IEEE Transactions on Information Theory最新文献

{"title":"Efficient Decoding of Twisted GRS Codes and Roth–Lempel Codes","authors":"Runtian Zhu;Lingfei Jin","doi":"10.1109/TIT.2026.3697359","DOIUrl":"https://doi.org/10.1109/TIT.2026.3697359","url":null,"abstract":"MDS codes play a central role in practice due to their broad applications. To date, most known MDS codes are generalized Reed–Solomon (GRS) codes, leaving codes that are not equivalent to GRS codes comparatively less understood. Studying this non-GRS regime is therefore of intrinsic theoretical interest, and is also practically relevant since the strong algebraic structure of GRS codes can be undesirable in cryptographic settings. Among the known non-GRS codes, twisted generalized Reed–Solomon (TGRS) codes and Roth–Lempel codes are two representative families of non-GRS codes that have attracted significant attention. Though substantial work has been devoted to the construction and structural analysis of TGRS and Roth–Lempel codes, comparatively little attention has been paid to their decoding, and many problems remain open. In this paper, we propose list and unique decoding algorithms for TGRS codes and Roth–Lempel codes based on the Guruswami–Sudan algorithm. Under suitable parameter conditions, our algorithms achieve near-linear running time in the code length, improving upon the previously best-known quadratic-time complexity. Our TGRS decoder supports fixed-rate TGRS codes with up to <inline-formula> <tex-math>$O(n^{2})$ </tex-math></inline-formula> twists, substantially extending prior work that only handled the single-twist case. For Roth–Lempel codes, we provide what appears to be the first efficient decoder. Moreover, our list decoders surpass the classical unique-decoding radius for a broad range of parameters. Finally, we incorporate algebraic manipulation detection (AMD) codes into the list-decoding framework, enabling recovery of the correct message from the output list with high probability.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4881-4894"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512264","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":"Sequence Reconstruction Problem for Ternary Deletion Channels","authors":"Xiang Wang;Han Li;Fang-Wei Fu","doi":"10.1109/TIT.2026.3693578","DOIUrl":"https://doi.org/10.1109/TIT.2026.3693578","url":null,"abstract":"The sequence reconstruction problem was proposed by Levenshtein in 2001. In this model, a sequence from a code is transmitted over several channels, and the decoder receives the distinct outputs from each channel. The main problem is to determine the minimum number of channels required to reconstruct the transmitted sequence. In the combinatorial context, the sequence reconstruction problem is equivalent to finding the value of <inline-formula> <tex-math>$N_{q}(n,d,t)$ </tex-math></inline-formula>, defined as the size of the largest intersection of two metric balls of radius <inline-formula> <tex-math>$t$ </tex-math></inline-formula>, where the distance between their centers is at least <inline-formula> <tex-math>$d$ </tex-math></inline-formula> and the sequences are <inline-formula> <tex-math>$q$ </tex-math></inline-formula>-ary sequences of length <inline-formula> <tex-math>$n$ </tex-math></inline-formula>. Levenshtein first discussed this problem in the uncoded sequence setting and determined the value of <inline-formula> <tex-math>$N_{q}(n,1,t)$ </tex-math></inline-formula> for any <inline-formula> <tex-math>$ngeq t$ </tex-math></inline-formula>. Moreover, Gabrys and Yaakobi studied this problem in the context of binary one-deletion-correcting codes and determined the value of <inline-formula> <tex-math>$N_{2}(n,2,t)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$tgeq 2$ </tex-math></inline-formula>. In this paper we study this problem for 3-ary sequences of length <inline-formula> <tex-math>$n$ </tex-math></inline-formula> over the deletion channel, where the transmitted sequence belongs to a one-deletion-correcting code and there are <inline-formula> <tex-math>$t$ </tex-math></inline-formula> deletions in every channel. Specifically, we determine <inline-formula> <tex-math>$N_{3}(n,2,t)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$tgeq 2$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4802-4827"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509421","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":"One-Bit Phase Retrieval: Optimal Rates and Efficient Algorithms","authors":"Junren Chen;Ming Yuan","doi":"10.1109/TIT.2026.3692592","DOIUrl":"https://doi.org/10.1109/TIT.2026.3692592","url":null,"abstract":"In this paper, we study the sample complexity and develop efficient algorithms for 1-bit phase retrieval, i.e., the recovery of a signal <inline-formula> <tex-math>$mathbf {x}in mathbb {R}^{n}$ </tex-math></inline-formula> from <inline-formula> <tex-math>$m$ </tex-math></inline-formula> phaseless bits <inline-formula> <tex-math>${mathop {mathrm {sign}}nolimits (|mathbf {a}_{i}^{top } mathbf {x} |-tau)}_{i=1}^{m}$ </tex-math></inline-formula> with standard Gaussian <inline-formula> <tex-math>$mathbf {a}_{i}$ </tex-math></inline-formula>. By investigating a phaseless version of random hyperplane tessellation, we show that (constrained) hamming distance minimization uniformly recovers all unstructured signals with Euclidean norm bounded away from zero and infinity to the error <inline-formula> <tex-math>$mathcal {O}left ({ frac {n}{m}log left ({ frac {m}{n}}right)}right)$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$mathcal {O}left ({ frac {k}{m}log left ({ frac {mn}{k^{2}}}right)}right)$ </tex-math></inline-formula> when restricting to <inline-formula> <tex-math>$k$ </tex-math></inline-formula>-sparse signals. Both error rates are information-theoretically optimal up to a logarithmic factor. Intriguingly, the optimal rate for sparse recovery matches that of 1-bit compressed sensing, suggesting that the phase information is non-essential for 1-bit compressed sensing. We also develop efficient and near-optimal algorithms for 1-bit (sparse) phase retrieval. Specifically, we prove that (thresholded) gradient descent with respect to the one-sided <inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>-loss, when initialized via spectral methods, converges linearly and attains the near-optimal reconstruction error, with sample complexity <inline-formula> <tex-math>$mathcal {O}(n)$ </tex-math></inline-formula> for unstructured signals and <inline-formula> <tex-math>$mathcal {O}left ({ k^{2}log (n)log ^{2}left ({ frac {m}{k}}right)}right)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$k$ </tex-math></inline-formula>-sparse signals. Our proof is based upon the observation that a certain local approximate invertibility condition is respected by Gaussian measurements. Our results establish the major findings of (memoryless) 1-bit compressed sensing in a phaseless setting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5251-5292"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512050","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":"New Sphere-Packing Bounds for Finite-Blocklength Coding Over Additive Noise Channels","authors":"Kaixuan Bao;Wei Xu;Xiaohu You;H. Vincent Poor","doi":"10.1109/TIT.2026.3689501","DOIUrl":"https://doi.org/10.1109/TIT.2026.3689501","url":null,"abstract":"Ultra-reliable low-latency communication (uRLLC) is of increasing importance in the evolution of 5G and beyond wireless communication networks. Since the communication latency is bounded by the blocklength of codewords, channel coding theory at finite blocklength is important in the design and analysis of uRLLC systems. Based on the concept of sphere-packing introduced by Shannon in 1959, in this paper, we introduce a new codebook design, namely the volume-uniform random coding codebook, and derive a corresponding achievability result in closed form. Comparing to conventional sphere-packing codebook designs where all codewords are located on the surface of the sphere, the proposed design allows codewords to lie inside the sphere, which provides greater freedom in the codebook. A concise and explicit approximation bound is obtained as <inline-formula> <tex-math>$epsilon approx exp left {{ -nleft [{ E_{0}(P)-R+Oleft ({ frac {1}{n}}right) }right] }right }$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> is the decoding error probability, <inline-formula> <tex-math>$n$ </tex-math></inline-formula> is the blocklength, <inline-formula> <tex-math>$P$ </tex-math></inline-formula> is the signal-to-noise ratio (SNR), and <inline-formula> <tex-math>$E_{0}$ </tex-math></inline-formula> is a simple explicit function of only <inline-formula> <tex-math>$P$ </tex-math></inline-formula>. It is shown by both simulation and analysis that the derived bounds are much tighter compared to existing bounds, especially when the blocklength is short, e.g., <inline-formula> <tex-math>$nleq 100$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4468-4490"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509502","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":"Maximally Recoverable Codes With Locality and Availability","authors":"Umberto Martínez-Peñas;V. Lalitha","doi":"10.1109/TIT.2026.3694571","DOIUrl":"https://doi.org/10.1109/TIT.2026.3694571","url":null,"abstract":"In this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of <inline-formula> <tex-math>$ t $ </tex-math></inline-formula> symbols belong each to <inline-formula> <tex-math>$ N $ </tex-math></inline-formula> local repair sets, which are pairwise disjoint after removing the <inline-formula> <tex-math>$ t $ </tex-math></inline-formula> symbols, and which are of size <inline-formula> <tex-math>$ r+delta -1 $ </tex-math></inline-formula> and can correct <inline-formula> <tex-math>$ delta -1 $ </tex-math></inline-formula> erasures locally. Classical LRCs with <inline-formula> <tex-math>$ N $ </tex-math></inline-formula> disjoint repair sets and LRCs with <inline-formula> <tex-math>$ N $ </tex-math></inline-formula>-availability are recovered when setting <inline-formula> <tex-math>$ t = 1 $ </tex-math></inline-formula> and <inline-formula> <tex-math>$ t=delta -1=1 $ </tex-math></inline-formula>, respectively. Allowing <inline-formula> <tex-math>$ t gt 1 $ </tex-math></inline-formula> enables our codes to reduce the storage overhead for the same locality and availability. In this setting, we define maximally recoverable LRCs (MR-LRCs) as those that can correct any globally correctable erasure pattern given the locality and availability constraints. We then identify a large class of global erasure patterns that can be corrected by such MR-LRCs and prove that they are all the correctable patterns when <inline-formula> <tex-math>$ t=1 $ </tex-math></inline-formula>. We provide three explicit constructions of LRCs that can correct such erasure patterns (thus MR-LRCs for <inline-formula> <tex-math>$ t=1 $ </tex-math></inline-formula>), based on MSRD codes, each attaining the smallest finite-field sizes for some parameter regime. Finally, we extend the known lower bound on finite-field sizes from classical MR-LRCs to our setting (for any value of <inline-formula> <tex-math>$ t $ </tex-math></inline-formula>).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4661-4674"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11523567","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510994","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":"Using the Schur Product to Solve the Code Equivalence Problem","authors":"Michele Battagliola;Rocco Mora;Paolo Santini","doi":"10.1109/TIT.2026.3694630","DOIUrl":"https://doi.org/10.1109/TIT.2026.3694630","url":null,"abstract":"Given two linear codes, the Code Equivalence Problem asks to find (if it exists) an isometry mapping one code into the other. A special case is the Permutation Equivalence Problem (PEP), where the isometry must be a permutation. The hardness of PEP is crucially dependent on the &lt;italic&gt;hull&lt;/i&gt; of a code, that is, the intersection between a code and its dual. Indeed, most of the known algorithms have running time that grows exponentially with the hull dimension. Since random codes have very small hull with large probability, PEP is deemed easy for random codes. In this paper we study how the so-called Schur product between linear codes can be employed to solve PEP. The basic idea is to transform a given PEP instance by computing the square of the given codes. While it is well known that the square code operation preserves equivalence between linear codes, we show that, regardless of the hull dimension of the starting codes, their square codes have trivial hull with high probability. Furthermore, we show that as long as the code rate is sufficiently low, no additional permutations mapping the square codes exist with high probability. This effectively generates a new pair of equivalent codes with trivial hulls, where the underlying permutation remains identical to that of the original instance. This observation allows us to leverage existing hull-based attacks to recover the permutation for the square codes, and consequently, for the original codes. Furthermore, we improve this attack by exploiting the structural relationship between hulls: if a permutation maps two codes, the same permutation also maps their respective hulls. We show that by considering the square of the hull as a code in its own right, its hull also becomes trivial with high probability. This allows for the identification of new weak instances of PEP, leading to an attack whose complexity no longer depends on the initial hull dimension, as it is the case of most known algorithm. In particular, we show that our attack achieves average polynomial-time complexity (since the square of the hull, when seen as a code, intersects with its dual in a low dimensional space with large probability) as long as &lt;inline-formula&gt; &lt;tex-math&gt;$k lt sqrt {2n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; or &lt;inline-formula&gt; &lt;tex-math&gt;$h lt sqrt {2n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, where &lt;inline-formula&gt; &lt;tex-math&gt;$n$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt; &lt;tex-math&gt;$k$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, and &lt;inline-formula&gt; &lt;tex-math&gt;$h$ &lt;/tex-math&gt;&lt;/inline-formula&gt; denote the code length, dimension, and hull dimension, respectively. We corroborate our analysis, which relies on some (plausible) heuristics, with intensive numerical simulations. As a concrete application, we consider the updatable encryption scheme proposed by Albrecht, Benčina, and Lai at Eurocrypt 2025. All the recommended instances fall into the range of weak PEP instances identified in this paper; hence, they are susceptible to our attack. As a ","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4675-4694"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510995","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":"Approximating Local Properties by Tensor Network States With Constant Bond Dimension","authors":"Yichen Huang","doi":"10.1109/TIT.2026.3694133","DOIUrl":"https://doi.org/10.1109/TIT.2026.3694133","url":null,"abstract":"Classical simulation of quantum many-body systems is a fundamental challenge due to their exponentially large Hilbert spaces. Tensor network states are a powerful ansatz to efficiently represent many physically relevant quantum states. A key question is the bond dimension—which determines the number of parameters in the ansatz—required to approximate all local properties to accuracy <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>. In one dimension, we prove that an area law for the Rényi entanglement entropy <inline-formula> <tex-math>$R_{alpha } $ </tex-math></inline-formula> with index <inline-formula> <tex-math>$alpha lt 1$ </tex-math></inline-formula> implies a matrix product state representation with bond dimension <inline-formula> <tex-math>$mathop {mathrm {poly}}nolimits (1/delta)$ </tex-math></inline-formula>. For (at most constant-fold degenerate) ground states of one-dimensional gapped Hamiltonians, a bond dimension almost linear in <inline-formula> <tex-math>$1/delta $ </tex-math></inline-formula> suffices. In two dimensions, an area law for <inline-formula> <tex-math>$R_{alpha } (alpha lt 1)$ </tex-math></inline-formula> implies a projected entangled pair state representation with bond dimension <inline-formula> <tex-math>$e^{O(1/delta)}$ </tex-math></inline-formula>. In both one and two dimensions, analogous results are obtained for states with logarithmic corrections to the area law. These findings rigorously justify the common practice of using a system-size-independent bond dimension in tensor network simulations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4930-4935"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511770","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 Design of Five-Valued Spectra (Vectorial) Boolean Functions and Their Use in Constructing Bent Functions Outside $mathcal{M}^{#}$","authors":"WeiGuo Zhang;Chaofan Song;Enes Pasalic","doi":"10.1109/TIT.2026.3697107","DOIUrl":"https://doi.org/10.1109/TIT.2026.3697107","url":null,"abstract":"Whereas the design and properties of single-output almost optimal five-valued spectra (AOFVS) Boolean functions on &lt;inline-formula&gt; &lt;tex-math&gt;$mathbb {F}_{2}^{n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, whose Walsh spectra take the values in &lt;inline-formula&gt; &lt;tex-math&gt;${0, pm 2^{left lfloor { n/2 }right rfloor }, pm 2^{left lfloor { n/2 }right rfloor +1}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, have been considered in several works, to the best of our knowledge the design of their vectorial counterpart &lt;inline-formula&gt; &lt;tex-math&gt;$F:mathbb {F}_{2}^{n} to mathbb {F} _{2}^{m}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; has not been addressed so far. Based on a special kind of partitioning the vector space &lt;inline-formula&gt; &lt;tex-math&gt;$mathbb {F}_{2}^{n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; into disjoint linear codes (not all of them having the same dimension), for the first time we were able to specify vectorial AOFVS functions &lt;inline-formula&gt; &lt;tex-math&gt;$F:mathbb {F}_{2}^{n} to mathbb {F} _{2}^{n/2+1}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, for even &lt;inline-formula&gt; &lt;tex-math&gt;$n$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. This has been achieved by identifying certain properties of the dual codes in the partition of &lt;inline-formula&gt; &lt;tex-math&gt;$mathbb {F}_{2}^{n}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Moreover, for the first time, we could specify suitable quadruples &lt;inline-formula&gt; &lt;tex-math&gt;$(f_{1}, ldots, f_{4})$ &lt;/tex-math&gt;&lt;/inline-formula&gt; of AOFVS functions in a generic manner, whose concatenation &lt;inline-formula&gt; &lt;tex-math&gt;$f=f_{1}|f_{2}|f_{3}|f_{4}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; is bent. Due to a particular specification of the constituent functions &lt;inline-formula&gt; &lt;tex-math&gt;$f_{i}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, we could also establish their exclusion from the completed Maiorana-McFarland (&lt;inline-formula&gt; &lt;tex-math&gt;${mathcal {M}}^{#}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;) class. Lastly, we introduce the &lt;inline-formula&gt; &lt;tex-math&gt;${{mathcal {D}}}_{0}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; class of AOFVS functions (similarly to the Carlet’s &lt;inline-formula&gt; &lt;tex-math&gt;${{mathcal {D}}}_{0}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; class of bent functions) and specify again suitable quadruples within this class, whose concatenation is provably bent and outside the &lt;inline-formula&gt; &lt;tex-math&gt;${{mathcal {M}}}^{#}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; class. Most notably, by doubly modifying functions in the generalized Maiorana-McFarland (&lt;inline-formula&gt; &lt;tex-math&gt;${mathcal {GMM}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;) class, we obtain AOFVS quadruples &lt;inline-formula&gt; &lt;tex-math&gt;$(f_{1},ldots,f_{4})$ &lt;/tex-math&gt;&lt;/inline-formula&gt; for which we can fully specify the so-called &lt;inline-formula&gt; &lt;tex-math&gt;${mathcal {M}}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-subspaces of each &lt;inline-formula&gt; &lt;tex-math&gt;$f_{i}$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. This allows us to determine their linearity index (the maximal dimension of any subspace &lt;inline-formula&gt; &lt;tex-math&gt;$V$ &lt;/tex-math&gt;&lt;/inline-formula&gt; for which &lt;inline-formula&gt; &lt;tex-math&gt;$D_{a}D_{b} f_{i} =0$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, f","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5217-5236"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511771","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":"Phase Transitions of the Additive Uniform Noise Channel With Peak Amplitude and Cost Constraint","authors":"Jonas Stapmanns;Luke Eilers;Catarina Dias;Tobias Kühn;Jean-Pascal Pfister","doi":"10.1109/TIT.2026.3687151","DOIUrl":"https://doi.org/10.1109/TIT.2026.3687151","url":null,"abstract":"Under which conditions is a discrete input distribution optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the convexity or concavity of the cost function. We find that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is strictly convex and the cost constraint is active, the support of the capacity-achieving input distribution spans the entire interval and is given by a mixture of continuous and discrete components. For the cases where the optimal input distribution is discrete, we derive the analytical expressions for the locations and the probability masses of the mass points and the corresponding channel capacity. For the case where the support of the optimal input distribution spans the interval, we derive an upper and a lower bound on the capacity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4565-4586"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11494094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512042","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":"When Should Selfish Miners Double-Spend?","authors":"Mustafa Doger;Sennur Ulukus","doi":"10.1109/TIT.2026.3676731","DOIUrl":"https://doi.org/10.1109/TIT.2026.3676731","url":null,"abstract":"Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle. In this paper, we give a rigorous stochastic analysis of an attack where the goal of the adversary is to double-spend while mining selfishly. To do so, we first combine stubborn and selfish mining attacks, <italic>i.e.</i>, construct a strategy where the attacker acts stubborn until its private branch reaches a certain length and then switches to act selfish. We provide the optimal stubbornness for each parameter regime. Next, we provide the maximum stubbornness that is still more profitable than honest mining and argue a connection between the level of stubbornness and the <inline-formula> <tex-math>$k$ </tex-math></inline-formula>-confirmation rule. We show that, at each attack cycle, if the level of stubbornness is higher than <inline-formula> <tex-math>$k$ </tex-math></inline-formula>, the adversary gets a free shot at double-spending. At each cycle, for a given stubbornness level, we rigorously formulate how great the probability of double-spending is. We further modify the attack in the stubborn regime in order to conceal the attack and increase the double-spending probability.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5139-5159"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512151","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}