Sol10 - CHAPTER 10 Error Detection and Correction Solutions...

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1 CHAPTER 10 Error Detection and Correction Solutions to Review Questions and Exercises Review Questions 1. In a single bit error only one bit of a data unit is corrupted; in a burst error more than one bit is corrupted (not necessarily contiguous). 2. Redundancy is a technique of adding extra bits to each data unit to determine the accuracy of transmission. 3. In forward error correction , the receiver tries to correct the corrupted codeword; in error detection by retransmission , the corrupted message is discarded (the sender needs to retransmit the message). 4. A linear block code is a block code in which the exclusive-or of any two code- words results in another codeword. A cyclic code is a linear block code in which the rotation of any codeword results in another codeword. 5. The Hamming distance between two words (of the same size) is the number of differences between the corresponding bits. The Hamming distance can easily be found if we apply the XOR operation on the two words and count the number of 1s in the result. The minimum Hamming distance is the smallest Hamming distance between all possible pairs in a set of words. 6. The single parity check uses one redundant bit for the whole data unit. In a two- dimensional parity check , original data bits are organized in a table of rows and columns. The parity bit is then calculated for each column and each row. 7. a. The only relationship between the size of the codeword and dataword is the one based on the definition: n = k + r ., where n is the size of the codeword, k is the size of the dataword, and r is the size of the remainder. b. The remainder is always one bit smaller than the divisor . c. The degree of the generator polynomial is one less than the size of the divisor . For example, the CRC-32 generator (with the polynomial of degree 32) uses a 33-bit divisor.
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2 d. The degree of the generator polynomial is the same as the size of the remainder (length of checkbits). For example, CRC-32 (with the polynomial of degree 32) creates a remainder of 32 bits. 8. One’s complement arithmetic is used to add data items in checksum calculation. In this arithmetic, when a number needs more than n bits, the extra bits are wrapped and added to the number. In this arithmetic, the complement of a number is made by inverting all bits. 9. At least three types of error cannot be detected by the current checksum calcula- tion. First, if two data items are swapped during transmission, the sum and the checksum values will not change. Second, if the value of one data item is increased (intentionally or maliciously) and the value of another one is decreased (intention- ally or maliciously) the same amount, the sum and the checksum cannot detect these changes. Third, if one or more data items is changed in such a way that the change is a multiple of 2 16 1, the sum or the checksum cannot detect the changes.
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This homework help was uploaded on 04/18/2008 for the course JAVA CDA 4506 taught by Professor Eisler during the Spring '08 term at University of Central Florida.

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Sol10 - CHAPTER 10 Error Detection and Correction Solutions...

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