ℓp-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Institute of Electrical and Electronics Engineers (IEEE)
Polyanskiy, Yury. ℓp-norms of Codewords from Capacity- and Dispersion-achieveing Gaussian Codes. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 294-301. Institute of Electrical and Electronics Engineers, 2012.
Author's final manuscript