(a) Find the best code of length 3 with four codewords for binary symmetric channel with error probability = 0.1. What is the probability of error for this code? (Note that all possible received sequences should be mapped onto possible codewords)

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Chapter1: Combinatorial Analysis
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(b) What is the probability of error if we used all the 8 possible sequences of length 3 as
codewords?
(c) Now consider a binary erasure channel with erasure probability 0.1. Again, if we used
the two codeword code 000 and 111, then received sequences 00E,OEO,E00,0EE, EOE.EEO
would all be decoded as 0, and similarly we would decode 11E, 1E1,E11, 1EE,E1E, EE1
as 1. If we received the sequence EEE we would not know if it was a 000 or a 111 that
was sent - so we choose one of these two at random, and are wrong half the time. What
is the probability of error for this code over the erasure channel?
Transcribed Image Text:(b) What is the probability of error if we used all the 8 possible sequences of length 3 as codewords? (c) Now consider a binary erasure channel with erasure probability 0.1. Again, if we used the two codeword code 000 and 111, then received sequences 00E,OEO,E00,0EE, EOE.EEO would all be decoded as 0, and similarly we would decode 11E, 1E1,E11, 1EE,E1E, EE1 as 1. If we received the sequence EEE we would not know if it was a 000 or a 111 that was sent - so we choose one of these two at random, and are wrong half the time. What is the probability of error for this code over the erasure channel?
4.
(a) Find the best code of length 3 with four codewords for binary symmetric channel with
error probability € = 0.1. What is the probability of error for this code? (Note that all
possible received sequences should be mapped onto possible codewords)
1
Transcribed Image Text:4. (a) Find the best code of length 3 with four codewords for binary symmetric channel with error probability € = 0.1. What is the probability of error for this code? (Note that all possible received sequences should be mapped onto possible codewords) 1
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