derive capacity bounds

This work investigates the local behavior of mutual information for discrete channels near capacity-achieving input distributions: specifically, how mutual information decays as the input distribution deviates from the optimal set. For discrete channels subject to finitely many linear constraints, we derive the first explicit quadratic upper bound on mutual information loss in terms of the distance to the optimal input set, along with computable neighborhood radius and decay coefficient. Our approach integrates Topsøe’s identity, convex analysis, information geometry, and localized Taylor-type upper bounding techniques. A key contribution is the rigorous identification of constraint cardinality as a fundamental determinant of local concavity: we prove that such a quadratic bound fails under infinitely many linear constraints and construct an explicit counterexample. These results provide theoretical foundations and quantitative tools for input distribution optimization, convergence analysis of iterative coding algorithms, and robust design in channel coding.

This paper investigates the implicit communication capacity in linear-quadratic-Gaussian (LQG) control systems: specifically, how much information a controller can reliably embed into and transmit via its control actions to an observer, while satisfying a closed-loop performance constraint—namely, an upper bound on the LQ cost. Methodologically, it employs a synthesis of information theory, optimal control, and feedback coding theory, leveraging state-space modeling, Gaussian noise characterization, and quadratic cost analysis. The contributions are threefold: (i) a convex-optimization-based upper bound on the implicit communication capacity; (ii) an exact characterization for scalar systems, unifying several existing theoretical results; and (iii) a tight sufficient condition for vector systems expressed via the algebraic Riccati equation. Numerical experiments demonstrate that the bound is highly tight for vector cases—strongly suggesting it coincides with the true capacity. This work establishes the first analytically tractable and computationally feasible framework for characterizing implicit communication capacity in joint communication–control design.

This study investigates the capacity of a binary channel with continuous input and discrete output, along with the structure of its optimal input distribution. Through information-theoretic analysis, convex optimization, and Beta-Binomial modeling—augmented by minimax redundancy constructions and divergence measures including relative entropy and χ² divergence—the authors prove that the optimal input distribution is discrete, unique, symmetric about 1/2, and includes the endpoints of the interval. Key contributions include tightening the upper bound on the support size of the optimal input from O(n) to O(n/2) and establishing the first lower bound of Ω(√(n log log n)). They further show that the output distribution induced by Beta(1/2,1/2) is asymptotically optimal, derive non-asymptotic capacity bounds, and establish that C(n) = ½ log(nπ/(2e)) + o(1), with numerical experiments corroborating the theoretical findings.

This paper investigates the fundamental capacity-distortion tradeoff for state-dependent integrated sensing and communication (ISAC) over a multiple-access channel (MAC), where two transmitters simultaneously convey messages to a receiver while jointly estimating a sequence of channel-coupled state parameters via shared echo signals. To address this, we propose a novel achievable scheme featuring message cooperation and joint compression of historical codewords with echo observations. We further develop a new outer bound framework integrating dependence balance, auxiliary state estimators, and distortion constraints. Leveraging discrete memoryless MAC models, joint source-channel coding, state-dependent information theory, and rate-distortion theory, we derive tight inner and outer bounds on the capacity-distortion region—strictly improving upon prior state-of-the-art results. Numerical evaluations confirm substantial performance gains under typical ISAC scenarios.

This work investigates the capacity region of the two-user broadcast channel (BC) with bidirectional finite-capacity conferencing decoders. Addressing scenarios where receivers exchange information via low-rate bidirectional links, we derive a tight outer bound and propose a novel achievable rate region. For the first time, we establish the exact capacity region for semi-deterministic BCs and prove that a single round of conferencing suffices to achieve capacity. Methodologically, our approach integrates the Csiszár–Körner identity, Marton’s coding scheme, and a quantize–bin–forward strategy, extending these techniques to broader BC classes—including those supporting both common and private messages, as well as unidirectional conferencing. The key contribution is the first tight capacity characterization for the bidirectional-conferencing BC, accompanied by a theoretical optimality proof; this significantly improves both the precision and applicability of existing capacity bounds.

This study investigates a tight lower bound on the support size of input distributions that achieve the capacity of the binomial channel. By analyzing the structure of the output distribution and leveraging the asymptotic optimality of the Beta-binomial distribution, the authors establish a refined approximation linking channel capacity to the Beta-binomial law, employing tools from information-theoretic capacity analysis, relative entropy, and χ²-divergence comparisons. The main contribution is an improvement of the known lower bound on the support size from √n to the order of √(n log log n), proving that any capacity-achieving input distribution must contain at least this many mass points. Additionally, the paper provides an asymptotic expression for the channel capacity: C(n) = ½ log(nπ/2e) + o(1).

This study resolves the long-standing open problem of determining the channel capacity of an additive uniform noise channel under an average input power constraint. By establishing a periodization identity for the output density and innovatively incorporating Fourier-analytic techniques, the authors rigorously derive a closed-form expression for the channel capacity and fully characterize the capacity-achieving input and output distributions. The work reveals, for the first time, the intrinsic periodic structure of the output density in uniform noise channels and successfully integrates Fourier analysis into the information-theoretic framework for capacity computation. This approach establishes a novel paradigm for analyzing non-Gaussian noise channels, offering both theoretical insight and methodological advancement in the field.

This work investigates the minimum number of support points, denoted $K_\varepsilon(A)$, required for a discrete input distribution to achieve within $\varepsilon$ of the channel capacity over an AWGN channel under an amplitude constraint $A$. By replacing exact capacity optimization with an $\varepsilon$-suboptimality framework, the study reveals that the empirically observed scaling laws arise from distinct $\varepsilon$-decay mechanisms. Leveraging Gaussian mixture approximation, $\chi^2$-divergence–based entropy control, and a “wrapping” technique, the authors establish tight bounds: when $\varepsilon = A^{-\beta}$ with $\beta \geq 1$, $K_\varepsilon(A) = \Theta(A \sqrt{\log A})$; for exponentially small $\varepsilon$, they provide matching upper and lower bounds that lie between $A \sqrt{\log A}$ and $A^{3/2}$.

This study investigates the asymptotic performance of computing Boolean functions over point-to-point communication channels, where the receiver must reliably recover the value of an unknown Boolean function—known to belong to a specified class—from a length-$n$ codeword. The goal is to characterize the rate function describing how the message length $m$ scales with $n$, and the associated computation capacity. By extending classical channel coding to the setting of function computation and leveraging information-theoretic tools together with Hamming-weight-based characterizations of Boolean function classes, the paper fully determines the rate function for a broad class of Boolean functions and establishes tight upper and lower bounds on the computation capacity, whose gap is at most a factor of two.

This work investigates the channel capacity of an additive white Gaussian noise (AWGN) channel followed by a subtractive dithered uniform quantizer under both average power and peak amplitude constraints. By invoking the Schuchman condition, the system is modeled as an effective additive noise channel with noise distributed as the sum of Gaussian and uniform components. Leveraging the entropy power inequality and constructing a maximum-entropy input distribution, a computable lower bound on capacity is derived. A tighter lower bound is then obtained by optimizing K-point discrete constellations, leading to a concise capacity approximation suitable for moderate signal-to-noise ratios (SNR). Numerical results demonstrate that with K-level quantization, only K mass points are sufficient to closely approach the optimal rate, and the proposed upper and lower bounds exhibit excellent agreement in the moderate-SNR regime.