IEEE Transactions on Information Theory最新文献

{"title":"Convergence of Flow-Based Generative Models via Proximal Gradient Descent in Wasserstein Space","authors":"Xiuyuan Cheng;Jianfeng Lu;Yixin Tan;Yao Xie","doi":"10.1109/TIT.2024.3422412","DOIUrl":"10.1109/TIT.2024.3422412","url":null,"abstract":"Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be \u0000<inline-formula> <tex-math>$O(varepsilon ^{2})$ </tex-math></inline-formula>\u0000 when using \u0000<inline-formula> <tex-math>$N lesssim log (1/varepsilon)$ </tex-math></inline-formula>\u0000 many JKO steps (N Residual Blocks in the flow) where \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000 is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-\u0000<inline-formula> <tex-math>$mathcal {W}_{2}$ </tex-math></inline-formula>\u0000 mixed error guarantees. The non-asymptotic convergence rate of the JKO-type \u0000<inline-formula> <tex-math>$mathcal {W}_{2}$ </tex-math></inline-formula>\u0000-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest. The analysis framework can extend to other first-order Wasserstein optimization schemes applied to flow-based generative models.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8087-8106"},"PeriodicalIF":2.2,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harnessing the Power of Sample Abundance: Theoretical Guarantees and Algorithms for Accelerated One-Bit Sensing","authors":"Arian Eamaz;Farhang Yeganegi;Deanna Needell;Mojtaba Soltanalian","doi":"10.1109/TIT.2024.3422918","DOIUrl":"10.1109/TIT.2024.3422918","url":null,"abstract":"One-bit quantization with time-varying sampling thresholds (also known as random dithering) has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what one may refer to as sample abundance. We show that sample abundance plays a pivotal role in many signal recovery and optimization problems that are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints. Of particular interest to our work are low-rank matrix recovery and compressed sensing applications that take advantage of one-bit quantization. We demonstrate that the sample abundance paradigm allows for the transformation of such problems to merely linear feasibility problems by forming large-scale overdetermined linear systems—thus removing the need for handling costly optimization constraints and objectives. To make the proposed computational cost savings achievable, we offer enhanced randomized Kaczmarz algorithms to solve these highly overdetermined feasibility problems and provide theoretical guarantees in terms of their convergence, sample size requirements, and overall performance. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6690-6713"},"PeriodicalIF":2.2,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10583929","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modulation and Estimation With a Helper","authors":"Anatoly Khina;Neri Merhav","doi":"10.1109/TIT.2024.3422308","DOIUrl":"10.1109/TIT.2024.3422308","url":null,"abstract":"The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate \u0000<inline-formula> <tex-math>$R_{mathrm {h}}$ </tex-math></inline-formula>\u0000 to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable \u0000<inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>\u0000-th moment of the estimation error and show that they coincide for small values of \u0000<inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>\u0000 and for high values of \u0000<inline-formula> <tex-math>$R_{mathrm {h}}$ </tex-math></inline-formula>\u0000. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys \u0000<inline-formula> <tex-math>$R_{mathrm {h}}$ </tex-math></inline-formula>\u0000 bits essentially error-free and the rest of the rate—over the same AWGN channel without help, with the error-free bits being allocated to the most significant bits of the quantized parameter. We then concentrate on the setting with a total transmit energy constraint, for which we derive achievability results for both channel coding and parameter modulation for several scenarios: when the helper assists only the transmitter or only the receiver and knows the noise, and when the helper assists the transmitter and/or the receiver and knows both the noise and the message. In particular, for the message-informed helper that assists both the receiver and the transmitter, it is shown that the error probability in the channel-coding task decays doubly exponentially. Finally, we translate these results to those for continuous-time power-limited AWGN channels with unconstrained bandwidth. As a byproduct, we show that the capacity with a message-informed helper that is available only at the transmitter can exceed the sum of the capacity without help and the help rate \u0000<inline-formula> <tex-math>$R_{mathrm {h}}$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6189-6210"},"PeriodicalIF":2.2,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Information Theoretic Secure Aggregation With Uncoded Groupwise Keys","authors":"Kai Wan;Xin Yao;Hua Sun;Mingyue Ji;Giuseppe Caire","doi":"10.1109/TIT.2024.3422087","DOIUrl":"10.1109/TIT.2024.3422087","url":null,"abstract":"Secure aggregation, which is a core component of federated learning, aggregates locally trained models from distributed users at a central server. The “secure” nature of such aggregation consists of the fact that no information about the local users’ data must be leaked to the server except the aggregated local models. In order to guarantee security, some keys may be shared among the users (this is referred to as the key sharing phase). After the key sharing phase, each user masks its trained model which is then sent to the server (this is referred to as the model aggregation phase). This paper follows the information theoretic secure aggregation problem originally formulated by Zhao and Sun, with the objective to characterize the minimum communication cost from the \u0000<inline-formula> <tex-math>$mathsf K$ </tex-math></inline-formula>\u0000 users in the model aggregation phase. Due to user dropouts, which are common in real systems, the server may not receive all messages from the users. A secure aggregation scheme should tolerate the dropouts of at most \u0000<inline-formula> <tex-math>${mathsf K}-{mathsf U}$ </tex-math></inline-formula>\u0000 users, where \u0000<inline-formula> <tex-math>$mathsf U$ </tex-math></inline-formula>\u0000 is a system parameter. The optimal communication cost is characterized by Zhao and Sun, but with the assumption that the keys stored by the users could be any random variables with arbitrary dependency. On the motivation that uncoded groupwise keys are more convenient to be shared and could be used in large range of applications besides federated learning, in this paper we add one constraint into the above problem, namely, that the key variables are mutually independent and each key is shared by a group of \u0000<inline-formula> <tex-math>$mathsf S$ </tex-math></inline-formula>\u0000 users, where \u0000<inline-formula> <tex-math>$mathsf S$ </tex-math></inline-formula>\u0000 is another system parameter. To the best of our knowledge, all existing secure aggregation schemes (with information theoretic security or computational security) assign coded keys to the users. We show that if \u0000<inline-formula> <tex-math>${mathsf S}gt {mathsf K}-{mathsf U}$ </tex-math></inline-formula>\u0000, a new secure aggregation scheme with uncoded groupwise keys can achieve the same optimal communication cost as the best scheme with coded keys; if \u0000<inline-formula> <tex-math>${mathsf S}leq {mathsf K}-{mathsf U}$ </tex-math></inline-formula>\u0000, uncoded groupwise key sharing is strictly sub-optimal. Finally, we also implement our proposed secure aggregation scheme into Amazon EC2, which are then compared with the existing secure aggregation schemes with offline key sharing.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6596-6619"},"PeriodicalIF":2.2,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bridging Hamming Distance Spectrum With Coset Cardinality Spectrum for Overlapped Arithmetic Codes","authors":"Yong Fang","doi":"10.1109/TIT.2024.3421253","DOIUrl":"10.1109/TIT.2024.3421253","url":null,"abstract":"Distributed Source Coding (DSC), a scheme that encodes multiple correlated sources separately while decoding their bitstreams jointly, is an important branch of network information theory. Due to the advantages of shifting complexity burden from the encoder to the decoder and canceling the flow of data across terminals, DSC has potential applications in many scenarios, e.g., wireless sensor network, distributed genome data compression, etc. There are two forms (lossless and lossy) of DSC. Overlapped arithmetic codes, featured by overlapped intervals, are a variant of arithmetic codes that can implement distributed lossless compression, or the so-called Slepian-Wolf coding. For uniform binary sources, an overlapped arithmetic code is essentially a nonlinear many-to-one mapping that partitions source space into unequal-sized cosets. To analyze overlapped arithmetic codes, two theoretical tools have been proposed, i.e., Coset Cardinality Spectrum (CCS) and Hamming Distance Spectrum (HDS). The former describes how source space is partitioned into cosets (equally or unequally), and the latter describes how codewords are structured within each coset (densely or sparsely). However, until now, these two tools are almost parallel to each other, and it seems that there is no intersection between them. The main contribution of this paper is tightly bridging HDS with CCS. Specifically, HDS can be quickly and accurately calculated with CCS in some cases. In addition, the paper also proves the necessary and sufficient condition for the convergence of HDS and reveals the close relation between divergent HDS and polynomial division. All theoretical analyses are verified by experimental results.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6714-6745"},"PeriodicalIF":2.2,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"List Privacy Under Function Recoverability","authors":"Ajaykrishnan Nageswaran;Prakash Narayan","doi":"10.1109/TIT.2024.3420892","DOIUrl":"10.1109/TIT.2024.3420892","url":null,"abstract":"For a given function of user data, a querier must recover with at least a prescribed probability, the value of the function based on a user-provided query response. Subject to this requirement, the user forms the query response so as to minimize the likelihood of the querier guessing a list of prescribed size to which the data value belongs based on the query response. We obtain a general converse upper bound for maximum list privacy. This bound is shown to be tight for the case of a binary-valued function through an explicit achievability scheme that involves an add-noise query response.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6620-6626"},"PeriodicalIF":2.2,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Best Arm Identification With Fixed Confidence in Restless Bandits","authors":"P. N. Karthik;Vincent Y. F. Tan;Arpan Mukherjee;Ali Tajer","doi":"10.1109/TIT.2024.3419924","DOIUrl":"10.1109/TIT.2024.3419924","url":null,"abstract":"We study best arm identification in a restless multi-armed bandit setting with finitely many arms. The discrete-time data generated by each arm forms a homogeneous Markov chain taking values in a common, finite-state space. The state transitions in each arm are captured by an ergodic transition probability matrix (TPM) that is a member of a single-parameter exponential family of TPMs. The real-valued parameters of the arm TPMs are unknown and belong to a given space. Given a function f defined on the common state space of the arms, the goal is to identify the best arm—the arm with the largest average value of f evaluated under the arm’s stationary distribution—with the fewest number of samples, subject to an upper bound on the decision’s error probability (i.e., the fixed-confidence regime). A lower bound on the growth rate of the expected stopping time is established in the asymptote of a vanishing error probability. Furthermore, a policy for best arm identification is proposed, and its expected stopping time is proved to have an asymptotic growth rate that matches the lower bound. It is demonstrated that tracking the long-term behavior of a certain Markov decision process and its state-action visitation proportions are the key ingredients in analyzing the converse and achievability bounds. It is shown that under every policy, the state-action visitation proportions satisfy a specific approximate flow conservation constraint and that these proportions match the optimal proportions dictated by the lower bound under any asymptotically optimal policy. The prior studies on best arm identification in restless bandits focus on independent observations from the arms, rested Markov arms, and restless Markov arms with known arm TPMs. In contrast, this work is the first to study best arm identification in restless bandits with unknown arm TPMs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"7349-7384"},"PeriodicalIF":2.2,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient Coding With Iterative Block Leverage Score Sampling","authors":"Neophytos Charalambides;Mert Pilanci;Alfred O. Hero","doi":"10.1109/TIT.2024.3420222","DOIUrl":"10.1109/TIT.2024.3420222","url":null,"abstract":"Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this paper, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized \u0000<inline-formula> <tex-math>$ell _{2}$ </tex-math></inline-formula>\u0000-subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid \u0000<inline-formula> <tex-math>$ell _{2}$ </tex-math></inline-formula>\u0000-subspace embedding, and that our resulting approximation converges to the optimal solution.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6639-6664"},"PeriodicalIF":2.2,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Version of q-Ary Varshamov-Tenengolts Codes With More Efficient Encoders: The Differential VT Codes and The Differential Shifted VT Codes","authors":"Tuan Thanh Nguyen;Kui Cai;Paul H. Siegel","doi":"10.1109/TIT.2024.3417894","DOIUrl":"10.1109/TIT.2024.3417894","url":null,"abstract":"The problem of correcting deletions and insertions has recently received significantly increased attention due to the DNA-based data storage technology, which suffers from deletions and insertions with extremely high probability. In this work, we study the problem of constructing non-binary burst-deletion/insertion correcting codes. Particularly, for the quaternary alphabet, our designed codes are suited for correcting a burst of deletions/insertions in DNA storage. Non-binary codes correcting a single deletion or insertion were introduced by Tenengolts (1984), and the results were extended to correct a fixed-length burst of deletions or insertions by Schoeny et al. (2017). Recently, Wang et al. (2021) proposed constructions of non-binary codes of length n, correcting a burst of length at most two for q-ary alphabets with redundancy \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$log n+O(log q log log n)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 bits, for arbitrary even q. The common idea in those constructions is to convert non-binary sequences into binary sequences, and the error decoding algorithms for the q-ary sequences are mainly based on the success of recovering the corresponding binary sequences, respectively. In this work, we look at a natural solution that the error detection and correction algorithms are performed directly over q-ary sequences, and for certain cases, our codes provide a more efficient encoder with lower redundancy than the best-known encoder in the literature. Particularly, (Single-error correction codes) We first present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion, providing an alternative simpler and more efficient encoder of the construction by Tenengolts (1984). Our construction is based on the differential vector, and the codes are referred to as the differential VT codes. In addition, we provide linear-time algorithms that encode user messages into these codes of length n over the q-ary alphabet for \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$q geqslant 2$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 with at most \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$lceil log _{q} nrceil +1$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 redundant symbols, while the optimal redundancy required is at least \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$log _{q} n+log _{q} (q-1)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 symbols. Our designed encoder reduces the redundancy of the best-known encoder of Tenengolts (1984) by at least 2 redundant symbols or equivalently \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$2log _{2} q$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 bits. (Burst-error correction codes) We use the idea of the binary shifted VT codes to define the q-ary differential shifted VT codes, and propose non-binary codes correcting a burst of up to two deletions (or two insertions) with redundancy \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$log n+3log log n+ O(log q)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;\u0000 bits, which improves a recent result of Wang et al. (2021) with redundancy \u0000&lt;inline-formula&gt; &lt;tex-math&gt;$log n+O(log q log log","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"6989-7004"},"PeriodicalIF":2.2,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Substring Density Estimation From Traces","authors":"Kayvon Mazooji;Ilan Shomorony","doi":"10.1109/TIT.2024.3418377","DOIUrl":"10.1109/TIT.2024.3418377","url":null,"abstract":"In the trace reconstruction problem, one seeks to reconstruct a binary string s from a collection of traces, each of which is obtained by passing s through a deletion channel. It is known that \u0000<inline-formula> <tex-math>$exp (tilde {O}(n^{1/5}))$ </tex-math></inline-formula>\u0000 traces suffice to reconstruct any length-n string with high probability. We consider a variant of the trace reconstruction problem where the goal is to recover a “density map” that indicates the locations of each length-k substring throughout s. We show that when \u0000<inline-formula> <tex-math>$k = c log n$ </tex-math></inline-formula>\u0000 where c is constant, \u0000<inline-formula> <tex-math>$epsilon ^{-2}cdot text { poly} (n)$ </tex-math></inline-formula>\u0000 traces suffice to recover the density map with error at most \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000. As a result, when restricted to a set of source strings whose minimum “density map distance” is at least \u0000<inline-formula> <tex-math>$1/text {poly}(n)$ </tex-math></inline-formula>\u0000, the trace reconstruction problem can be solved with polynomially many traces.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 8","pages":"5782-5798"},"PeriodicalIF":2.2,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10571548","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}