ℓp-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
ℓp-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
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ℓ实现容量和色散的高斯码的码字的 p-范数
DOI：
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发表时间：
2012
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通讯作者：
Yury Polyanskiy
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文献类型：
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作者：
Yury Polyanskiy
证明了加性高斯白噪声信道的好码的码字在接近基本极限时变得越来越各向同性(在二次型意义上)，并且类似于白高斯噪声(在ℓp范数意义下)。特别地，证明了最优高斯码必须具有logn阶的峰均功率比。
It is demonstrated that codewords of good codes for the additive white Gaussian noise (AWGN) channel become more and more isotropically distributed (in the sense of evaluating quadratic forms) and resemble white Gaussian noise (in the sense of ℓp norms) as the code approaches closer to the fundamental limits. In particular, it is shown that the optimal Gaussian code must necessarily have peak-to-average power ratio (PAPR) of order log n.