Pub Date : 2025-07-30DOI: 10.1109/TIT.2025.3594174
Guodong Wang;Hongwei Liu;Jinquan Luo
In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively. Moreover, these two optimized decoding algorithms can be applied to the decoding of a more general class of twisted Goppa codes.
本文首先研究了一类扭曲广义Reed-Solomon （TGRS）码的译码，给出了TGRS码的关键方程的精确刻画，并提出了译码算法。其次，进一步研究了近mds TGRS码的译码，并给出了译码算法。与[Sun et al., IEEE-TIT， 2024]和[Sui et al., IEEE-TIT， 2023]中提出的解码算法相比，这两种解码算法在性能上更加高效。此外，这两种优化的解码算法可以应用于更一般的扭曲Goppa码的解码。
{"title":"Improved Decoding Algorithms for MDS and Almost-MDS Codes From Twisted GRS Codes","authors":"Guodong Wang;Hongwei Liu;Jinquan Luo","doi":"10.1109/TIT.2025.3594174","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594174","url":null,"abstract":"In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively. Moreover, these two optimized decoding algorithms can be applied to the decoding of a more general class of twisted Goppa codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7688-7698"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110254","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}
Pub Date : 2025-07-30DOI: 10.1109/TIT.2025.3593888
Longguang Li
In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons whose arrival rates are corrupted by a dark current. When the average input intensity $mathcal {E}$ is small, the capacity of the Gaussian optical intensity channel is shown to scale as $mathcal {E}sqrt {frac {log frac {1}{mathcal {E}}}{2}}$ , and the capacity of the Poisson optical intensity channel as $mathcal {E}log log frac {1}{mathcal {E}}$ . This closes the gaps between previously-derived upper and lower bounds on the asymptotic capacity of these two types of channels.
{"title":"Low-SNR Asymptotic Capacity of Two Types of Optical Wireless Channels Under Average-Intensity Constraints","authors":"Longguang Li","doi":"10.1109/TIT.2025.3593888","DOIUrl":"https://doi.org/10.1109/TIT.2025.3593888","url":null,"abstract":"In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons whose arrival rates are corrupted by a dark current. When the average input intensity <inline-formula> <tex-math>$mathcal {E}$ </tex-math></inline-formula> is small, the capacity of the Gaussian optical intensity channel is shown to scale as <inline-formula> <tex-math>$mathcal {E}sqrt {frac {log frac {1}{mathcal {E}}}{2}}$ </tex-math></inline-formula>, and the capacity of the Poisson optical intensity channel as <inline-formula> <tex-math>$mathcal {E}log log frac {1}{mathcal {E}}$ </tex-math></inline-formula>. This closes the gaps between previously-derived upper and lower bounds on the asymptotic capacity of these two types of channels.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7504-7517"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110268","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}
Pub Date : 2025-07-30DOI: 10.1109/TIT.2025.3594183
Reza K. Farsani;Wei Yu
The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple applications of the Csiszár-Körner identity. Achievable rate regions are derived by using Marton’s coding as the transmission scheme, together with different combinations of decode-and-forward and quantize-bin-and-forward strategies at the receivers. It is shown that the outer bound coincides with the achievable rate region for a new class of semi-deterministic BCs with degraded message sets; for this class of channels, one-round cooperation is sufficient to achieve the capacity. Capacity result is also derived for a class of more capable semi-deterministic BCs with both common and private messages and one-sided conferencing. For the Gaussian BC with conferencing decoders, if the noises at the decoders are perfectly correlated (i.e., the correlation is either 1 or −1), the new outer bound yields exact capacity region for two cases: 1) BC with degraded message sets; 2) BC with one-sided conferencing from the weaker receiver to the stronger receiver. When the noises have arbitrary correlation, the outer bound is shown to be within half a bit from the capacity region for these same two cases. Finally, for the general Gaussian BC, a one-sided cooperation scheme based on decode-and-forward from the stronger receiver to the weaker receiver is shown to achieve the capacity region to within $frac {1}{2}log left ({{frac {2}{1-|lambda |}}}right)$ bits, where $lambda $ is the noise correlation. An interesting implication of these results is that for a Gaussian BC with perfectly negatively correlated noises and conferencing decoders with finite cooperation link capacities, it is possible to achieve a strictly positive rate using only an infinitesimal amount of transmit power.
考虑了由有限容量的双向合作链路连接的双用户广播信道（BC），即会议解码器。基于Csiszár-Körner恒等式的多重应用，建立了一种新的容量域外界。采用马尔顿编码作为传输方案，在接收端采用译码转发和量子化转发策略的不同组合，导出了可实现的速率区域。结果表明，对于一类具有降级消息集的半确定性bc，其外边界与可达到的速率区域重合；对于这类渠道，一轮合作就足以实现容量。对于具有公共消息和私有消息以及单边会议的一类更有能力的半确定性bc，还导出了容量结果。对于具有会议解码器的高斯BC，如果解码器处的噪声是完全相关的（即相关性为1或- 1），则新的外边界产生两种情况的精确容量区域：1)具有降级消息集的BC；2)从较弱的接收方到较强的接收方单向会议的BC。当噪声具有任意相关性时，表明这两种情况下的外界距离容量区域在半位以内。最后，对于一般高斯BC，给出了一种基于从强接收机到弱接收机的解码转发的单边合作方案，以实现到$frac {1}{2}log left ({{frac {2}{1-|lambda |}}}right)$位以内的容量区域，其中$lambda $为噪声相关。这些结果的一个有趣的含义是，对于具有完全负相关噪声的高斯BC和具有有限合作链路容量的会议解码器，仅使用无限小的发射功率就可以实现严格的正速率。
{"title":"Capacity Bounds for Broadcast Channels With Bidirectional Conferencing Decoders","authors":"Reza K. Farsani;Wei Yu","doi":"10.1109/TIT.2025.3594183","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594183","url":null,"abstract":"The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple applications of the Csiszár-Körner identity. Achievable rate regions are derived by using Marton’s coding as the transmission scheme, together with different combinations of decode-and-forward and quantize-bin-and-forward strategies at the receivers. It is shown that the outer bound coincides with the achievable rate region for a new class of semi-deterministic BCs with degraded message sets; for this class of channels, one-round cooperation is sufficient to achieve the capacity. Capacity result is also derived for a class of more capable semi-deterministic BCs with both common and private messages and one-sided conferencing. For the Gaussian BC with conferencing decoders, if the noises at the decoders are perfectly correlated (i.e., the correlation is either 1 or −1), the new outer bound yields exact capacity region for two cases: 1) BC with degraded message sets; 2) BC with one-sided conferencing from the weaker receiver to the stronger receiver. When the noises have arbitrary correlation, the outer bound is shown to be within half a bit from the capacity region for these same two cases. Finally, for the general Gaussian BC, a one-sided cooperation scheme based on decode-and-forward from the stronger receiver to the weaker receiver is shown to achieve the capacity region to within <inline-formula> <tex-math>$frac {1}{2}log left ({{frac {2}{1-|lambda |}}}right)$ </tex-math></inline-formula> bits, where <inline-formula> <tex-math>$lambda $ </tex-math></inline-formula> is the noise correlation. An interesting implication of these results is that for a Gaussian BC with perfectly negatively correlated noises and conferencing decoders with finite cooperation link capacities, it is possible to achieve a strictly positive rate using only an infinitesimal amount of transmit power.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7484-7503"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110335","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}
In this note, we present examples showing that several natural ways of constructing lattices from error-correcting codes do not in general yield a correspondence between minimum-weight non-zero codewords and shortest non-zero lattice vectors. From these examples, we conclude that the main results in two works of Vlăduţ (Moscow J. Comb. Number Th., 2019 and Discrete Comput. Geom., 2021) on constructing lattices with exponential kissing number from error-correcting codes are invalid. A more recent preprint (arXiv, 2024) that Vlăduţ posted after an initial version of this work was made public is also invalid. Exhibiting a family of lattices with exponential kissing number therefore remains an open problem (as of July 2025).
{"title":"Difficulties Constructing Lattices With Exponential Kissing Number From Codes","authors":"Huck Bennett;Alexander Golovnev;Noah Stephens-Davidowitz","doi":"10.1109/TIT.2025.3593195","DOIUrl":"https://doi.org/10.1109/TIT.2025.3593195","url":null,"abstract":"In this note, we present examples showing that several natural ways of constructing lattices from error-correcting codes do not in general yield a correspondence between minimum-weight non-zero codewords and shortest non-zero lattice vectors. From these examples, we conclude that the main results in two works of Vlăduţ (Moscow J. Comb. Number Th., 2019 and Discrete Comput. Geom., 2021) on constructing lattices with exponential kissing number from error-correcting codes are invalid. A more recent preprint (arXiv, 2024) that Vlăduţ posted after an initial version of this work was made public is also invalid. Exhibiting a family of lattices with exponential kissing number therefore remains an open problem (as of July 2025).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7644-7648"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110193","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}
Pub Date : 2025-07-28DOI: 10.1109/TIT.2025.3592995
Yiqi Chen;Tobias J. Oechtering;Holger Boche;Mikael Skoglund;Yuan Luo
Distribution-preserving integrated sensing and communication is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence distribution and the original state distribution to force the system to preserve the statistical property of the channel states. An inner bound of the distribution-preserving capacity-distortion region is provided with some capacity region results under special cases. Furthermore, we consider the case where the system aims to keep the reconstructed sequence secret from an eavesdropper who also observes the channel output and receives rate-limited side information about the estimator. An inner bound of the tradeoff region and a capacity-achieving special case are presented. In addition, we provide some numerical examples to illustrate the tradeoff between the communication rate, distortion, and the preservation of the distribution.
{"title":"Distribution-Preserving Integrated Sensing and Communication","authors":"Yiqi Chen;Tobias J. Oechtering;Holger Boche;Mikael Skoglund;Yuan Luo","doi":"10.1109/TIT.2025.3592995","DOIUrl":"https://doi.org/10.1109/TIT.2025.3592995","url":null,"abstract":"Distribution-preserving integrated sensing and communication is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence distribution and the original state distribution to force the system to preserve the statistical property of the channel states. An inner bound of the distribution-preserving capacity-distortion region is provided with some capacity region results under special cases. Furthermore, we consider the case where the system aims to keep the reconstructed sequence secret from an eavesdropper who also observes the channel output and receives rate-limited side information about the estimator. An inner bound of the tradeoff region and a capacity-achieving special case are presented. In addition, we provide some numerical examples to illustrate the tradeoff between the communication rate, distortion, and the preservation of the distribution.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7518-7539"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11097316","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110278","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}
Pub Date : 2025-07-25DOI: 10.1109/TIT.2025.3592631
Alexander Barg;Nolan J. Coble;Dominik Hangleiter;Christopher Kang
Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. In this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit $pi /2^{k}~Z$ -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.
{"title":"Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes","authors":"Alexander Barg;Nolan J. Coble;Dominik Hangleiter;Christopher Kang","doi":"10.1109/TIT.2025.3592631","DOIUrl":"https://doi.org/10.1109/TIT.2025.3592631","url":null,"abstract":"Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. In this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal <italic>X</i> and <italic>Z</i> operators acting on subcubes of particular dimensions. This characterization leads us to define <italic>subcube operators</i> composed of single-qubit <inline-formula> <tex-math>$pi /2^{k}~Z$ </tex-math></inline-formula>-rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-<italic>Z</i> gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 1","pages":"415-436"},"PeriodicalIF":2.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808559","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}
Pub Date : 2025-07-25DOI: 10.1109/TIT.2025.3592704
Joonhyuk Yang;Hye Won Chung
We study community detection in multiple networks with jointly correlated node attributes and edges. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship patterns and correlated attributes across different platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (Contextual SBM or CSBM), we introduce the correlated CSBM, which incorporates structural and attribute correlations across graphs. To build intuition, we first analyze correlated Gaussian Mixture Models, wherein only correlated node attributes are available without edges, and identify the conditions under which an estimator minimizing the distance between attributes achieves exact matching of nodes across the two databases. For the correlated CSBMs, we develop a two-step procedure that first applies k-core matching to most nodes using edge information, then refines the matching for the remaining unmatched nodes by leveraging their attributes with a distance-based estimator. We identify the conditions under which the algorithm recovers the exact node correspondence, enabling us to merge the correlated edges and average the correlated attributes for enhanced community detection. Crucially, by aligning and combining graphs, we identify regimes in which community detection is impossible in a single graph but becomes feasible when side information from correlated graphs is incorporated. Our results illustrate how the interplay between graph matching and community recovery can boost performance, broadening the scope of multi-graph, attribute-based community detection.
{"title":"Exact Matching in Correlated Networks With Node Attributes for Improved Community Recovery","authors":"Joonhyuk Yang;Hye Won Chung","doi":"10.1109/TIT.2025.3592704","DOIUrl":"https://doi.org/10.1109/TIT.2025.3592704","url":null,"abstract":"We study community detection in multiple networks with jointly correlated node attributes and edges. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship patterns and correlated attributes across different platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (Contextual SBM or CSBM), we introduce the correlated CSBM, which incorporates structural and attribute correlations across graphs. To build intuition, we first analyze correlated Gaussian Mixture Models, wherein only correlated node attributes are available without edges, and identify the conditions under which an estimator minimizing the distance between attributes achieves exact matching of nodes across the two databases. For the correlated CSBMs, we develop a two-step procedure that first applies <italic>k</i>-core matching to most nodes using edge information, then refines the matching for the remaining unmatched nodes by leveraging their attributes with a distance-based estimator. We identify the conditions under which the algorithm recovers the exact node correspondence, enabling us to merge the correlated edges and average the correlated attributes for enhanced community detection. Crucially, by aligning and combining graphs, we identify regimes in which community detection is impossible in a single graph but becomes feasible when side information from correlated graphs is incorporated. Our results illustrate how the interplay between graph matching and community recovery can boost performance, broadening the scope of multi-graph, attribute-based community detection.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7916-7941"},"PeriodicalIF":2.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110273","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}
Cascade connection architectures of nonlinear feedback shift registers (NFSRs) have been widely used as the main components in the design of cryptographic algorithms, such as the Grain family of stream ciphers. It is known that the cascade connection of an n-stage NFSR into an m-stage NFSR is equivalent to an $(n+m)$ -stage NFSR. However, the converse problem on decomposing an NFSR into the cascade connection of two smaller NFSRs has not been well addressed, which can be transformed to decomposing the characteristic function h of the NFSR into the form $h=f ast g$ for some nonlinear $f,g$ , where “$ast $ ” is a special composition of Boolean functions. In this paper, we present a complete and efficient method for such decomposition problem based on previous works. The framework of the decomposition consists of two steps. The first is to construct a candidate set for g as precise as possible, and the second is to verify each candidate g and recover the corresponding f. We propose the notion of $ast $ -multiples of Boolean functions, and present three ways to take derivatives of h to extract the low-degree $ast $ -multiples of g, which are useful to determine g efficiently. Compared to existing methods, the new approach can provide a very small candidate set for g in most cases, with the size being $O(deg (h))$ , thereby achieving lower and more stable time costs in determining whether h is $ast $ -reducible and enumerating all pairs $(f,g)$ such that $h=f ast g$ (if it is $ast $ -reducible). Moreover, we show that the decomposition method also applies to shift-invariant maps, by establishing a connection between the $ast $ -product of Boolean functions and the composition of shift-invariant maps.
{"title":"The Decomposition of Cascade Connections of NFSRs: Old and New Results","authors":"Xiao-Xin Zhao;Wen-Feng Qi;Zhong-Xiao Wang;Qun-Xiong Zheng;Deng Tang","doi":"10.1109/TIT.2025.3592293","DOIUrl":"https://doi.org/10.1109/TIT.2025.3592293","url":null,"abstract":"Cascade connection architectures of nonlinear feedback shift registers (NFSRs) have been widely used as the main components in the design of cryptographic algorithms, such as the Grain family of stream ciphers. It is known that the cascade connection of an <italic>n</i>-stage NFSR into an <italic>m</i>-stage NFSR is equivalent to an <inline-formula> <tex-math>$(n+m)$ </tex-math></inline-formula>-stage NFSR. However, the converse problem on decomposing an NFSR into the cascade connection of two smaller NFSRs has not been well addressed, which can be transformed to decomposing the characteristic function <italic>h</i> of the NFSR into the form <inline-formula> <tex-math>$h=f ast g$ </tex-math></inline-formula> for some nonlinear <inline-formula> <tex-math>$f,g$ </tex-math></inline-formula>, where “<inline-formula> <tex-math>$ast $ </tex-math></inline-formula>” is a special composition of Boolean functions. In this paper, we present a complete and efficient method for such decomposition problem based on previous works. The framework of the decomposition consists of two steps. The first is to construct a candidate set for <italic>g</i> as precise as possible, and the second is to verify each candidate <italic>g</i> and recover the corresponding <italic>f</i>. We propose the notion of <inline-formula> <tex-math>$ast $ </tex-math></inline-formula>-multiples of Boolean functions, and present three ways to take derivatives of <italic>h</i> to extract the low-degree <inline-formula> <tex-math>$ast $ </tex-math></inline-formula>-multiples of <italic>g</i>, which are useful to determine <italic>g</i> efficiently. Compared to existing methods, the new approach can provide a very small candidate set for <italic>g</i> in most cases, with the size being <inline-formula> <tex-math>$O(deg (h))$ </tex-math></inline-formula>, thereby achieving lower and more stable time costs in determining whether <italic>h</i> is <inline-formula> <tex-math>$ast $ </tex-math></inline-formula>-reducible and enumerating all pairs <inline-formula> <tex-math>$(f,g)$ </tex-math></inline-formula> such that <inline-formula> <tex-math>$h=f ast g$ </tex-math></inline-formula> (if it is <inline-formula> <tex-math>$ast $ </tex-math></inline-formula>-reducible). Moreover, we show that the decomposition method also applies to shift-invariant maps, by establishing a connection between the <inline-formula> <tex-math>$ast $ </tex-math></inline-formula>-product of Boolean functions and the composition of shift-invariant maps.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"8029-8047"},"PeriodicalIF":2.9,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110338","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}
Pub Date : 2025-07-24DOI: 10.1109/TIT.2025.3583661
{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2025.3583661","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583661","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 8","pages":"C3-C3"},"PeriodicalIF":2.2,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11095974","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695536","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}
Pub Date : 2025-07-24DOI: 10.1109/TIT.2025.3583663
{"title":"IEEE Transactions on Information Theory Publication Information","authors":"","doi":"10.1109/TIT.2025.3583663","DOIUrl":"https://doi.org/10.1109/TIT.2025.3583663","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 8","pages":"C2-C2"},"PeriodicalIF":2.2,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11095972","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695537","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}
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