high-snr capacity analysis

This work investigates the capacity of Gaussian channels under an input entropy constraint in the high signal-to-noise ratio (SNR) regime. By leveraging information-theoretic tools, asymptotic analysis, and the theory of discrete Gaussian distributions, it establishes for the first time that the capacity-achieving input distribution is a discrete Gaussian supported on a scaled integer lattice. The primary contribution lies in precisely characterizing the exponential decay rate of the gap between channel capacity and the entropy-constrained input’s mutual information. The authors prove that this gap vanishes exponentially fast as SNR increases, thereby fully elucidating the capacity behavior of entropy-constrained Gaussian channels in the high-SNR limit.

This paper addresses the asymptotic Shannon capacity analysis and computation for large-scale MIMO channels impaired by hardware nonlinearities and distortions. We propose a unified Bayesian asymptotic and information-theoretic framework, establishing for the first time that, in the large-antenna limit, both the channel capacity and the optimal input distribution are fully determined by the Fisher information of the single-output channel—characterized via a tilted Jeffreys factor. Furthermore, we design a log-likelihood receiver based on a compress-expand transformation, supporting canonical distortion models including 1-bit ADCs and Poisson channels. The derived closed-form capacity expression and asymptotically optimal input distribution achieve near-capacity performance across diverse hardware distortion scenarios, while maintaining receiver complexity independent of the number of antennas.

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 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.

Fundamental challenges in signal identification under event-triggered communication over additive white Gaussian noise (AWGN) and fading channels remain unresolved. Method: This paper proposes a deterministic identification code design framework tailored to AWGN, slow-fading, and fast-fading channels. It establishes, for the first time, a unified tight lower bound on identification capacity across all three channel models, rigorously proving that its scaling law fundamentally differs from Shannon capacity. Crucially, this bound is shown to be achievable even without channel state information at either the transmitter (CSIT) or receiver (CSIR). The framework leverages deterministic code construction and refined fading modeling to devise practical, high-efficiency identification codes that approach capacity under average power constraints. Contribution/Results: This work delivers the first systematic capacity theory and constructive coding paradigm for identification communication, bridging theoretical limits with implementable schemes.

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 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.

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 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 work investigates the error performance and achievable rates of random spherical codes over the real-valued additive white Gaussian noise channel in the high signal-to-noise ratio (SNR) regime. By employing ensemble analysis of random codes, high-SNR asymptotic expansions, and converse bounding techniques, the study reveals a three-phase transition behavior in the average error probability as the codebook size increases. Building on this characterization, it jointly quantifies—for the first time—the impact of blocklength and target reliability on the additive gap between achievable rates and converse bounds. This gap converges to a positive value dependent on both blocklength and target error probability, yet vanishes as blocklength grows; concurrently, the ratio of achievable rate to converse bound approaches unity, demonstrating their asymptotic tightness at high SNR.