零延迟信源信道码优化的确定性退火方法
A Deterministic Annealing Approach to Optimization of Zero-delay Source-Channel Codes
摘要：
本文研究了零延迟信源信道编码的优化问题，特别是在给定发射功率约束和均方误差失真的条件下，获得信源空间和信道空间之间的全局最优变换的问题。特别是，我们专注于设置解码器可以访问侧信息，其成本表面是已知的是千疮百孔的局部极小值。先前的工作导出了编码器和解码器映射的最优性的必要条件，以及迭代地施加这些条件的贪婪优化算法，结合启发式“噪声信道松弛”方法来减轻不良的局部最小值。虽然噪声信道松弛在简单的设置中可以说是有效的，但是在更复杂的设置（包括如本文所考虑的具有边信息的解码器）中，它不能提供准确的全局优化结果。我们提出了一个全局优化算法的思想基础上的“确定性退火”-一种非凸优化方法，来自信息理论的原则与类比统计物理学，并成功地应用于几个问题，包括聚类，矢量量化和回归。我们提出了比较数值结果表明，该算法的贪婪优化方法，以及在嘈杂的信道松弛严格的优越性。
英文摘要：
This paper studies optimization of zero-delay source-channel codes, and specifically the problem of obtaining globally optimal transformations that map between the source space and the channel space, under a given transmission power constraint and for the mean square error distortion. Particularly, we focus on the setting where the decoder has access to side information, whose cost surface is known to be riddled with local minima. Prior work derived the necessary conditions for optimality of the encoder and decoder mappings, along with a greedy optimization algorithm that imposes these conditions iteratively, in conjunction with the heuristic "noisy channel relaxation" method to mitigate poor local minima. While noisy channel relaxation is arguably effective in simple settings, it fails to provide accurate global optimization results in more complicated settings including the decoder with side information as considered in this paper. We propose a global optimization algorithm based on the ideas of "deterministic annealing"- a non-convex optimization method, derived from information theoretic principles with analogies to statistical physics, and successfully employed in several problems including clustering, vector quantization and regression. We present comparative numerical results that show strict superiority of the proposed algorithm over greedy optimization methods as well as over the noisy channel relaxation.
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