Lossy Joint Source-Channel Coding in the Finite Blocklength Regime
Lossy Joint Source-Channel Coding in the Finite Blocklength Regime
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DOI：
10.1109/tit.2013.2238657
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发表时间：
2013-05-01
影响因子：
2.5
通讯作者：
Verdu, Sergio
中科院分区：
文献类型：
--
作者：
Kostina, Victoria;Verdu, Sergio
本文发现了可实现的最佳有损联合源通道码率的新的严格有限块长度界限，并证明了联合源通道码设计比非渐近状态下的单独设计带来了相当大的性能优势。联合源通道码将 k 个源符号块映射到长度为 n 的通道码字上，接收端的再现保真度通过失真超过给定阈值 d 的概率 epsilon 来测量。对于无记忆源和通道，证明最佳联合源通道码的参数必须满足，nC - kR(d) 近似于根 nV + kV(d)Q(-1) (epsilon)，其中 C 和 V 分别是通道容量和通道色散； R(d) 和 V(d) 是源速率失真和速率色散函数； Q 是标准高斯互补累积分布函数。当源和信道满足一定的概率匹配条件时，已知逐个符号（未编码）传输可以达到香农极限。在本文中，我们表明，即使不满足这个条件，在某些情况下，逐个符号传输也是非渐近机制中最著名的策略。
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) approximate to root nV + kV(d)Q(-1) (epsilon), where C and V are the channel capacity and channel dispersion, respectively; R(d) and 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.