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Randomly chosen index assignments are asymptotically bad for uniform sources

机译:对于统一来源,随机选择的索引分配在渐近上是不利的

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摘要

It is known that among all redundancy-free codes (or index assignments), the natural binary code minimizes the mean-squared error (MSE) of the uniform source and uniform quantizer on a binary symmetric channel. We derive a code which maximizes the MSE and demonstrate that the code is linear and its distortion is asymptotically equivalent, as the block length grows, to the expected distortion of an index assignment chosen uniformly at random.
机译:众所周知,在所有无冗余码(或索引分配)中,自然二进制码使二进制对称信道上统一源和统一量化器的均方误差(MSE)最小。我们推导了一个使MSE最大化的代码,并证明了该代码是线性的,并且随着块长度的增加,其失真渐近等效于随机选择的均匀索引分配的预期失真。

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