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X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination is
- a)0.2
- b)0.3
- c)0.6
- d)0.1
Correct answer is option 'D'. Can you explain this answer?
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Source and Channel Model
- The source X is a binary memoryless source with P(X=0) = 0.3.
- The source is transmitted over a binary symmetric channel with crossover probability P = 0.1.
- No coding is employed, so the source is directly connected to the channel.
Error Probability Calculation
To calculate the error probability at the destination, we need to consider the probabilities of different events.
Event 1: Transmitted Bit is 0 and Received Bit is 1
- P(X=0) = 0.3 (probability of transmitting 0)
- P(Y=1|X=0) = P (probability of error in channel when transmitting 0) = 0.1 (crossover probability)
- P(X=0, Y=1) = P(X=0) * P(Y=1|X=0) = 0.3 * 0.1 = 0.03
Event 2: Transmitted Bit is 1 and Received Bit is 0
- P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7 (probability of transmitting 1)
- P(Y=0|X=1) = P (probability of error in channel when transmitting 1) = 0.1 (crossover probability)
- P(X=1, Y=0) = P(X=1) * P(Y=0|X=1) = 0.7 * 0.1 = 0.07
Error Probability at the Destination
The error probability at the destination is the sum of the probabilities of Event 1 and Event 2.
- P(Error) = P(X=0, Y=1) + P(X=1, Y=0) = 0.03 + 0.07 = 0.1
Answer Explanation
- The correct answer is option 'D' (0.1).
- The error probability at the destination is 0.1, which means that there is a 10% chance that the received bit is different from the transmitted bit.
- Since no coding is employed, the error probability is directly influenced by the crossover probability of the binary symmetric channel.
- The error probability is independent of the source probabilities (P(X=0) and P(X=1)) as the source and channel are directly connected.
- The error probability calculation is based on the assumption of a binary symmetric channel, where the crossover probability is the same for both 0 to 1 and 1 to 0 transitions.
- The error probability can be reduced by employing coding techniques such as error correction codes, which introduce redundancy to detect and correct errors at the destination.
- The source X is a binary memoryless source with P(X=0) = 0.3.
- The source is transmitted over a binary symmetric channel with crossover probability P = 0.1.
- No coding is employed, so the source is directly connected to the channel.
Error Probability Calculation
To calculate the error probability at the destination, we need to consider the probabilities of different events.
Event 1: Transmitted Bit is 0 and Received Bit is 1
- P(X=0) = 0.3 (probability of transmitting 0)
- P(Y=1|X=0) = P (probability of error in channel when transmitting 0) = 0.1 (crossover probability)
- P(X=0, Y=1) = P(X=0) * P(Y=1|X=0) = 0.3 * 0.1 = 0.03
Event 2: Transmitted Bit is 1 and Received Bit is 0
- P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7 (probability of transmitting 1)
- P(Y=0|X=1) = P (probability of error in channel when transmitting 1) = 0.1 (crossover probability)
- P(X=1, Y=0) = P(X=1) * P(Y=0|X=1) = 0.7 * 0.1 = 0.07
Error Probability at the Destination
The error probability at the destination is the sum of the probabilities of Event 1 and Event 2.
- P(Error) = P(X=0, Y=1) + P(X=1, Y=0) = 0.03 + 0.07 = 0.1
Answer Explanation
- The correct answer is option 'D' (0.1).
- The error probability at the destination is 0.1, which means that there is a 10% chance that the received bit is different from the transmitted bit.
- Since no coding is employed, the error probability is directly influenced by the crossover probability of the binary symmetric channel.
- The error probability is independent of the source probabilities (P(X=0) and P(X=1)) as the source and channel are directly connected.
- The error probability calculation is based on the assumption of a binary symmetric channel, where the crossover probability is the same for both 0 to 1 and 1 to 0 transitions.
- The error probability can be reduced by employing coding techniques such as error correction codes, which introduce redundancy to detect and correct errors at the destination.
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X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination isa)0.2b)0.3c)0.6d)0.1Correct answer is option 'D'. Can you explain this answer?
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X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination isa)0.2b)0.3c)0.6d)0.1Correct answer is option 'D'. 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 X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination isa)0.2b)0.3c)0.6d)0.1Correct answer is option 'D'. 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 X is a binary memory less source with P(x=0) = 0.3. This source is transmitted over a binary symmetric channel with crossover probability P = 0.1. Assume that the source is directly connected to the channel, i.e. no coding is employed. Then the error probability at the destination isa)0.2b)0.3c)0.6d)0.1Correct answer is option 'D'. Can you explain this answer?.
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