Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

Richard G. Wood; Tamás Linder; Serdar Yüksel

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Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

机译：马尔可夫源的最佳零延迟编码：固定和有限存储代码

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摘要

The optimal zero delay coding of a finite-state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of deterministic Markov (Walrand–Varaiya-type) coding policies for the finite time horizon problem, and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem. Our main result here shows that for any irreducible and aperiodic Markov source with a finite alphabet, deterministic and stationary Markov coding policies are optimal for the infinite horizon problem. In addition, the finite block length (time horizon) performance of an optimal (stationary and Markov) coding policy is shown to approach the infinite time horizon optimum at a rate . The results are extended to systems, where zero delay communication takes place across a noisy channel with noiseless feedback.

机译：考虑了有限状态马尔可夫源的最优零延迟编码。使用随机控制公式研究了最优代码的存在和结构。文献中的先验结果确定了确定性Markov（Walrand–Varaiya型）编码策略对于有限时间范围问题的最优性，以及确定性非平稳和随机平稳策略对于无限时间范围问题的最优性。我们的主要结果表明，对于任何具有有限字母的不可约且非周期性的马尔可夫源，确定性和平稳性的马尔可夫编码策略是无限地平线问题的最佳选择。另外，示出了最优（固定和马尔可夫）编码策略的有限块长度（时间范围）性能以一定速率接近无限时间范围最优。结果扩展到系统，其中零延迟通信通过无噪声反馈在嘈杂的信道上进行。

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来源
《IEEE Transactions on Information Theory》 |2017年第9期|5968-5980|共13页
作者
Richard G. Wood; Tamás Linder; Serdar Yüksel;
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作者单位

Department of Mathematics and Statistics, Queen’s University, Kingston, Kingston, ON, Canada;

Department of Mathematics and Statistics, Queen’s University, Kingston, Kingston, ON, Canada;

Department of Mathematics and Statistics, Queen’s University, Kingston, Kingston, ON, Canada;

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正文语种 eng
中图分类
关键词
Markov processes; Delays; Distortion; Channel coding; Source coding; Quantization (signal);

机译：马尔可夫过程;延迟;失真;通道编码;源编码;量化（信号）;

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专利

1. Source coding exponents for zero-delay coding with finite memory [J] . Merhav N., Kontoyiannis I. IEEE Transactions on Information Theory . 2003,第3期

机译：具有有限内存的零延迟编码的源编码指数
2. On Optimal Zero-Delay Coding of Vector Markov Sources [J] . Linder T., Yuksel S. Information Theory, IEEE Transactions on . 2014,第10期

机译：向量马尔可夫源的最佳零延迟编码
3. Optimal detection of discrete Markov sources over discrete memoryless channels/spl minus/applications to combined source-channel coding [J] . Phamdo N., Farvardin N. IEEE Transactions on Information Theory . 1994,第1期

机译：在离散无记忆通道/ spl减/组合源通道编码上的应用中最优检测离散Markov源
4. Optimality of Stationary and Deterministic Policies for Zero-Delay Coding of ℝd-Valued Linear Markov Sources with Quadratic Cost [C] . Meysam Ghomi, Tamás Linder, Serdar Yüksel IEEE Conference on Decision and Control . 2020

机译：具有二次成本的尺寸值线性马尔可夫光源零延迟编码的静止和确定性政策的最优性
5. Extremely Low-Delay Coding of Gaussian Sources with Side Information at the Decoder [D] . Chen, Xuechen 2012

机译：高斯源的极低延迟编码，在解码器中具有辅助信息
6. Zero-Delay Multiple Descriptions of Stationary Scalar Gauss-Markov Sources [O] . Andreas Jonas Fuglsig, Jan Østergaard 2019

机译：零延迟固定标量高斯 - 马尔可夫源的多次描述
7. Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes [O] . Richard G. Wood, Tamas Linder, Serdar Yuksel 2017

机译：马尔可夫源的最佳零延迟编码：静止和有限内存码

Optimal Zero Delay Coding of Markov Sources: Stationary and Finite Memory Codes

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