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arXiv:1601.06055 · IEEE International Symposium on Information Theory (ISIT)

Finite-blocklength bounds for wiretap channels

Wei Qing Yang, Rafael F. Schaefer, H. Vincent Poor

Published Jul 1, 2016• 61 citations
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Abstract

This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.

DOI
10.1109/isit.2016.7541867

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This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels.
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.
We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants εrand εsrespectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.
This paper studies the maximum secrecy rate for a semi-deterministic wiretap channel, in which the channel between the transmitter and the legitimate receiver is deterministic, while that between the transmitter and the eavesdropper is a discrete memoryless channel. For a given decoding error probability and information leakage (measured by the total variation distance), the optimal second-order secrecy rate is derived. Unlike the secrecy capacity, the second-order secrecy rate characterizes the optimal tradeoff between secrecy and reliability at finite blocklength.
In this paper, we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models and analyze their secrecy performance over several cases of concatenated code designs. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid both practical system analysis, including cryptanalysis, and practical system design when concatenated codes are used for physical-layer security. Furthermore, these new measures fill a void in the current landscape of practical security measures for physical-layer security coding and may assist in the wide-scale adoption of physical-layer techniques for security in real-world systems. We also show how the new metrics provide techniques for reducing realistic channel models to simpler discrete memoryless wiretap channel equivalents over which existing secrecy code designs may achieve information-theoretic security.
For physical-layer secrecy performance, existing studies only focus on coding schemes that can achieve the secrecy capacity. However, finite blocklength penalty could be fatal for security of private message. In this paper, we explore the impact of finite blocklength on secrecy for the wiretap channel model. We propose secrecy performance matrices for finite blocklength analysis and provide analytical expressions to evaluate the secrecy performance. We demonstrate trade-off between secrecy and reliability, and also provide an upper bound of secret information rate in finite blocklength case. The results are also applied to indicate asymptotic performance.
For physical-layer secrecy performance, existing studies only focus on coding schemes that can achieve the secrecy capacity. However, finite blocklength penalty could be fatal for security of private message. In this paper, we explore the impact of finite blocklength on secrecy for the wiretap channel model. We propose secrecy performance matrices for finite blocklength analysis and provide analytical expressions to evaluate the secrecy performance. We demonstrate trade-off between secrecy and reliability, and also provide an upper bound of secret information rate in finite blocklength case. The results are also applied to indicate asymptotic performance.