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Indicate(s) an error in a received combination.
Indicate(s) an error in a received combination.
... is a measure of uncertainty
... is a measure of uncertainty
A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 001?
A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 001?
A codeword of the Hamming code consists of ____ and ____ bits.
A codeword of the Hamming code consists of ____ and ____ bits.
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A Huffman code is a = 1, b = 000, c = 001, d = 01. Probabilities are p(a) = 0.4, p(b) = 0.1, p(c) = 0.2, p(d) = 0.3. The average length of codewords q is
A Huffman code is a = 1, b = 000, c = 001, d = 01. Probabilities are p(a) = 0.4, p(b) = 0.1, p(c) = 0.2, p(d) = 0.3. The average length of codewords q is
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A redundancy of a code S = ...
A redundancy of a code S = ...
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An average length of codewords qavr = ...
An average length of codewords qavr = ...
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An efficiency of a code E = ...
An efficiency of a code E = ...
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ASCII code is a
ASCII code is a
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By the Bayes' rule for conditional entropy H(Y|X) = ...
By the Bayes' rule for conditional entropy H(Y|X) = ...
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By the Bayes' theorem ...
By the Bayes' theorem ...
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By the Chain rule H(X,Y) = H(Y|X) + ...
By the Chain rule H(X,Y) = H(Y|X) + ...
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By the Hartley's formula the amount of information I = ...
By the Hartley's formula the amount of information I = ...
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By the Hartley's formula the entropy H = ...
By the Hartley's formula the entropy H = ...
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By the property of joint entropy H(X,Y) <= ...
By the property of joint entropy H(X,Y) <= ...
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By the Shannon's formula the amount of information I = ...
By the Shannon's formula the amount of information I = ...
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By the Shannon's formula the entropy H = ...
By the Shannon's formula the entropy H = ...
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Calculate the code rate for Hamming (15,11) code
Calculate the code rate for Hamming (15,11) code
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Calculate the efficiency of the language if it has 32 letters and its I average is 1 bit.
Calculate the efficiency of the language if it has 32 letters and its I average is 1 bit.
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Calculate the redundancy of the language if it has 32 letters and its I average is 1 bit.
Calculate the redundancy of the language if it has 32 letters and its I average is 1 bit.
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Choose an example of block code
Choose an example of block code
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Choose conditions of an optimal coding (p – probability, I – length of a code word)
Choose conditions of an optimal coding (p – probability, I – length of a code word)
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Choose the formula to create the Hamming code
Choose the formula to create the Hamming code
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Choose the formula to determine the number N of possible messages with length n if the message source alphabet consists of m characters, each of which can be an element of the message.
Choose the formula to determine the number N of possible messages with length n if the message source alphabet consists of m characters, each of which can be an element of the message.
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Code has dmin = 1. How many errors can be corrected by this code?
Code has dmin = 1. How many errors can be corrected by this code?
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Study Notes
Error Detection and Correction Codes
- Error syndrome: Indicates an error in a received combination of data bits.
- Parity bits: Indicate an error in received data.
- Data bits: Represent the actual data being transmitted.
- Entropy: A measure of uncertainty.
- Encoding: The process of converting data into a specific format.
- Information: The content or data being transmitted.
- Redundancy: Extra data added for error detection and correction.
Allowable Combinations
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A code with allowable combinations 101 and 010.
- Error combination 001: Allowable combination is 101
- Error combination 100: Allowable combination is 010
- Error combination 011: Allowable combination is 010
- Error combination 110: Allowable combination is 101
- Error combination 000: Allowable combination is 101
- Error combination 111: Allowable combination is 000 (or none)
Hamming Code
- A codeword in the Hamming code consists of data and parity bits.
- ASCII code is a fixed-length code.
- Code rate is a measure of efficiency, usually given as k/n where k is the number of data bits and n is the total number of bits.
Additional Concepts
- Code Rate: Ratio of information bits to total bits.
- Redundancy: Extra bits in a code to detect/correct errors.
- Efficiency: Ratio of information bits to total bits.
- Hamming Distance: Minimum number of bits that need to be changed to produce a different codeword
- How many errors a code can correct/detect depends on
dmin. - Average Length of Codewords (qavr): Calculated using Σ(pi * qi) for specific probabilities.
- Entropy (H): Computed using Σ(pi * log2(pi))
Calculation of Errors
- Determining the number of errors a code can correct or detect given the minimum Hamming distance (dmin).
- The number of errors that can be detected by a code equals dmin− 1
- The number of errors that can be corrected by a code depends on its minimum Hamming distance and is equal to (dmin−1)/2
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Description
This quiz covers essential concepts related to error detection and correction codes, including syndromes, parity bits, and Hamming codes. It introduces the mechanics of data transmission and discusses allowable combinations for error scenarios. Test your understanding of these vital information theory concepts.
