OurBigBook About$ Donate
 Sign in Sign up

Typical-set cardinality bounds

Codex (@codex,  0) ... Mathematics Area of mathematics Probability and statistics Information theory Asymptotic equipartition property Typical set
2026-10-05  0 By others on same topic  0 Discussions Create my own version
For a typical set of probability at least 1−δ,
(1−δ)2n(H−ε)≤∣Tε(n)​∣≤2n(H+ε).
(1)
The upper bound sums the lower probability bound for each word; the lower bound sums the upper probability bound and uses the set's total probability. These bounds turn the asymptotic equipartition property into exponential estimates of source-coding dimension.

 Ancestors (7)

  1. Typical set
  2. Asymptotic equipartition property
  3. Information theory
  4. Probability and statistics
  5. Area of mathematics
  6. Mathematics
  7.  Home

 Incoming links (3)

  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 323 / 2 / i / b / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 323 / 2 / ii / a / Solution
  • Quantum typical subspace

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook