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The back-off from capacity due to finite block-length can be assessed accurately from the channel dispersion. This paper analyzes the dispersion of a single-user, scalar, coherent fading channel with additive Gaussian noise. They obtain a convenient two-term expression for the channel dispersion which shows that, unlike the capacity, it depends crucially on the dynamics of the fading process. The paper is organized as follows. The channel model and the relevant literature, a heuristic derivation of the dispersion, rigorous results and the application of their results to a first-order auto-regressive Gaussian fading process.
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