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Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________
Correct answer is '0.048'. Can you explain this answer?
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Consider a BSC with cross-over probability of error P. Suppose that R ...
P(5 or less errors in 5 bits) =
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Consider a BSC with cross-over probability of error P. Suppose that R ...
Probability of Error in a Binary Symmetric Channel (BSC)
The Binary Symmetric Channel (BSC) is a common model used to analyze the performance of error-correcting codes. In a BSC, each transmitted bit has a probability of error, denoted as P, of being flipped.
Given Information
- Crossover probability of error, P = 0.01
- Number of bits in a source code word, R = 5
Probability of Having 5 or Less Bits in Error
To find the probability of having 5 or less bits in error in a code word, we need to calculate the probability of each possible number of error bits and sum them up.
Step 1: Probability of Having 0 Error Bits
The probability of having 0 error bits in a code word is the complement of the probability of having at least 1 error bit. In a BSC, the probability of error for each bit is the same, so we can calculate it as:
P(0 error bits) = (1 - P)^R
Substituting the given values, we have:
P(0 error bits) = (1 - 0.01)^5
P(0 error bits) = 0.99^5
P(0 error bits) = 0.9509900499
Step 2: Probability of Having 1 Error Bit
To calculate the probability of having 1 error bit, we need to consider all the different positions where the error can occur. In a code word of length 5, there are 5 possible positions for the error bit.
P(1 error bit) = R * P * (1 - P)^(R-1)
Substituting the given values, we have:
P(1 error bit) = 5 * 0.01 * (1 - 0.01)^(5-1)
P(1 error bit) = 0.04950495049
Step 3: Probability of Having 2 Error Bits
Similarly, we can calculate the probability of having 2 error bits by considering all the different combinations of 2 error bit positions.
P(2 error bits) = (R choose 2) * P^2 * (1 - P)^(R-2)
Substituting the given values, we have:
P(2 error bits) = (5 choose 2) * 0.01^2 * (1 - 0.01)^(5-2)
P(2 error bits) = 0.009801980198
Step 4: Probability of Having 3, 4, or 5 Error Bits
We can follow the same approach to calculate the probabilities of having 3, 4, or 5 error bits.
P(3 error bits) = (R choose 3) * P^3 * (1 - P)^(R-3)
P(4 error bits) = (R choose 4) * P^4 * (1 - P)^(R-4)
P(5 error bits) = (R choose 5) * P^5 * (1 - P)^(R-5)
Substituting the given values, we have:
P(3 error bits) =
The Binary Symmetric Channel (BSC) is a common model used to analyze the performance of error-correcting codes. In a BSC, each transmitted bit has a probability of error, denoted as P, of being flipped.
Given Information
- Crossover probability of error, P = 0.01
- Number of bits in a source code word, R = 5
Probability of Having 5 or Less Bits in Error
To find the probability of having 5 or less bits in error in a code word, we need to calculate the probability of each possible number of error bits and sum them up.
Step 1: Probability of Having 0 Error Bits
The probability of having 0 error bits in a code word is the complement of the probability of having at least 1 error bit. In a BSC, the probability of error for each bit is the same, so we can calculate it as:
P(0 error bits) = (1 - P)^R
Substituting the given values, we have:
P(0 error bits) = (1 - 0.01)^5
P(0 error bits) = 0.99^5
P(0 error bits) = 0.9509900499
Step 2: Probability of Having 1 Error Bit
To calculate the probability of having 1 error bit, we need to consider all the different positions where the error can occur. In a code word of length 5, there are 5 possible positions for the error bit.
P(1 error bit) = R * P * (1 - P)^(R-1)
Substituting the given values, we have:
P(1 error bit) = 5 * 0.01 * (1 - 0.01)^(5-1)
P(1 error bit) = 0.04950495049
Step 3: Probability of Having 2 Error Bits
Similarly, we can calculate the probability of having 2 error bits by considering all the different combinations of 2 error bit positions.
P(2 error bits) = (R choose 2) * P^2 * (1 - P)^(R-2)
Substituting the given values, we have:
P(2 error bits) = (5 choose 2) * 0.01^2 * (1 - 0.01)^(5-2)
P(2 error bits) = 0.009801980198
Step 4: Probability of Having 3, 4, or 5 Error Bits
We can follow the same approach to calculate the probabilities of having 3, 4, or 5 error bits.
P(3 error bits) = (R choose 3) * P^3 * (1 - P)^(R-3)
P(4 error bits) = (R choose 4) * P^4 * (1 - P)^(R-4)
P(5 error bits) = (R choose 5) * P^5 * (1 - P)^(R-5)
Substituting the given values, we have:
P(3 error bits) =
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Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer?
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Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer?.
Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer?.
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Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer?, a detailed solution for Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? has been provided alongside types of Consider a BSC with cross-over probability of error P. Suppose that R is the number of bits in a source code word that represents one of 2R possible levels at the output of quantizer. If R = 5, P = 0.01, then the probability of having 5 or less bits in error in a code word is_____________Correct answer is '0.048'. Can you explain this answer? theory, EduRev gives you an
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