We reinvestigate the general distributed secure source coding based on the common key cryptosystem proposed by Oohama and Santoso (ITW 2021). They proposed a framework of distributed source encryption and derived the necessary and sufficient conditions to have reliable and secure transmission. However, the bounds of the rate region, which specifies both necessary and sufficient conditions to have reliable and secure transmission under the proposed cryptosystem, were derived based on a self-tailored non-standard security criterion. In this paper we adopt the standard security criterion, i.e., standard mutual information. We successfully establish the bounds of the rate region based on this security criterion. Information spectrum method and a variant of Birkhoff-von Neumann theorem play important roles in deriving our result.
Recently, Huang and Zhang [1], [2] introduced the derivative as a fundamental structure of cyclic codes, based on which the derivative decoding was further presented. It is well known that some cyclic codes constructed based on finite geometries form a special class of low-density parity-check (LDPC) codes, which perform well under the sum-product algorithm. In this paper, we study the derivative structure of Euclidean geometry (EG) codes, with a special interest in EG-LDPC codes. It is proved that for µ = m −2, the derivative ascendant of the extended (µ,s)th-order EG code of length 2ms is the extended (µ+1,s)th-order twofold EG code of length 2ms. As a subcode of EG-LDPC code, the derivative descendant of the extend (1,s)th-order twofold EG code is characterized in terms of the roots of the generator polynomial. The new code relationship suggests that the twofold EG code can leverage the sum-product decoding of the derivative descendant for its derivative decoding.
In this paper, a new soft-decision decoding for extended Bose-Chaudhuri-Hocquenghem (eBCH) codes, referred to as CPC-SCL, is proposed, and it can achieve error-correction performance close to that of polarization-adjusted convolutional (PAC) codes in [1] when the code length n and dimension k are 128 and 64, respectively. Specifically, this paper first decomposes the eBCH code into a concatenated structure comprising an outer code and a Reed-Muller inner code. The outer code has a parity-check matrix characterized by a special block structure, which reveals that the positions of all frozen bits (including frozen zero bits and dynamic frozen bits) in the eBCH code are closely related to the index weights of elements from the perspective of the polar code. Subsequently, the CPC-SCL decoding of the eBCH codes is proposed by utilizing the cyclic property of codewords and parity-check-aided successive cancellation list (PC-SCL) decoding. Simulations also demonstrate that, over an additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) modulation, the proposed decoding can achieve near maximum-likelihood (ML) performance at n = 64, k = 24 or 45.
Levenshtein’s sequence reconstruction model plays an essential role in information retrieval in DNA-based storage systems. In this model, a word ${\text{x}} \in {\mathbb{Z}}_q^n$ is transmitted through N noisy channels, and the goal is to recover the original word exactly, or with a small uncertainty ${\mathcal{L}}$, using the outputs from these channels. Errors occurring in the channels usually involve substitutions, insertions or deletions. In this paper, we focus on insertion errors, which we represent using (so-called) insertion vectors. One of the main questions in this context is determining the minimum number of channels N required to recover the word either unambiguously or within a given precision ${\mathcal{L}}$. The original formulation of Levenshtein’s reconstruction problem requires that all the outputs from the channels are distinct. However, different channels may produce the same output word even when different errors occur. In this paper, we investigate two generalized reconstruction models where the channels are allowed to produce the same output word as long as, in each channel, different errors occur (that is, the errors correspond to different insertion vectors). Our objective is to determine the number of channels N required to uniquely recover the transmitted word x under these conditions. We present several results in this direction, some of which are optimal.
This paper shows that projection-aggregation (PA) decoding of Reed-Muller (RM) codes can decode up to half the minimum distance d efficiently. By generalizing the false vote matrix from 1-dimensional to higher-dimensional subspaces, we prove that projecting onto disjoint subspaces, regardless of their dimensions, provides at most d/2 − 1 false votes for each codeword bit. Thus, d disjoint subspaces guarantee the correction for errors of d/2 − 1 or less. Moreover, the flexibility in subspace dimensions allows projecting into repetition codes directly, resulting in decoding efficiency. Finally, we prove that PA decoding with d disjoint subspaces decodes up to half the minimum distance in $O(n\sqrt n )$ for RM codes of length n and half rate or less.
In a secret sharing scheme, a secret s is divided into multiple shares and distributed among n participants. As more shares are collected, the mutual information between the secret and the shares increases monotonically. In the perfect case, the best known explicit lower bound on the share size is given by $\frac{{{2^k} - 1}}{k} \cdot H(s)$, where H(s) is the entropy of the secret and k is the largest integer such that n ≥ 2k+k−2. This paper considers the non-perfect case, in which each share reveals at most a $\frac{1}{L}$ fraction of the secret's entropy, for an integer L > 1. A prior result in this setting provides a lower bound of $\frac{{{2^k} - 1}}{{kL}} \cdot H(s)$, under the condition n ≥ 2k+k+L−3. We provide a new lower bound that approaches the perfect-case bound, namely $\frac{{{2^k} - 2 + 1/L}}{k} \cdot H(s)$, which holds under the condition n ≥ 2k+k+2L−4. The proof generalizes perfect-case techniques by increasing the number of participants by 2(L−1). These results refine our understanding of the trade-off between share size and information leakage in non-perfect secret sharing. In particular, we construct non-perfect access structures that nearly attain the perfect lower bound with fewer participants than previous non-perfect bounds, thus complementing and extending prior work.
This paper extends the analysis of discrete age of information (AoI) to Ber/G/1/1 systems using the method of Probability Generation Functions (PGFs). The evolutions of AoI are characterized by defining a two-dimensional stochastic process. We derive the relationship between the PGF of arbitrary service time S and the system AoI in two different cases, where the packet service can or cannot be preempted by newly arrived packets. The closed-form expressions of the average AoI in both cases are obtained. Moreover, we prove that when fixing the mean of S, deterministic service time minimizes the system average AoI if packet service cannot be preempted. On the contrary, if preemption in the server is allowable, then deterministic S maximizes the average AoI.
Polar codes have been proven to be capable of achieving the optimal rate for the lossless compression problem. However, their finite-length performance is not satisfactory due to the insufficient polarization effect. In this work, we combine source polarization with several entropy coding techniques to improve the compression efficiency while keeping the additional complexity negligible. In our framework, the standard encoding of polar codes can be treated as a pre-transform on the source data, and only a small proportion of the transformed data needs further compression thanks to the source polarization. We show that our framework is compatible with the mainstream entropy coding schemes such as Huffman coding, arithmetic coding, and asymmetric number system (ANS). To optimize performance, an iterative algorithm is proposed for the set partitioning of the transformed data. Simulation results show that the improved scheme is superior to the original polar source coding.
This paper explores the application of reinforcement learning techniques to improve the performance of bit-flipping decoders and finding their optimal decisions. We begin by providing an overview of bit-flipping based decoders and reinforcement learning algorithms. We then outline the methodology for mapping the iterative decoding process into Markov Decision Processes (MDPs). We propose a feedback-based method to exploit and enhance the performance of existing well-established decoders by applying reinforcement learning algorithms after a selected decoder. In essence, we modify the MDP to reduce the number of states, making reinforcement learning algorithms feasible for low-rate and long-length codes. In addition, focusing on the correction of dominant error patterns of a selected decoder improves its error correction capability. Finally, we present experimental results for the Binary Symmetric Channel (BSC) to demonstrate the efficiency of the proposed methods.
In this paper, we propose an integrated sensing and communication (ISAC) system enabled by movable antennas (MAs), where the base station (BS) transmitter is equipped with MAs to enhance both sensing and communication performance. To characterize the benefits of MA-enabled ISAC systems, we focus on the line-of-sight (LoS) channel scenario and derive the Cramér-Rao bound (CRB) for angle estimation error, which is then minimized by jointly optimizing the antenna position vector (APV) and beamforming design, subject to a pre-defined signal-to-noise ratio (SNR) constraint to ensure the communication performance. Despite the non-convexity of the resulting problem, we develop a boundary traversal breadth-first search (BT-BFS) algorithm to obtain the global optimal solution, along with a lower-complexity boundary traversal depth-first search (BT-DFS) algorithm to find a local optimal solution efficiently. Extensive numerical results are presented to verify the effectiveness of the proposed algorithms, and demonstrate the superiority of the considered MA-enabled ISAC system over conventional ISAC systems with fixed-position antennas (FPAs).
U-UV codes are good-performing short-to-medium length channel codes constructed by several algebraic component codes. They are coupled through the (U|U+V) recursive structure. With eBCH codes as the component codes, U-UV codes can be interpreted as the generalized concatenated codes (GCCs) with inner polar codes and outer eBCH codes. With ordered statistic decoding (OSD) for the outer codes, the successive cancellation list (SCL) decoding of U-UV codes can outperform that of the cyclic redundancy check (CRC)-polar codes. But the complexity of the OSD grows exponentially with its decoding order, rendering the worst-case decoding complexity of U-UV codes being too high. This paper proposes the SCL2 decoding of eBCH based U-UV codes, in which both the inner codes and outer codes are decoded by the SCL decoding. In particular, the eBCH outer codes are interpreted as the concatenation of a polar code and a linear transform. Consequently, it can be decoded by SCL decoding with a sub-quadratic complexity. Our simulation results show that for eBCH based U-UV codes, SCL2 decoding can reduce the binary operations required in the existing (outer) OSD-(inner) SCL decoding by an order of magnitude, while maintain the decoding performance.
Group testing is traditionally considered effective only in settings with low infection rates. However, recent models that capture correlation among individuals, especially through hypergraphs, raise the question of whether group testing can remain efficient even when the infection rate is high. In this work, we study adaptive group testing under correlated settings modeled by hypergraphs and show that group testing can remain effective by leveraging these correlations to infer node states. We first state our results for k-partite hypergraphs and graphs with pairwise bounded edge intersections, and provide testing strategies that remain efficient even when the average number of infections is high. We then focus on a special class of hypergraphs called hypertrees, where infections originate from a single seed, and show that the number of tests depends on the Hamiltonian number of the underlying tree and the entropy of the edges. We then generalize the results to two seeds infection and more general contact graphs.
For polar codes, perturbing received information can enhance the error-correction performance of successive cancellation (SC) decoding. This is an effective approach for realizing low-latency yet high decoding performance for long polar codes, since each perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into the soft information perturbation. It first reveals that the PSC decoding can be equivalently viewed as perturbing the SC decoding a posteriori log-likelihood ratio (LLR) of the information bits. Such a revelation enables us to reduce the perturbation complexity by only targeting the information bits, resulting in an improved PSC (IPSC) decoding. By better utilizing the a posteriori LLRs, a set of possibly erroneous estimations can be formed to be perturbed, further reducing the perturbation complexity. Our simulation results show that, for various codeword lengths, the proposed IPSC decoding can achieve a similar performance as the PSC decoding, while yielding significant perturbation complexity reduction.
Function-Correcting Codes (FCCs) is a novel paradigm in Error Control Coding introduced by Lenz et al. 2023 for the binary substitution channel [1]. FCCs aim to protect the function evaluation of data against errors instead of the data itself, thereby relaxing the redundancy requirements of the code. Later R. Premlal et al. [4] gave new bounds on the optimal redundancy of FCCs and also extensively studied FCCs for linear functions. The notion of FCCs has also been extended to different channels such as symbol-pair read channel over the binary field by Xia et al. [2] and b-symbol read channel over finite fields by A.Singh et al. [3]. In this work, we study FCCs for linear functions for the b-symbol read channel. We provide the Plotkin-like bound on FCCs for b-symbol read channel which reduces to a Plotkin-like bound for FCCs for the symbol-pair read channel when b=2. FCCs reduce to classical Error Correcting Codes (ECCs) when the function is bijective. Analogous to this our bound reduces to the Plotkin-bound for classical ECCs for both the b-symbol and symbol-pair read channels [5], [6] when we consider linear bijective functions.
Central to the field of information theory is the study of the entropy function and the possible values it can attain when applied to subsets of sets of arbitrarily correlated random variables. The set of attainable entropy vectors over three variables $\Gamma _3^{\ast}$ is not fully understood. A complete description of $\Gamma _3^{\ast}$ requires the analysis and characterization of the faces of the related polymatroid, Γ3. Thus far, only three faces of Γ3 have been fully characterized. These faces are either one or two dimensional. Less concrete success has been attained for more complex faces. This paper focuses on a four-dimensional face $F_6^4$, and presents a novel approach to analyzing a complex face of Γ3 by reducing the problem to a two-dimensional subset of the face. Through this approach, this paper attains novel insights and a tighter inner bound on $F_6^4$ than those that have been established thus far. This method demonstrates a possible way to fully characterize $F_6^4$ through the analysis of the simpler two dimensional subset.
Physically Unclonable Functions (PUFs) have emerged as critical primitives for secure authentication and key generation. However, classical PUFs are increasingly vulnerable to machine learning and quantum-enabled attacks. Quantum PUFs, leveraging the principles of quantum mechanics, provide a promising alternative offering information-theoretic security. In this work, we present an information-theoretic framework for two key applications of QPUFs: secret key generation and secure data storage. We rigorously characterize the trade-offs between achievable key and storage rates under various privacy leakage constraints—unconditional, conditional, and zero-leakage—extending classical results into the quantum domain. We derive single-letter capacity expressions based on Holevo information and analyze the impact of shared private randomness on achieving zero privacy leakage. Our results establish fundamental performance limits for QPUF-based security systems and lay the foundation for cryptographic key generation and storage protocols in future quantum-resilient communication infrastructures.
We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. We employ a novel generalization of Hayashi’s theorem (Hayashi, J. Phys. A: Math. Gen. 34, 3413, 2001) concerning the asymptotics of quantum relative entropy, which we adapt to the infinite-dimensional setting. This enables us to prove that the QUSUM strategy retains its asymptotic optimality, characterized by the relationship between the expected detection delay and the average false alarm time for any pair of states with finite relative entropy. Thus, our findings apply broadly, including continuous-variable systems (e.g., Gaussian states), facilitating the development of optimal change-point detection schemes in quantum optics and other physical platforms, and rendering experimental verification feasible.
Quantum Key Distribution (QKD) relies on quantum mechanics to enable secure communication, with the reconciliation phase playing an essential role in correcting discrepancies in shared keys caused by noise. Conventional Low-Density Parity-Check (LDPC) codes, while robust against random errors, often struggle with burst errors arising from localized noise sources in practical QKD implementations. To address this challenge, we introduce specialized uniform LDPC codes over Galois fields explicitly designed to correct burst errors effectively. We further present a highly efficient parallel decoder for these LDPC codes, operating within the complexity class NC (Nick’s Class), making it particularly suitable for GPU-based implementation. Our decoder provides guaranteed high-performance reconciliation as long as the number of burst errors remains below a designated threshold. Additionally, we discuss an extension to our decoding approach: when configured to handle higher error rates, the algorithm becomes a Las Vegas algorithm, introducing a small but controlled probability of failure. Finally, we propose a basic algorithm for generating these specialized LDPC codes and highlight prospective optimizations required for constructing larger matrices.
The refined sphere-packing bound refers to a tight exponential lower bound to the error probability in channel coding. In the work, we present a derivation of the non-asymptotic refined sphere-packing bound for classical-quantum channels with constant composition codes. Our derivation not only offers much simpler and more transparent arguments, but also deepens the conceptual understanding of the relations between the tilted distribution and hypothesis testing.
This paper studies the problem of recovering a low-rank matrix from noisy bilinear measurements, which arises in a range of real-world applications. We propose a novel estimator that minimizes a least-squares loss regularized by a nonconvex penalty to promote low-rank structure. To solve the resulting nonconvex problem, we develop an efficient proximal gradient descent algorithm. We show that, under mild conditions, the proposed estimator consistently recovers the underlying matrix and achieves the statistically optimal convergence rate. Numerical experiments on both synthetic and real-world datasets validate the theoretical guarantees and demonstrate the practical effectiveness of the proposed method.
