Peak-to-average power ratio of good codes for Gaussian channel

Yury Polyanskiy, Yihong Wu

Research output: Contribution to journalArticlepeer-review


Consider a problem of forward error-correction for the additive white Gaussian noise (AWGN) channel. For finite blocklength codes, the backoff from the channel capacity is inversely proportional to the square root of the blocklength. In this paper, it is shown that the codes achieving this tradeoff must necessarily have peak-to-average power ratio (PAPR) proportional to logarithm of the blocklength. This is extended to codes approaching capacity slower, and to PAPR measured at the output of an orthogonal frequency division multiplexing modulator. As a by-product, the convergence of (Smith's) amplitude-constrained AWGN capacity to Shannon's classical formula is characterized in the regime of large amplitudes. This converse-type result builds upon recent contributions in the study of empirical output distributions of good channel codes.

Original languageEnglish (US)
Article number6948255
Pages (from-to)7655-7660
Number of pages6
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 1 2014
Externally publishedYes


  • Gaussian channels
  • Shannon theory
  • channel coding
  • converse
  • peak-to-average power ratio

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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