presents a trade-off between the runtime (i.e., convergence rate) of SGD and the error of the model. Towards optimizing the error-runtime trade-off, we investigate distributed SGD with adaptive~$k$, i.e., varying $k$ throughout the runtime of the algorithm. We first design an adaptive policy for varying $k$ that optimizes this trade-off based on an upper bound on the error as a function of the wall-clock time that we derive. Then, we propose and implement an algorithm for adaptive distributed SGD that is based on a statistical heuristic. Our results show that the adaptive version of distributed SGD can reach lower error values in less time compared to non-adaptive implementations. Moreover, the results also show that the adaptive version is communication-efficient, where the amount of communication required between the master and the workers is less than that of non-adaptive versions.

cs.LG↗

arXiv2022

Coding for Trace Reconstruction over Multiple Channels with Vanishing Deletion Probabilities

Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each bit of the input codeword $\mathbf{x} \in \{0,1\}^n$ independently with probability $p$. We focus on the regime where the deletion probability $p \to 0$ when $n\to \infty$. Our main contribution is designing a novel code for trace reconstruction that allows reconstructing a coded sequence efficiently from a constant number of traces. We provide theoretical results on the performance of our code in addition to simulation results where we compare the performance of our code to other reconstruction techniques in terms of the edit distance error.

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arXiv2021

Optimal Codes Correcting Localized Deletions

We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of size $k$, where the positions of the deletions within this window are not necessarily consecutive. Localized deletions are thus a generalization of burst deletions that occur in consecutive positions. We present novel explicit codes that are efficiently encodable and decodable and can correct up to $k$ localized deletions. Furthermore, these codes have $\log n+\mathcal{O}(k \log^2 (k\log n))$ redundancy, where $n$ is the length of the information message, which is asymptotically optimal in $n$ for $k=o(\log n/(\log \log n)^2)$.

cs.IT↗

arXiv2021

Detecting Deletions and Insertions in Concatenated Strings with Optimal Redundancy

We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a converse result which shows that the redundancy of our codes is asymptotically optimal in $\del$ among all families of deletion detecting codes, and particularly optimal among all block-by-block decodable codes. For the case of insertions, we construct codes that can detect up to $2$ insertions in each concatenated binary string.

cs.IT↗

arXiv2021

Codes for Correcting Localized Deletions

We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $δ\leq w$ deletions are localized in a window of size $w$ bits. These $δ$ deletions do not necessarily occur in consecutive positions, but are restricted to the window of size $w$. The localized deletions model is a generalization of the bursty model, in which all the deleted bits are consecutive. In this paper, we construct new explicit codes for the localized model, based on the family of Guess & Check codes which was previously introduced by the authors. The codes that we construct can correct, with high probability, $δ\leq w$ deletions that are localized in a single window of size $w$, where $w$ grows with the block length. Moreover, these codes are systematic; have low redundancy; and have efficient deterministic encoding and decoding algorithms. We also generalize these codes to deletions that are localized within multiple windows in the codeword.

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arXiv2020

Adaptive Distributed Stochastic Gradient Descent for Minimizing Delay in the Presence of Stragglers

We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or unresponsive workers who cause delays. One solution studied in the literature is to wait at each iteration for the responses of the fastest $k<n$ workers before updating the model, where $k$ is a fixed parameter. The choice of the value of $k$ presents a trade-off between the runtime (i.e., convergence rate) of SGD and the error of the model. Towards optimizing the error-runtime trade-off, we investigate distributed SGD with adaptive $k$. We first design an adaptive policy for varying $k$ that optimizes this trade-off based on an upper bound on the error as a function of the wall-clock time which we derive. Then, we propose an algorithm for adaptive distributed SGD that is based on a statistical heuristic. We implement our algorithm and provide numerical simulations which confirm our intuition and theoretical analysis.

cs.LG↗

arXiv2019

List Decoding of Deletions Using Guess & Check Codes

Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes are deterministic and run in polynomial time for a constant number of deletions $δ$. The unique decoding properties of GC codes were examined in a previous work by the authors. In this paper, we investigate the list decoding performance of these codes. Namely, we study the average size and the maximum size of the list obtained by a GC decoder for a constant number of deletions $δ$. The theoretical results show that: (i) the average size of the list approaches $1$ as $k$ grows; and (ii) there exists an infinite sequence of GC codes indexed by $k$, whose maximum list size in upper bounded by a constant that is independent of $k$. We also provide numerical simulations on the list decoding performance of GC codes for multiple values of $k$ and $δ$.

cs.IT↗

arXiv2018

Guess & Check Codes for Deletions, Insertions, and Synchronization

We consider the problem of constructing codes that can correct $δ$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes, dating back to 1965, are zero-error single deletion $(δ=1)$ correcting codes, and have an asymptotically optimal redundancy. Finding similar codes for $δ\geq 2$ deletions remains an open problem. In this work, we relax the standard zero-error (i.e., worst-case) decoding requirement by assuming that the positions of the $δ$ deletions (or insertions) are independent of the codeword. Our contribution is a new family of explicit codes, that we call Guess & Check (GC) codes, that can correct with high probability up to a constant number of $δ$ deletions (or insertions). GC codes are systematic; and have deterministic polynomial time encoding and decoding algorithms. We also describe the application of GC codes to file synchronization.

cs.IT↗

arXiv2017

Guess & Check Codes for Deletions and Synchronization

We consider the problem of constructing codes that can correct $δ$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(δ=1)$ with an asymptotically optimal redundancy. Finding similar codes for $δ\geq 2$ deletions is an open problem. We propose a new family of codes, that we call Guess & Check (GC) codes, that can correct, with high probability, a constant number of deletions $δ$ occurring at uniformly random positions within an arbitrary string. The GC codes are based on MDS codes and have an asymptotically optimal redundancy that is $Θ(δ\log n)$. We provide deterministic polynomial time encoding and decoding schemes for these codes. We also describe the applications of GC codes to file synchronization.

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