Fixed-length lossy compression in the finite blocklength regime

Details Fixed-length lossy compression in the finite blocklength regime Fixed-length lossy compression in the finite blocklength regime

2011-02-19

arxiv.org/abs/1102.3944v2

Computer Science

Information Theory

to appear in IEEE Transactions on Information Theory

Scientific paper

This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength. For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be closely approximated by $R(d) + \sqrt{\frac{V(d)}{n}} \Qinv{\epsilon}$, where $R(d)$ is the rate-distortion function, $V(d)$ is the {\it rate dispersion}, a characteristic of the source which measures its stochastic variability, and $\Qinv{\cdot}$ is the inverse of the standard Gaussian complementary cdf.

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