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MMLU-Pro / 10646 / Consider an additive white Gaussian noise channel with an expected output power…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Consider an additive white Gaussian noise channel with an expected output power constraint P=2P=2. Thus Y=X+ZY = X + Z, Z∼N(0,1)Z \sim N(0, 1), ZZ is independent of XX, and E(Y)2≤2E(Y)^2 \leq 2. Find the channel capacity in bits.
Plain-text mathematical notation (without MathML)
Consider an additive white Gaussian noise channel with an expected output power constraint P=2. Thus Y=X+Z, Z∼N(0,1), Z is independent of X, and E(Y)²≤2. Find the channel capacity in bits.
Original LaTeX notation
Consider an additive white Gaussian noise channel with an expected output power constraint $P=2$. Thus $Y = X + Z$, $Z \sim N(0, 1)$, $Z$ is independent of $X$, and $E(Y)^2 \leq 2$. Find the channel capacity in bits.

category

computer science

options

  1. 0.25
  2. 2
  3. 4
  4. 0.75
  5. 1
  6. 0.5
  7. 1.75
  8. 3
  9. 2.5
  10. 1.5

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10646
task_id
715d9dba-6f75-57c8-8449-0ffc4f8fdb42
task_key
default--test--10646
task_revision_id
1
config / split
default / test

Official source

initial import