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arXiv 0812.3709cs.ITmath.IT
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带衰落边信息的高斯信源编码的最小期望失真

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

Chris T. K. Ng, Chao Tian, Andrea J. Goldsmith, Shlomo Shamai

摘要:

编码器受速率约束,希望描述平方误差失真下的高斯源。解码器除了接收编码器的描述之外,还观察由经受慢衰落和噪声的未压缩源符号组成的边信息。解码器知道衰落实现,但编码器只知道它的分布。同时满足所有衰落状态的失真约束的率失真函数是由Heegard和Berger导出的。考虑分层编码策略,其中每个码字层针对给定的衰落状态。当边信息信道具有两个离散的衰落状态时,通过在两个码字层之间最优地分配编码速率来最小化期望的失真。对于多个衰落状态,最小期望失真被公式化为具有线性多变量和约束的凸优化问题的解。通过对原始解和对偶解的限制过程,表明当衰落概率密度函数是连续的和准凹的(例如,Rayleigh、Rician、Nakagami和对数正态分布)。特别地,在瑞利衰落下,最佳单码字层以最不利的状态为目标,就好像边信息不存在一样。

英文摘要:

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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