Optimal causal quantization of Markov Sources with distortion constraints
Optimal causal quantization of Markov Sources with distortion constraints
复制标题
具有失真约束的马尔可夫源的最优因果量化
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Meyn
中科院分区：
文献类型：
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作者：
S. Yuksel;T. Başar;S. Meyn
对于马尔可夫源，研究了在均方失真约束下使总通信速率最小化的最优因果编码器结构。考虑的源类存在于连续的字母表中，并且允许编码器是可变速率的。同时考虑了有限视界和无限视界问题。在有限视界情况下，问题是非凸的，而在无限视界情况下，问题在一定的假设下是凸的。对于有限视界问题，k阶马尔可夫源的最优确定性因果编码器仅使用最近的k个源符号和接收器上可用的信息，而无记忆源的最优因果编码器是无记忆的。对于无限视界问题，采用了凸解析方法。在编码器和解码器之间缺乏共同随机性的情况下，随机平稳量化器是次优的。如果存在共同随机性，则最优量化器要求最多两个确定性量化器的随机化。在没有共同随机性的情况下，最优量化器是非平稳的，基于递归的两个确定性量化器分时是最优的。考虑了一个由高斯噪声驱动的线性源。如果过程稳定，则创新编码在高速率下几乎是最优的，而如果源不稳定，则即使是高速率时不变创新编码方案也会导致不稳定的估计过程。
For Markov sources, the structure of optimal causal encoders minimizing the total communication rate subject to a mean-square distortion constraint is studied. The class of sources considered lives in a continuous alphabet, and the encoder is allowed to be variable-rate. Both the finite-horizon and the infinite-horizon problems are considered. In the finite-horizon case, the problem is non-convex, whereas in the infinite-horizon case the problem can be convexified under certain assumptions. For a finite horizon problem, the optimal deterministic causal encoder for a kth-order Markov source uses only the most recent k source symbols and the information available at the receiver, whereas the optimal causal coder for a memoryless source is memoryless. For the infinite-horizon problem, a convex-analytic approach is adopted. Randomized stationary quantizers are suboptimal in the absence of common randomness between the encoder and the decoder. If there is common randomness, the optimal quantizer requires the randomization of at most two deterministic quantizers. In the absence of common randomness, the optimal quantizer is non-stationary and a recurrence-based time-sharing of two deterministic quantizers is optimal. A linear source driven by Gaussian noise is considered. If the process is stable, innovation coding is almost optimal at high-rates, whereas if the source is unstable, then even a high-rate time-invariant innovation coding scheme leads to an unstable estimation process.