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qid 10463 · computer science

Question: Suppose that feedback is used on a binary symmetric channel with parameter $p=0.5$. Each time a $Y$ is received, it becomes the next transmission. Thus $X_1$ is Bern(1/2), $X_2=Y_1$, $X_3=Y_2$, \ldots, X_n=Y_{n-1}. Find $\lim_{n\to\infty} \frac{1}{n} I(X_n;Y_n)$ in bits.

  1. 1.25
  2. 1.0
  3. 2.0
  4. 1.5
  5. 0.5
  6. 0.75
  7. 0.9
  8. 0.0
  9. 0.25
  10. 0.1

Our answer: H. 0.0 Source quote machine-checked (exact quote)

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Stored method, replayed by code (kind: formula)

card: formula · card sha256 a07f6d936a0b15f6…

Current source

Wikipedia, "Binary symmetric channel", Capacity section

https://en.wikipedia.org/wiki/Binary_symmetric_channel

“The channel capacity of the binary symmetric channel, in bits, is:”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T00:10:15.824Z

page text sha256 bb0cc90557d31efd… · content sha256 a167a29a6d0ab7e3…

addendum formula_qid10463.formula_ADDENDUM_source_rs20260918T001015Z · sha256 fcd183810fd628e5… · replaces the version below, addendum sha256 6ae087d430548752…

Earlier version (superseded)

https://en.wikipedia.org/wiki/Binary_symmetric_channel

Source weak (http_get_200_text_and_question_terms)

retrieved 2026-09-17T09:30:22.110Z

page text sha256 923db0a99bfa6a2a… · content sha256 —

addendum formula_qid10463.formula_ADDENDUM_source_bf20260917T093022Z · sha256 6ae087d430548752… · replaces the version below, addendum sha256 fc00dae4cd57e2b2…

Earlier version (superseded)

No public source has been found for this card yet (2 places checked internally).

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