Synchronization errors, including insertions, deletions, and substitutions, may occur in bursts in communication systems such as DNA data storage, file synchronization, and magnetic recording. In this paper, we study an error model consisting of one burst of t-deletions and one burst of t-substitutions. By reformulating the original sequence into a matrix form, we propose an explicit construction of error-correcting codes capable of correcting one burst of t-deletions and one burst of t-substitutions with O(log n) redundancy.
This paper gives some efficient designs for binary block codes capable of controlling 0-errors, namely, the deletion of the symbol "0" (termed 0-deletions) and/or the insertion of the symbol "0" (termed 0-insertions). Based on Reed-Solomon codes, for all t, k ∈ ℕ − {0}, efficient designs are provided for t-Sy0EC constant weight codes with k information bits and length n ∈ ℕ bits. These codes are self synchronizing and can correct t 0-errors, detect (t +1) 0-errors, and simultaneously detect all occurrences of either only 0-insertions or only 0-deletions in every received word (i. e., they are t-Sy0EC/(t + 1)-Sy0ED/AU0ED). The length of the proposed codes is n(t, k) = k + O(t log log n) whenever 1/[C log2 log2 (k + t)] ≲ k/t = O(log log n), where C ∈ ℝ+ is a positive real constant. Hence, if t is sufficiently large so that t = Ω(k/log log n), but t < Cklog2 log2(k +t) then the redundancy, r = n − k, scales as O(t log log n). This result is remarkable as it demonstrates that, for certain large values of t, the optimal asymptotic redundancy is lower than the well known t log n asymptotic redundancy achieved for small values of t.
Classical binary group testing can only detect user identities, while tropical group testing overcomes this drawback and makes it well-suited for joint detection in the asynchronous massive multiple-access channel (MAC). Unfortunately, existing tropical-code assisted joint user activity and delay detection works only for the noiseless MAC without channel fading, which severely limits practical interest. This paper introduces the first noisy tropical-coded design that can jointly estimate channel gains and detect user delays and activities in an asynchronous massive MAC. Via random tropical coding analysis, vanishing detection error probability for users’ activity and delays and mean-squared estimation error of channel gain can be shown. Beyond random construction, an explicit combinatorial tropical-coded detector is constructed with aids of classical orthogonal pilot sequences. Simulation results also verify that a vast number of users can be supported using a small number of pilot sequences for this explicit construction.
Convertible codes are of interest in adaptive distributed storage systems. Existing works on convertible codes primarily focus on preserving the MDS property and optimizing access or bandwidth cost, without considering node repair efficiency. In this paper, we study convertible codes from the perspective of regenerating codes and focus on preserving optimal repair properties during code conversion. Specifically, we consider the merge regime and construct convertible codes whose initial and final codes are both minimum storage regenerating (MSR) codes. Moreover, the proposed construction achieves optimal access cost.
In this paper, we develop a symbolic algorithm to find all admissible linear network coding schemes over the binary field that are resilient to adversarial erasures. Such codes are required to be resilient to any erasure patterns in a given collection. Our algorithm is based on the binary characteristic set method, which can be used to derive the equivalence conditions for the symbolic matrices over the binary field to have full rank, thereby guaranteeing the decodability of the codes.
The problem of efficiently constructing codes capable of correcting edits has attracted considerable attention due to the prevalence of such errors in DNA data storage. In this paper, two families of q-ary codes capable of correcting two edits are proposed for even q by interleaving two classes of binary codes that correct two edits. The constructed codes achieve redundancies of 6⌈log2 q⌉ log n+O(log log n) and 6⌈log2 q log n+ 8⌈log2 q⌉, respectively. Furthermore, in the scenario of b⌉ bursts of edits each of length exactly t, we first establish a necessary and sufficient condition under which a code correcting b such bursts is equivalent to a code capable of correcting b + 1 types of errors. Based on this condition, two families of binary codes capable of correcting two bursts of edits of length t are presented via interleaving binary codes that correct two edits. These codes achieve redundancies of 6t log n + O(log log n) and 6t log n + 8t, respectively. The corresponding decoding procedures for the constructed codes are incorporated in the proofs.
This paper studies the fundamental relationships between mutual information, parametric and non-parametric Fisher information, minimum mean squared error (MMSE), and conditional variance. In particular, we introduce a unified and novel framework called Equivalent Polynomial Representation (EPR), which represents these quantities within a common polynomial space for dual-scaled parametric MIMO Gaussian channels. Within this framework, classical identities such as de Bruijn’s identity and the I-MMSE relationship, are recovered as special cases. Beyond these, the EPR framework yields new fourth-degree identities connecting MMSE derivatives, parametric Fisher information, and conditional variance under general parametric scaling regimes. These results reveal hidden algebraic structure underlying the interplay between estimation-theoretic and information-theoretic quantities.
The zero-error capacity region of a two-receiver degraded broadcast channel with ideal feedback links from the receivers to the transmitter is studied. An achievable region is derived by combining ideas related to superposition coding and zero-error list decoding. An example is provided showing that the proposed achievable region can outperform time-sharing between the capacity region’s corner points.
We present methods to accelerate the construction of variable-to-fixed-length (VF) codes based on sets of parse trees, or parse forests. Conventional construction requires iterative tree-wise dynamic programming (DP) with computational cost O(KD2) per iteration, where K and D are the numbers of trees and codewords. By exploiting a conditional concavity property of the DP objective, we derive a condition under which the DP can be executed with only O(KD) operations without loss of optimality. Additionally, we show that a suboptimal one-shot construction with O(KD) of computational cost yields reasonable parse forests even when the condition does not hold.
Decentralized secure aggregation (DSA) considers a fully-connected network of K users, each holding a private input. The goal is for every user to compute the sum of all inputs without revealing additional information, even if up to T users collude. Traditional DSA often requires large key sizes to protect all information except the input sum. To reduce key overhead, we study DSA with arbitrary collusion and heterogeneous security constraints, where the inputs of predefined user subsets, called the security set $\mathcal{S}$, must be protected from predefined collusion sets $\mathcal{T}$. For any $\mathcal{S} \in \mathcal{S}$ and $\mathcal{T} \in \mathcal{T}$, we characterize the optimal communication and source key rates. In particular, we determine the minimum number of key bits per input bit required for secure aggregation, which in general reduces to solving a linear program.
In contrast to conventional low-density parity-check (LDPC) code construction, we propose to construct a sparse decoding matrix with auxiliary variable nodes (AVNs) and then derive the corresponding high-density parity-check (HDPC) code for encoding. To leverage the sparsity gain of AVNs while controlling AVN-induced harmful substructures, we adopt a parity-check row block (PCRB) structure and show that arranging PCRBs to obtain a 4-cycle-free decoding matrix forms a class of social golfer problems (SGPs). Focusing on an explicit affine-plane-based SGP solution, we construct a family of AVN-aided affine plane (AAP) codes. For the same blocklength and minimum distance, AAP codes achieve equal or greater dimension than Reed-Muller codes and exhibit low error floors under iterative decoding, which extend finite-geometry LDPC constructions to additional code families with 4-cycle-free decoding matrices.
We study joint communication and sensing in an OFDM system, involving a transmitter sending a message to a receiver while enabling radar sensing by generating back-scattered signals. The sensing task is ranging, modeled by on-grid recovery of target delays that remain fixed over the transmission block, and formulated as a multiple hypothesis testing problem. We establish the exact tradeoff between the achievable communication rate and the ranging error exponent, and show that the tradeoff relies only on the power allocation across subcarriers. We further identify scenarios where uniform power allocation is optimal and sub-optimal for the ranging task.
Determining the ultimate limits of distillable entanglement of a shared state remains a central challenge in quantum information theory due to the phenomenon of superadditivity. This work develops Riemannian optimization methods to establish computable upper bounds on the one-way distillable entanglement. Our method systematically searches for state extensions that minimize known information-theoretic bounds. We achieve this by parameterizing the space of all possible extensions as a Stiefel manifold, enabling a universal search that overcomes the limitations of previous ad-hoc constructions. Combined with an improved upper bound on the one-way distillable entanglement based on a refined continuity bound on quantum conditional entropy, our approach yields new state-of-the-art upper bounds on the quantum capacity of the qubit depolarizing channel for large values of the depolarizing parameter, strictly improving the previously best-known bounds.
An integrated sensing and communication (ISAC) system in the presence of an external sensing eavesdropper is investigated, where the transmitter concurrently transmits a message to the legitimate receiver while estimating unknown state parameters from the corresponding echo signals. The transmitter and the legitimate receiver share a sufficiently long secret key, and the eavesdropper attempts to infer sensitive environmental information that the transmitter seeks to conceal. The fundamental performance tradeoff among communication, sensing, and sensing security is characterized by a capacity-distortion function. It is found that, with a sufficiently long secret key, the distortion attainable by the sensing eavesdropper is effectively capped by that of its symbol-by-symbol estimator fed solely with the received signals. Consequently, an input-constrained coding scheme with a deterministic encoder suffices to achieve the optimal capacity–distortion trade-off. Numerical examples are further provided to illustrate the inherent communication-sensing-security tradeoff.
