Problem 4. A channel encoder map blocks of two bits to five-bit (channel) codewords. The four possible codewords are 00000, 01000, 10001, and 11111. A codeword is transmitted over the BSC with crossover probability p = 0.1. (a) What is the minimum (Hamming) distance dmin among the codewords?
Problem 4. A channel encoder map blocks of two bits to five-bit (channel) codewords. The four possible codewords are 00000, 01000, 10001, and 11111. A codeword is transmitted over the BSC with crossover probability p = 0.1. (a) What is the minimum (Hamming) distance dmin among the codewords?
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![Problem 4. A channel encoder map blocks of two bits to five-bit (channel) codewords.
The four possible codewords are 00000, 01000, 10001, and 11111. A codeword is transmitted
over the BSC with crossover probability p = 0.1.
(a) What is the minimum (Hamming) distance dmin among the codewords?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4144d2e-3562-4105-8a14-6679c4147201%2F9487faf5-9313-4fd3-86ef-09332f6152f8%2Fygrxxob_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4. A channel encoder map blocks of two bits to five-bit (channel) codewords.
The four possible codewords are 00000, 01000, 10001, and 11111. A codeword is transmitted
over the BSC with crossover probability p = 0.1.
(a) What is the minimum (Hamming) distance dmin among the codewords?
![(b) Suppose the codeword x = 10001 was transmitted. What is the probability that the
receiver observes y = 01001 at the output of the BSC.
(c) Assume that all four codewords are equally likely to be transmitted. Suppose the
receiver observes 01001 at the output of the BSC. What is the most likely codeword
that was transmitted?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4144d2e-3562-4105-8a14-6679c4147201%2F9487faf5-9313-4fd3-86ef-09332f6152f8%2Fzbmofud_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Suppose the codeword x = 10001 was transmitted. What is the probability that the
receiver observes y = 01001 at the output of the BSC.
(c) Assume that all four codewords are equally likely to be transmitted. Suppose the
receiver observes 01001 at the output of the BSC. What is the most likely codeword
that was transmitted?
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