Problem-1.2) PRECODING and COLLABORATIVE DECISION MAKING A source intends to use any one of the following...

 

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Problem-1.2) PRECODING and COLLABORATIVE DECISION MAKING A source intends to use any one of the following two strategies, to transmit independent and equiprobable BITS B₁, B₂ € {-1,1} over an INDEPENDENT GAUSSIAN NOISE CHANNEL; Treat the BITS as BERNOULLI ½ random variables and V₁: i E {1,2} as zero mean INDEPENDENT Gaussian r. vs with variance o². Assuming (Single BIT per channel use): Y₁ =B₁ + V₁ Y₂ = B₂ + V₂ Devise a suitable Inferencing rule For detecting bits B₁ and B₂, when Measurements at the receiver's side are available as Y₁ = y₁ and Y₂ = y2 Determine the Prob(ERROR). Assuming (WITH PRE-CODING): Y₁ =B₁ + B₂ + V₁ Y₂ = B₁-B₂ + V₂ Devise a suitable Inferencing rule For detecting bits B₁ and B₂, when Measurements at the receiver's side are available as Y₁ = y₁ and Y₂ = y₂ Determine the Prob(ERROR). Compare the Prob(ERROR) in both cases and comment!! Problem-1.2) PRECODING and COLLABORATIVE DECISION MAKING A source intends to use any one of the following two strategies, to transmit independent and equiprobable BITS B₁, B₂ € {-1,1} over an INDEPENDENT GAUSSIAN NOISE CHANNEL; Treat the BITS as BERNOULLI ½ random variables and V₁: i E {1,2} as zero mean INDEPENDENT Gaussian r. vs with variance o². Assuming (Single BIT per channel use): Y₁ =B₁ + V₁ Y₂ = B₂ + V₂ Devise a suitable Inferencing rule For detecting bits B₁ and B₂, when Measurements at the receiver's side are available as Y₁ = y₁ and Y₂ = y2 Determine the Prob(ERROR). Assuming (WITH PRE-CODING): Y₁ =B₁ + B₂ + V₁ Y₂ = B₁-B₂ + V₂ Devise a suitable Inferencing rule For detecting bits B₁ and B₂, when Measurements at the receiver's side are available as Y₁ = y₁ and Y₂ = y₂ Determine the Prob(ERROR). Compare the Prob(ERROR) in both cases and comment!!

Answer rating: 100% (QA)

When the bits are treated as Bernoulli random variables and the channel is an independent Gaussian noise channel the optimal decision rule is to choos... View the full answer