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João Ribeiro

Publications and source records attributed to João Ribeiro.

At least 19 recordsLinked to original sources
arXiv2026

Discrepancy for Random Linear Codes

We show that random linear codes (RLCs) possess nearly optimal discrepancy-type properties in a broad range of settings. Our main results are two general discrepancy theorems: one controls all translates of a fixed test, and the other controls large families of Fourier-pseudorandom tests. Two motivating examples follow: First, RLCs behave essentially like unstructured random codes for list-decoding from errors above capacity. More precisely, an RLC $C\subseteq \mathbb{F}_q^n$ of rate $1 - \frac{1}{n}\log_q|B_ρ| + \varepsilon$, where $|B_ρ|$ is the volume of a radius-$ρ$ Hamming ball in $\mathbb{F}_q^n$, satisfies $|C \cap B| = (1\pm o(1)) \frac{|C|\cdot |B|}{q^n}$ simultaneously for all radius-$ρ$ Hamming balls $B$ with high probability. This vastly generalizes the previously best known fact that RLCs of this rate have covering radius at most $ρn$ with high probability (Blinovsky, 1987). Second, over prime fields, RLCs behave essentially like unstructured random codes for zero-error list-recovery, and list-recovery from erasures, above capacity. More precisely, for a prime $q>2$ and input list size $2\leq \ell\leq q-1$, an RLC $C\subseteq \mathbb{F}_q^n$ of rate $1-\log_q \ell+\varepsilon$ will satisfy $|C \cap S| = (1\pm o(1)) \frac{|C|\cdot \ell^n}{q^n}$ simultaneously for all combinatorial rectangles $S=S_1\times S_2\times\cdots\times S_n$, where $|S_i|=\ell$ for all $i$, with high probability. An analogous result also holds when we can bound $|S_i|$ only for some of the $i$'s. We use this to show the abundance of locally leakage-resilient $n$-party linear ramp secret sharing schemes with any linear reconstruction threshold and sublinear threshold gap $O(n/\log n)$ over fields of polynomial size $q=Θ(n^γ)$ for a constant $γ\in(0,1/5)$. Prior work was stuck at reconstruction thresholds above $n/2$ for both threshold and ramp schemes.

cs.IT↗
arXiv2026

Capacity of Additive-Noise Sticky Channels

Sticky channels, which never destroy nor create runs, are some of the simplest types of channels with synchronization errors (such as deletions, insertions, and replications). Despite their simplicity, we know little about the capacity of the sticky channels considered in the literature so far beyond what can be gleaned from purely numerical methods. Towards a broader and systematic exploration of these channels, we initiate the study of additive-noise sticky channels, a basic family of sticky channels that extend each input run by an amount independently sampled from a fixed noise distribution. The capacity of these channels corresponds to the capacity per unit cost of additive-noise memoryless channels over the non-negative integers, and they capture some aspects of the loss of synchronization caused by homopolymer length miscalls in DNA sequencing. We first focus on the setting of Bernoulli additive noise with parameter $p$, and uncover curious behavior of the capacity beyond what numerical methods can tell us. For example, the capacity is constant when $p\in [1/φ^2,1/2]$ with $φ\approx 1.618$ the golden ratio, achieved by zero-error runlength-constrained coding, and behaves differently when $p\approx 0$ vs. when $p\approx 1$. More generally, we determine the capacity exactly for all $p\leq 1/2$, and when $1/2<p<1$ we give analytical bounds that allow us to characterize the asymptotic behavior of the capacity as $p\to 1$. We also extend our analysis to the setting where input strings have bounded runlengths, motivated by DNA-based data storage. Then, we study additive-noise sticky channels beyond Bernoulli noise. We derive capacity lower bounds for all additive-noise sticky channels whose noise distributions have a given mean and support. These lower bounds allow us to characterize the regime where zero-error runlength-constrained coding is never optimal.

cs.IT↗
arXiv2026

The Insertion List-Decoding Capacity and an Improved Bound on the Deletion List-Decoding Capacity

Informally, the capacity of list-decoding in a given adversarial error model is the largest rate at which we can list-decode with list size polynomial in the block length. The capacity of list-decoding from insertions and deletions is a basic, yet poorly understood, aspect of coding against synchronization errors. For example, when dealing with a $δ>1/2$ fraction of insertions, the best known lower bounds give little more than the fact that the capacity is positive. Beyond that regime we also only have loose bounds, with the lower bounds stemming from the analysis of uniformly random codes. We make progress in our understanding of the limits of list-decoding binary codes from insertions and deletions. We show that the capacity of list-decoding from a $δ$-fraction of insertions is exactly \begin{equation*} (1+δ)\left(1-h\left(\fracδ{1+δ}\right)\right) \end{equation*} for all $δ\in[0,1]$, achieved with high probability by a code sampled according to a symmetric $2$-state Markov chain. Curiously, we complement this by showing that such an approach does not beat uniformly random coding in list-decoding from deletions. We also give an improved upper bound on the capacity of list-decoding from a $δ$-fraction of deletions, showing in particular that it behaves like $1-h(δ)$ when $δ\to 0$. This matches the asymptotic behavior of the capacity of the binary deletion channel for vanishing deletion probability.

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

Correcting Contextual Deletions in DNA Nanopore Readouts

The problem of designing codes for deletion-correction and synchronization has received renewed interest due to applications in DNA-based data storage systems that use nanopore sequencers as readout platforms. In almost all instances, deletions are assumed to be imposed independently of each other and of the sequence context. These assumptions are not valid in practice, since nanopore errors tend to occur within specific contexts. We study contextual nanopore deletion-errors through the example setting of deterministic single deletions following (complete) runlengths of length at least $k$. The model critically depends on the runlength threshold $k$, and we examine two regimes for $k$: a) $k=C\log n$ for a constant $C\in(0,1)$; in this case, we study error-correcting codes that can protect from a constant number $t$ of contextual deletions, and show that the minimum redundancy (ignoring lower-order terms) is between $(1-C)t\log n$ and $2(1-C)t\log n$, meaning that it is a ($1-C$)-fraction of that of arbitrary $t$-deletion-correcting codes. To complement our non-constructive redundancy upper bound, we design efficiently and encodable and decodable codes for any constant $t$. In particular, for $t=1$ and $C>1/2$ we construct efficient codes with redundancy that essentially matches our non-constructive upper bound; b) $k$ equal a constant; in this case we consider the extremal problem where the number of deletions is not bounded and a deletion is imposed after every run of length at least $k$, which we call the extremal contextual deletion channel. This combinatorial setting arises naturally by considering a probabilistic channel that introduces contextual deletions after each run of length at least $k$ with probability $p$ and taking the limit $p\to 1$. We obtain sharp bounds on the maximum achievable rate under the extremal contextual deletion channel for arbitrary constant $k$.

cs.IT↗
arXiv2026

Channels with Input-Correlated Synchronization Errors

"Independent and identically distributed" errors do not accurately capture the noisy behavior of real-world data storage and information transmission technologies. Motivated by this, we study channels with input-correlated synchronization errors, meaning that the distribution of synchronization errors (such as deletions and insertions) applied to the $i$-th input $x_i$ may depend on the whole input string $x$. We begin by identifying conditions on the input-correlated synchronization channel under which the channel's information capacity is achieved by a stationary ergodic input source and is equal to its coding capacity. These conditions capture a wide class of channels, including channels with correlated errors observed in DNA-based data storage systems and their multi-trace versions, and generalize prior work. To showcase the usefulness of the general capacity theorem above, we combine it with techniques of Pernice-Li-Wootters (ISIT 2022) and Brakensiek-Li-Spang (FOCS 2020) to obtain explicit capacity-achieving codes for multi-trace channels with runlength-dependent deletions, motivated by error patterns observed in DNA-based data storage systems.

cs.IT↗
arXiv2026

Nearly-Linear Time Seeded Extractors with Short Seeds

Seeded extractors are fundamental objects in pseudorandomness and cryptography, and a deep line of work has designed polynomial-time seeded extractors with nearly-optimal parameters. However, existing constructions of seeded extractors with short seed length and large output length run in time $Ω(n \log(1/\varepsilon))$ and often slower, where $n$ is the input source length and $\varepsilon$ is the error of the extractor. Since cryptographic applications of extractors require $\varepsilon$ to be small, the resulting runtime makes these extractors impractical. Motivated by this, we explore constructions of strong seeded extractors with short seeds computable in nearly-linear time $O(n \log^c n)$, for any error $\varepsilon$. We show that an appropriate combination of modern condensers and classical approaches for constructing seeded extractors for high min-entropy sources yields such extractors. More precisely, we obtain strong extractors for $n$-bit sources with any min-entropy $k$ and any target error $\varepsilon$ with seed length $d=O(\log(n/\varepsilon))$ and output length $m=(1-η)k$ for an arbitrarily small constant $η>0$, running in nearly-linear time. When $k$ or $\varepsilon$ are very small, our construction requires a reasonable one-time preprocessing step. These extractors directly yield privacy amplification protocols with nearly-linear time complexity (possibly after a one-time preprocessing step), large output length, and low communication complexity. As a second contribution, we give an instantiation of Trevisan's extractor that can be evaluated in truly linear time in the RAM model, as long as the number of output bits is at most $\frac{n}{\log(1/\varepsilon)polylog(n)}$. Previous fast implementations of Trevisan's extractor ran in $\widetilde{O}(n)$ time in this setting.

cs.CC↗
arXiv2025

List-Recovery of Random Linear Codes over Small Fields

We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate $ε$-close to capacity, and aim to bound the dependence of the output list size $L$ on $ε$, the input list size $\ell$, and the alphabet size $q$. Prior to our work, the best upper bound was $L = q^{O(\ell/ε)}$ (Zyablov and Pinsker, Prob. Per. Inf. 1981). Previous work has identified cases in which linear codes provably perform worse than non-linear codes with respect to list-recovery. While there exist non-linear codes that achieve $L=O(\ell/ε)$, we know that $L \ge \ell^{Ω(1/ε)}$ is necessary for list recovery from erasures over fields of small characteristic, and for list recovery from errors over large alphabets. We show that in other relevant regimes there is no significant price to pay for linearity, in the sense that we get the correct dependence on the gap-to-capacity $ε$ and go beyond the Zyablov-Pinsker bound for the first time. Specifically, when $q$ is constant and $ε$ approaches zero: - For list-recovery from erasures over prime fields, we show that $L \leq C_1/ε$. By prior work, such a result cannot be obtained for low-characteristic fields. - For list-recovery from errors over arbitrary fields, we prove that $L \leq C_2/ε$. Above, $C_1$ and $C_2$ depend on the decoding radius, input list size, and field size. We provide concrete bounds on the constants above, and the upper bounds on $L$ improve upon the Zyablov-Pinsker bound whenever $q\leq 2^{(1/ε)^c}$ for some small universal constant $c>0$.

cs.IT↗
arXiv2025

Low-Degree Polynomials Are Good Extractors

We prove that random low-degree polynomials (over $\mathbb{F}_2$) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to our work, such results were only known for the small families of (1) uniform sources, (2) affine sources, and (3) local sources. We significantly generalize these results, and prove the following. 1. Low-degree polynomials extract from small families. We show that a random low-degree polynomial is a good low-error extractor for any small family of sources. In particular, we improve the positive result of Alrabiah, Chattopadhyay, Goodman, Li, and Ribeiro (ICALP 2022) for local sources, and give new results for polynomial and variety sources via a single unified approach. 2. Low-degree polynomials extract from sumset sources. We show that a random low-degree polynomial is a good extractor for sumset sources, which are the most general large family of sources (capturing independent sources, interleaved sources, small-space sources, and more). Formally, for any even $d$, we show that a random degree $d$ polynomial is an $\varepsilon$-error extractor for $n$-bit sumset sources with min-entropy $k=O(d(n/\varepsilon^2)^{2/d})$. This is nearly tight in the polynomial error regime. Our results on sumset extractors imply new complexity separations for linear ROBPs, and the tools that go into its proof may be of independent interest. The two main tools we use are a new structural result on sumset-punctured Reed-Muller codes, paired with a novel type of reduction between extractors. Using the new structural result, we obtain new limits on the power of sumset extractors, strengthening and generalizing the impossibility results of Chattopadhyay, Goodman, and Gurumukhani (ITCS 2024).

cs.CC↗
arXiv2024

Parameterized Inapproximability of the Minimum Distance Problem over all Fields and the Shortest Vector Problem in all $\ell_p$ Norms

We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite field and parameterized by the input distance bound is W[1]-hard to approximate within any constant factor. We also prove analogous results for the parameterized Shortest Vector Problem (SVP) on integer lattices. Specifically, we prove that SVP in the $\ell_p$ norm is W[1]-hard to approximate within any constant factor for any fixed $p >1$ and W[1]-hard to approximate within a factor approaching $2$ for $p=1$. (We show hardness under randomized reductions in each case.) These results answer the main questions left open (and explicitly posed) by Bhattacharyya, Bonnet, Egri, Ghoshal, Karthik C. S., Lin, Manurangsi, and Marx (Journal of the ACM, 2021) on the complexity of parameterized MDP and SVP. For MDP, they established similar hardness for binary linear codes and left the case of general fields open. For SVP in $\ell_p$ norms with $p > 1$, they showed inapproximability within some constant factor (depending on $p$) and left open showing such hardness for arbitrary constant factors. They also left open showing W[1]-hardness even of exact SVP in the $\ell_1$ norm.

cs.CC↗
arXiv2024

Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages

Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is $2$-split-state tampering. Here, a codeword is split into two parts and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length $n$, any message length at most $n^{Ω(1)}$, and error $ε=2^{-{n^{Ω(1)}}}$. In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to $1/11$.

cs.CR↗
arXiv2023

Semi-Quantitative Group Testing for Efficient and Accurate qPCR Screening of Pathogens with a Wide Range of Loads

Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease control and transmission prevention. Group testing is a well-established method for reducing the number of tests needed to screen large populations when the disease prevalence is low. However, it does not fully utilize the quantitative information provided by qPCR methods, nor is it able to accommodate a wide range of pathogen loads. To address these issues, we introduce a novel adaptive semi-quantitative group testing (SQGT) scheme to efficiently screen populations via two-stage qPCR testing. The SQGT method quantizes cycle threshold ($Ct$) values into multiple bins, leveraging the information from the first stage of screening to improve the detection sensitivity. Dynamic $Ct$ threshold adjustments mitigate dilution effects and enhance test accuracy. Comparisons with traditional binary outcome GT methods show that SQGT reduces the number of tests by $24$% while maintaining a negligible false negative rate.

q-bio.QM↗
arXiv2023

Computational Quantum Secret Sharing

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in $\mathsf{monotone~P}$, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to $1.5^{n+o(n)}$, improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in $\mathsf{P}$ and $\mathsf{NP}$ when the quantum secret sharing scheme is given multiple of copies of the secret.

quant-ph↗
arXiv2022

Simple Codes and Sparse Recovery with Fast Decoding

Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors $K$. Moreover, we design a simple, nearly optimal syndrome decoder for the code as well. The running time of the decoder is only logarithmic in the block length of the code, and nearly linear in the number of errors $K$. This decoder can be applied to exact for-all sparse recovery over any field, improving upon previous results with the same number of measurements. Furthermore, computation of the syndrome from a received word can be done in nearly linear time in the block length. We also demonstrate an application of these techniques in non-adaptive group testing, and construct simple explicit measurement schemes with $O(K^2 \log^2 N)$ tests and $O(K^3 \log^2 N)$ recovery time for identifying up to $K$ defectives in a population of size $N$.

cs.IT↗
arXiv2022

Low-Degree Polynomials Extract from Local Sources

We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly random input bits. Also known as local sources, this model was introduced by De and Watson (TOCT 2012) and Viola (SICOMP 2014), and is closely related to sources generated by $\mathsf{AC}^0$ circuits and bounded-width branching programs. In particular, extractors for local sources also work for sources generated by these classical computational models. Despite being introduced a decade ago, little progress has been made on improving the entropy requirement for extracting from local sources. The current best explicit extractors require entropy $n^{1/2}$, and follow via a reduction to affine extractors. To start, we prove a barrier showing that one cannot hope to improve this entropy requirement via a black-box reduction of this form. In particular, new techniques are needed. In our main result, we seek to answer whether low-degree polynomials (over $\mathbb{F}_2$) hold potential for breaking this barrier. We answer this question in the positive, and fully characterize the power of low-degree polynomials as extractors for local sources. More precisely, we show that a random degree $r$ polynomial is a low-error extractor for $n$-bit local sources with min-entropy $Ω(r(n\log n)^{1/r})$, and we show that this is tight. Our result leverages several new ingredients, which may be of independent interest. Our existential result relies on a new reduction from local sources to a more structured family, known as local non-oblivious bit-fixing sources. To show its tightness, we prove a "local version" of a structural result by Cohen and Tal (RANDOM 2015), which relies on a new "low-weight" Chevalley-Warning theorem.

cs.CC↗
arXiv2021

Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage. One of the most basic versions of this problem was settled more than 50 years ago by Levenshtein, or one substitution, with nearly optimal redundancy. However, this approach fails to extend to many simple and natural variations of the binary single-edit error setting. In this work, we make progress on the code design problem above in three such variations: We construct linear-time encodable and decodable length-$n$ non-binary codes correcting a single edit error with nearly optimal redundancy $\log n+O(\log\log n)$, providing an alternative simpler proof of a result by Cai, Chee, Gabrys, Kiah, and Nguyen (IEEE Trans. Inf. Theory 2021). This is achieved by employing what we call weighted VT sketches, a notion that may be of independent interest. We construct linear-time encodable and list-decodable binary codes with list-size $2$ for one deletion and one substitution with redundancy $4\log n+O(\log\log n)$. This matches the existential bound up to an $O(\log\log n)$ additive term. We show the existence of a binary code correcting one deletion or one adjacent transposition with nearly optimal redundancy $\log n+O(\log\log n)$.

cs.IT↗
arXiv2021

Mean-Based Trace Reconstruction over Oblivious Synchronization Channels

Mean-based reconstruction is a fundamental, natural approach to worst-case trace reconstruction over channels with synchronization errors. It is known that $\exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based worst-case trace reconstruction over the deletion channel, and this result was also extended to certain channels combining deletions and geometric insertions of uniformly random bits. In this work, we use a simple extension of the original complex-analytic approach to show that these results are examples of a much more general phenomenon. We introduce oblivious synchronization channels, which map each input bit to an arbitrarily distributed sequence of replications and insertions of random bits. This general class captures all previously considered synchronization channels. We show that for any oblivious synchronization channel whose output length follows a sub-exponential distribution either mean-based trace reconstruction is impossible or $\exp(O(n^{1/3}))$ traces suffice for this task.

cs.IT↗