finite-blocklength analysis

To address the ultra-reliable low-latency communication (URLLC) and massive machine-type communication (mMTC) requirements of 6G, this work overcomes the limitations of classical asymptotic information theory—which assumes infinite blocklengths and vanishing error probabilities—by establishing a non-asymptotic theoretical framework for finite-blocklength, short-packet communication with non-zero error probability. Method: We first unify tight bounds and high-accuracy approximations for non-asymptotic source coding, channel coding, and joint source-channel coding. Then, we propose a unified analytical paradigm combining achievability and converse bounds based on random coding and polar code constructions, explicitly modeling the three-way tradeoff among distortion, rate, and blocklength. Contribution/Results: Our analysis reveals substantial performance gains of joint source-channel coding over separation-based schemes in the short-blocklength regime. Moreover, we derive practically implementable performance limits and design guidelines for short-packet communication at the ~100-bit scale, enabling concrete engineering deployment for 6G URLLC and mMTC.

This work investigates the finite-blocklength performance limits of dirty-paper coding over the Gaussian broadcast channel, characterizing the fundamental trade-off between code rate and error probability. For this problem, the dependence testing bound is extended to the broadcast setting for the first time, and two novel achievability bounds are established by integrating the κβ method—yielding an upper bound on the average error probability and a lower bound on the maximum codebook size. By combining dirty-paper coding with channel dispersion analysis and finite-blocklength information-theoretic tools, the authors derive tight non-asymptotic bounds that fill a critical gap in the theory of finite-blocklength Gaussian broadcast channels, thereby providing a rigorous performance benchmark for practical multiuser communication system design.

This work addresses the fundamental lossless compression rate bound for short blocklengths under stringent reliability requirements, focusing on i.i.d. sources subject to exponentially small excess-rate probability constraints. Methodologically, it integrates large deviations theory, Gaussian approximation, prefix/non-prefix code analysis, and error exponent inversion—bypassing conventional normal approximations and classical error exponent bounds. The key contribution is the first non-asymptotic, exact characterization of the optimal compression rate with explicit constants, revealing that, in the short-block regime, the optimal rate deviates significantly from entropy and is governed by the inverse error exponent function. The derived bound achieves superior accuracy in the low excess-rate region and provides a verifiable, practical rate design criterion for ultra-low-latency, high-reliability compression systems—such as edge communication and real-time sensing applications.

This paper investigates the block error probability threshold of linear codes over the binary erasure channel (BEC) under capacity-approaching regimes, focusing on decoding reliability analysis at capacity. Addressing the limitation of conventional bit error thresholds—which fail to characterize block error performance—we propose the first general threshold transformation framework based on the support weight spectrum of subcodes, establishing a quantitative relationship between block and bit error thresholds. Our key innovation lies in analyzing the minimum support weight of low-dimensional subcodes, leveraging combinatorial coding theory and the algebraic structure of Reed–Muller (RM) codes to enable exact enumeration of the support weight spectrum. This approach yields the simplest and most general proof paradigm to date for achieving block error probability convergence to zero at capacity with polynomial decoding complexity for RM codes over the BEC.

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 work addresses the unified characterization of achievability and converse bounds for channel coding under finite blocklength (one-shot) settings by introducing a novel framework based on the pairwise error probability (PEP) error spectrum with a randomized tie-breaking decoder. By establishing two variational identities applicable to arbitrary decoding metrics and revealing the joint convexity of the error spectrum under maximum-likelihood mismatched decoding, the framework reformulates the minimax meta-converse bound with prior optimization into a linear program. Leveraging the Neyman–Pearson β-function, inverse channel modeling, and convex optimization techniques, this approach unifies and reproduces classical bounds by Polyanskiy–Poor–Verdú, Han–Verdú, and Matthews, while demonstrating superior tightness and prior-optimization advantages on both the AWGN and binary Z channels.

This work addresses performance guarantees for finite-blocklength lossy joint source-channel coding (JSCC) in non-stationary settings where the source distribution is known but the channel is unknown. By introducing achievability bounds under mismatched design, along with mismatched rates and rate dispersion quantities, the authors construct a second-order universal JSCC scheme applicable to arbitrary standard Borel alphabets. The encoder and decoder are designed via Poisson functional representations, employing a parametrized Gibbs posterior as the decoding kernel whose envelope recovers the generalized mutual information. Notably, on block-erasure channels, the proposed approach incurs no performance loss due to channel mismatch, thereby achieving second-order optimality within a universal JSCC framework.