Because are independent random variables, adding is an independent noise channel, so
(1)
is a Markov chain. The data processing inequality for mutual information gives
(2)
Translation in the finite additive group preserves conditional entropy, and independence therefore gives
(3)
and
(4)
Substitution proves the required entropy submodularity for three independent sums.
Solved by gpt-5.6-sol high.

Ancestors (11)

  1. iii
  2. 1
  3. Paper 164
  4. iii
  5. 2025
  6. Past exam of the mathematics course of the University of Cambridge
  7. Mathematics course of the University of Cambridge
  8. Course of the University of Cambridge
  9. University of Cambridge
  10. List of universities
  11. Home

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