IEEE Transactions on Information Theory最新文献

{"title":"Normality of 8-bit Bent Functions","authors":"Valérie Gillot;Philippe Langevin;Alexandr Polujan","doi":"10.1109/TIT.2026.3685370","DOIUrl":"https://doi.org/10.1109/TIT.2026.3685370","url":null,"abstract":"Bent functions are Boolean functions in an even number of variables that are indicators of Hadamard difference sets in elementary abelian 2-groups. A bent function <inline-formula> <tex-math>$f$ </tex-math></inline-formula> in <inline-formula> <tex-math>$m$ </tex-math></inline-formula> variables is said to be normal if it is constant on an affine space of dimension <inline-formula> <tex-math>$m/2$ </tex-math></inline-formula>. In this paper, we demonstrate that all bent functions in <inline-formula> <tex-math>$m = 8$ </tex-math></inline-formula> variables, whose exact count, determined by Langevin and Leander (Des. Codes Cryptogr. 59(1–3): 193–205, 2011), is approximately <inline-formula> <tex-math>$2^{106}$ </tex-math></inline-formula>, share a common algebraic property: every 8-variable bent function is normal, up to the addition of a linear function. With this result, we complete the analysis of the normality of bent functions for the last unresolved case, <inline-formula> <tex-math>$m=8$ </tex-math></inline-formula>. It is already known that all bent functions in <inline-formula> <tex-math>$m$ </tex-math></inline-formula> variables are normal for <inline-formula> <tex-math>$m leq 6$ </tex-math></inline-formula>, while for <inline-formula> <tex-math>$m geq 10$ </tex-math></inline-formula>, there exist bent functions that cannot be made normal by adding linear functions. Consequently, we provide a complete solution to an open problem by Charpin (J. Complex. 20(2-3): 245-265, 2004).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4352-4364"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11488348","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148508892","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":"Batched Stochastic Bandit for Nondegenerate Functions","authors":"Yu Liu;Yunlu Shu;Tianyu Wang","doi":"10.1109/TIT.2025.3559092","DOIUrl":"https://doi.org/10.1109/TIT.2025.3559092","url":null,"abstract":"This paper studies batched bandit learning problems for nondegenerate functions. Over a compact doubling metric space <inline-formula> <tex-math>$({mathcal {X}}, {mathcal {D}})$ </tex-math></inline-formula>, a function <inline-formula> <tex-math>$f: {mathcal {X}} to mathbb {R}$ </tex-math></inline-formula> is called nondegenerate if there exists <inline-formula> <tex-math>$ L ge lambda gt 0 $ </tex-math></inline-formula> and <inline-formula> <tex-math>$q ge 1$ </tex-math></inline-formula>, such that <inline-formula> <tex-math>$lambda left ({{ {mathcal {D}} left ({{mathbf {x}, mathbf {x}^{*}}}right) }}right)^{q} le f left ({{mathbf {x}}}right) {-} f left ({{mathbf {x}^{*}}}right) le L left ({{ {mathcal {D}} left ({{mathbf {x}, mathbf {x}^{*}}}right) }}right)^{q}, ; mathbf {x} in {mathcal {X}}$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$mathbf {x}^{*} = arg min _{mathbf {z} in {mathcal {X}}} f (mathbf {z}) $ </tex-math></inline-formula> is the unique minimizer of <italic>f</i> over <inline-formula> <tex-math>${mathcal {X}}$ </tex-math></inline-formula>. In this paper, we introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm, called Geometric Narrowing (GN), whose regret bound is of order <inline-formula> <tex-math>$ widetilde {{mathcal {O}}} (A_{+}^{d} sqrt {T}) $ </tex-math></inline-formula>, where <italic>d</i> is the doubling dimension of <inline-formula> <tex-math>$({mathcal {X}},{mathcal {D}})$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$A_{+}$ </tex-math></inline-formula> is a constant independent of <inline-formula> <tex-math>$ d $ </tex-math></inline-formula> and the time horizon <italic>T</i>. In addition, GN only needs <inline-formula> <tex-math>$ {{mathcal {O}}} (log log T) $ </tex-math></inline-formula> batches to achieve this regret. We also provide lower bound analysis for this problem. More specifically, we prove that over some (compact) doubling metric space of doubling dimension <italic>d</i>: 1. For any policy <inline-formula> <tex-math>$pi $ </tex-math></inline-formula>, there exists a problem instance on which <inline-formula> <tex-math>$pi $ </tex-math></inline-formula> admits a regret of order <inline-formula> <tex-math>${Omega } (A_{-}^{d} sqrt {T})$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$A_{-}$ </tex-math></inline-formula> is a constant independent of <inline-formula> <tex-math>$ d $ </tex-math></inline-formula> and <italic>T</i>; 2. No policy can achieve a regret of order <inline-formula> <tex-math>$ A_{-}^{d} sqrt {T} $ </tex-math></inline-formula> over all problem instances, using less than <inline-formula> <tex-math>$ Omega (log log T) $ </tex-math></inline-formula> rounds of communications. Our lower bound analysis shows that the GN algorithm achieves near optimal regret with minimal number of batches.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4166-4186"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509117","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":"Geometrical Constructions of Purity Testing Protocols and Their Applications to Quantum Communication","authors":"Róbert Trényi;Simeon Ball;David G. Glynn;Marcos Curty","doi":"10.1109/TIT.2026.3678348","DOIUrl":"https://doi.org/10.1109/TIT.2026.3678348","url":null,"abstract":"Purity testing protocols (PTPs), also known as Bell state testing protocols, i.e., protocols that decide with high probability whether or not a distributed bipartite quantum state is a tensor product of Bell states, have been proven to be a useful tool in many quantum communication applications. In this paper, we provide geometrical constructions for such protocols that originate directly from classical linear error correcting codes (LECCs), in a way that the properties of the resulting PTP are completely determined from those of the LECC used in the construction. We investigate the implications of our results in various quantum communication tasks, including error detection, entanglement purification for general quantum error models and quantum message authentication.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4041-4055"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11457055","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510088","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":"Communication Complexity of Exact Sampling Under Rényi Information","authors":"Spencer Hill;Fady Alajaji;Tamás Linder","doi":"10.1109/TIT.2026.3680805","DOIUrl":"https://doi.org/10.1109/TIT.2026.3680805","url":null,"abstract":"We study the problem of exact sampling under an exponential communication cost, specifically Campbell’s average codeword length <inline-formula> <tex-math>$boldsymbol {L(t)}$ </tex-math></inline-formula> of order <inline-formula> <tex-math>$boldsymbol {t}$ </tex-math></inline-formula>, and Rényi’s entropy. We provide a lower bound on the Campbell cost of exact sampling that grows approximately as <inline-formula> <tex-math>$boldsymbol {D_{1/alpha }(P||Q)}$ </tex-math></inline-formula>, the Rényi divergence of order <inline-formula> <tex-math>$boldsymbol {1/alpha }$ </tex-math></inline-formula>, with <inline-formula> <tex-math>$boldsymbol {alpha = 1 / 1 + t}$ </tex-math></inline-formula>. Using the Poisson functional representation of Li and El Gamal (2017), we prove an upper bound on <inline-formula> <tex-math>$boldsymbol {L(t)}$ </tex-math></inline-formula> whose leading Rényi divergence term has order within <inline-formula> <tex-math>$boldsymbol {epsilon }$ </tex-math></inline-formula> of that of the lower bound. Our results reduce to the bounds of Harsha et al. (2010) as <inline-formula> <tex-math>$boldsymbol {alpha to 1}$ </tex-math></inline-formula>. We also provide numerical examples comparing the bounds in the cases of normal and Laplacian distributions, demonstrating that the upper and lower bounds are typically within 5-10 bits of each other. Our results characterize exactly the optimal asymptotic Campbell cost <inline-formula> <tex-math>$boldsymbol {L(t)}$ </tex-math></inline-formula> per sample as the number of independent and identically distributed (i.i.d.) samples grows to infinity. We show that under the exponential cost, any causal sampler performs strictly worse asymptotically than noncausal samplers. This contrasts with the case of expected message length, where both causal and noncausal samplers have the same optimal asymptotic cost.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3525-3538"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511751","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":"Two Fast Erasure Decoding Algorithms for Reed–Solomon Codes Based on LCH-FFT","authors":"Chao Chen;Sian-Jheng Lin;Nianqi Tang;Yunghsiang S. Han;Suihua Cai;Leilei Yu;Zhongwei Li;Baoming Bai;Bo Bai","doi":"10.1109/TIT.2026.3685291","DOIUrl":"https://doi.org/10.1109/TIT.2026.3685291","url":null,"abstract":"Based on a recently proposed fast Fourier transform by Lin, Chung, and Han, this paper presents two fast erasure decoding algorithms for Reed–Solomon (RS) codes over binary extension fields of length <inline-formula> <tex-math>$N$ </tex-math></inline-formula> and dimension <inline-formula> <tex-math>$K$ </tex-math></inline-formula>. The first algorithm applies to low-rate RS codes (i.e., <inline-formula> <tex-math>$frac {K}{N} leq 0.5$ </tex-math></inline-formula>) and achieves a complexity of <inline-formula> <tex-math>$O(N log K)$ </tex-math></inline-formula>. The second algorithm applies to high-rate RS codes (i.e., <inline-formula> <tex-math>$frac {K}{N} geq 0.5$ </tex-math></inline-formula>) and achieves a complexity of <inline-formula> <tex-math>$O(N log (N-K))$ </tex-math></inline-formula>. Compared to recent state-of-the-art algorithms, both proposed algorithms achieve the best complexity, resulting in significant throughput improvements in Single Instruction Multiple Data (SIMD) based simulations. Besides yielding new fast algorithms for RS codes, this paper also presents a new interpolation formula, as well as related results, which may be of independent interest.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3784-3798"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148508895","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":"From List-Decodability to Proximity Gaps","authors":"Yiwen Gao;Dongliang Cai;Yang Xu;Haibin Kan","doi":"10.1109/TIT.2026.3679739","DOIUrl":"https://doi.org/10.1109/TIT.2026.3679739","url":null,"abstract":"Proximity testing for linear codes is a fundamental problem in coding theory with critical applications in cryptographic protocols, blockchain, and distributed storage systems. This work addresses the proximity gaps for linear codes, a crucial aspect for efficiently verifying whether a batch of words is close to a given code. We present a general framework for deriving proximity gaps from the list-decodability properties of the underlying linear code. Our main result show that for any <inline-formula> <tex-math>$(p,L)$ </tex-math></inline-formula>-list-decodable code <inline-formula> <tex-math>$Csubseteq mathbb {F}_{q}^{n}$ </tex-math></inline-formula> with minimum relative distance <inline-formula> <tex-math>$Delta _{C}gt p$ </tex-math></inline-formula>, the probability that a random combination of a batch of <inline-formula> <tex-math>$t$ </tex-math></inline-formula> words containing a <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>-far word (for <inline-formula> <tex-math>$delta le 1-sqrt {1-p+varepsilon }$ </tex-math></inline-formula>) remains <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>-far from <inline-formula> <tex-math>$C$ </tex-math></inline-formula> is bounded by <inline-formula> <tex-math>$Oleft ({{frac {tL^{2}pn}{q}+frac {t}{varepsilon q}}}right)$ </tex-math></inline-formula>. This result also establishes a form of (mutual) correlated agreement for linear codes, which can be used to strengthen soundness analyses in protocols that rely on proximity testing, thereby reducing query complexity and enabling practical instantiations over smaller finite fields. In particular, we apply our main result to randomly punctured Reed–Solomon codes and folded Reed–Solomon codes—both of which are known to achieve list-decodability up to capacity—and derive linear proximity gaps for these families of codes under the Johnson bound.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3809-3819"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509730","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":"Characterizations of Primitive and Projective Self-Orthogonal BCH Codes and Their Parameters","authors":"Shuying Dong;Chengju Li;Haifeng Qian","doi":"10.1109/TIT.2026.3683480","DOIUrl":"https://doi.org/10.1109/TIT.2026.3683480","url":null,"abstract":"Self-orthogonal codes are an important type of linear codes since they are very closely related to designs, lat tices, and quantum codes. Bose-Chaudhuri-Hocquenghem codes (BCH codes) have various practical applications in communication and storage due to their efficient encoding and decoding algorithms. In this paper, we will focus on the primitive and projective self-orthogonal BCH codes in both Euclidean and Hermitian cases. Our main objective is to characterize primitive and projective Euclidean and Hermitian self-orthogonal BCH codes and investigate their parameters. For the Euclidean case, the primitive and projective self-orthogonal BCH codes are characterized completely by using their designed distances. For the Hermitian case, a sufficient and necessary condition for all primitive BCH codes being self-orthogonal are presented, while the characterizations of projective Hermitian self-orthogonal BCH codes are obtained in some cases. Moreover, the dimensions of some Euclidean and Hermitian self-orthogonal BCH codes are determined explicitly and lower bounds on their minimum distances are given.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3665-3677"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511060","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":"The Shannon Upper Bound for the Error Exponent","authors":"Sergey Tridenski;Anelia Somekh-Baruch","doi":"10.1109/TIT.2026.3683949","DOIUrl":"https://doi.org/10.1109/TIT.2026.3683949","url":null,"abstract":"For the discrete-time additive white generalized Gaussian noise channel with a generalized input power constraint, with the respective shape and power parameters <inline-formula> <tex-math>$geq 1$ </tex-math></inline-formula>, we derive an upper bound on the optimal block error exponent. Explicit asymptotic upper bounds in the limit of a large block length <inline-formula> <tex-math>$n$ </tex-math></inline-formula> are given for three special cases: the Laplace noise channel and the Gaussian noise channel with the average absolute value constraint, and for the Laplace noise channel with the average squared value constraint. The derivation uses the method of types with finite alphabets of sizes depending on the block length <inline-formula> <tex-math>$n$ </tex-math></inline-formula> and with the number of types sub-exponential in <inline-formula> <tex-math>$n$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3539-3555"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511191","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":"Exponential Error Bounds for Information Bottleneck Source Coding Problems","authors":"Han Wu;Hamdi Joudeh","doi":"10.1109/TIT.2026.3684477","DOIUrl":"https://doi.org/10.1109/TIT.2026.3684477","url":null,"abstract":"We study the information bottleneck (IB) source coding problem, also known as remote lossy source coding under logarithmic loss. Based on a rate-limited description of noisy observations, the receiver produces a soft estimate for the remote source, i.e., a probability distribution, evaluated under the logarithmic loss. We focus on the excess distortion probability of IB source coding and investigate how fast it converges to 0 or 1, depending on whether the rate is above or below the rate-distortion function. The latter case is also known as the exponential strong converse. We establish both the exact error exponent and the exact strong converse exponent for IB source coding by deriving matching upper and lower exponential bounds. The obtained exponents involve optimizations over auxiliary random variables. The matching converse bounds are derived through non-trivial extensions of existing sphere packing and single-letterization techniques, which we adapt to incorporate auxiliary random variables. In the second part of this paper, we establish a code-level connection between IB source coding and source coding with a helper, also known as the Wyner-Ahlswede-Körner (WAK) problem. We show that every code for the WAK problem is a code for IB source coding. This requires noticing that IB source coding, under the excess distortion criterion, is equivalent to source coding with a helper available at <italic>both</i> the transmitter <italic>and</i> the receiver; the latter in turn relates to the WAK problem. Through this connection, we re-derive the best known sphere packing exponent of the WAK problem, and provide it with an operational interpretation.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3597-3620"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511753","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 Unified Method for Determining Parameters of Augmented Codes (I): p-Ary Linear Codes","authors":"Yansheng Wu;Yao Zhou;Weibei Fan","doi":"10.1109/TIT.2026.3687201","DOIUrl":"https://doi.org/10.1109/TIT.2026.3687201","url":null,"abstract":"In coding theory, augmented codes are a useful tool for constructing new linear codes from old ones, and in general it is hard to determine the parameters of those augmented codes. In this paper, we present a unified method to settle the above problem by considering the homogenization of multi-variable functions. Firstly, we extend the results by Hyun et al. (Finite Fields Appl., 103: 102589, 2025) from the binary case to any prime cases. Secondly, we compute the weight distributions of augmented codes of the linear codes constructed from two kinds of simplicial complexes by Hyun et al. (Discret. Appl. Math., 254: 135-145, 2019) and Hu et al. (IEEE Trans. Inf. Theory, 70(3): 1823-1835, 2024). Many classes of optimal and almost optimal linear codes, and some codes with small Griesmer defect values are also obtained. This confirms the strength of the resulting constructions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3862-3884"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509776","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}