A binary channel I always transmits 0 correctly but transmits 1 as 1 or 0 with probabilities P and Q = P, where 0

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Exercise 5.9
A binary channel I always transmits 0 correctly but transmits 1 as 1 or 0 with probabilities P and
Q = P, where 0 < P < 1. Write down the channel matrix and describe the maximum likelihood
rule. If the input probabilities of 0 and 1 are p and p, find Pre. To improve reliability, 0 and 1 are
encoded as 000 and 111. Describe the resulting maximum likelihood rule; is it the same as (i)
majority decoding, (ii) nearest neighbor decoding? Find the resulting rate and error-probability.
What happens if instead we use the binary repetition code Rn, and let n → ∞ ?
Transcribed Image Text:Exercise 5.9 A binary channel I always transmits 0 correctly but transmits 1 as 1 or 0 with probabilities P and Q = P, where 0 < P < 1. Write down the channel matrix and describe the maximum likelihood rule. If the input probabilities of 0 and 1 are p and p, find Pre. To improve reliability, 0 and 1 are encoded as 000 and 111. Describe the resulting maximum likelihood rule; is it the same as (i) majority decoding, (ii) nearest neighbor decoding? Find the resulting rate and error-probability. What happens if instead we use the binary repetition code Rn, and let n → ∞ ?
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