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Lossy Joint Source-Channel Coding in the Finite Blocklength Regime

机译：有限块长体制中的有损联合源信道编码

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摘要

This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the nonasymptotic regime. A joint source-channel code maps a block of $k$ source symbols onto a length-$n$ channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability $epsilon$ that the distortion exceeds a given threshold $d$. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy $nC - kR(d) approx sqrt {nV + k {cal V}(d)} Q^{-1}left(epsilon right)$, where $C$ and $V$ are the channel capacity and channel dispersion, respectively; $R(d)$ and ${cal V}(d)$ are the source rate-distortion and rate-dispersion functions; and $Q$ is the standard Gaussian complementary cumulative distribution function. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and channel satisfy a certain probabilistic matching condition. In this paper, we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the nonasymptotic regime.
机译：本文找到了可以实现最佳有损联合源通道代码速率的新的严格的有限块长边界，并证明了在非渐近状态下，联合源通道代码设计比单独的联合方法具有显着的性能优势。联合源通道代码将 $ k $ 源符号的块映射到length- $ n $ 通道码字，并通过概率 $ epsilon $ 失真超过给定阈值的 $ d $ 。对于无记忆源和通道，已证明最佳联合源通道代码的参数必须满足 $ nC-kR（d）大约sqrt {nV + k {cal V}（d）} Q ^ {-1} left（epsilon right）$ ，其中 $ C $ 和 $ V $ 分别是信道容量和信道分散度； $ R（d）$ 和 $ {cal V}（d）$ 是源速率失真和速率分散函数；和 $ Q $ 是标准的高斯互补累积分布函数。当信源和信道满足一定的概率匹配条件时，已知逐符号（未编码）传输达到香农极限。在本文中，我们表明，即使不满足此条件，在某些情况下，逐符号传输也是非渐近体制中最著名的策略。

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