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Consider the following linear block code: Each codeword consists of 3 data bits and 3 parity check bits, i.e., [i,,i2,i3,PuP2, P3]- The parity check bits are defined by P1 = i1 + iz P2 = i1 + iz mod 2 P3 = i2 + iz mod 2 mod 2 a. Determine the generator matrix. b. List all the legitimate codewords. c. Determine the minimum distance. d. Suppose that a single error occurs at the first bit. Compute the syndrome. Similarly, compute the syndrome for a single error at each of the other bits. e. Suppose that at most one error occurs. Correct the received vector [010001] by syndrome decoding.

Consider the following linear block code: Each codeword consists of 3 data bits and 3 parity check bits, i.e., [i,,i2,i3,PuP2, P3]- The parity check bits are defined by P1 = i1 + iz P2 = i1 + iz mod 2 P3 = i2 + iz mod 2 mod 2 a. Determine the generator matrix. b. List all the legitimate codewords. c. Determine the minimum distance. d. Suppose that a single error occurs at the first bit. Compute the syndrome. Similarly, compute the syndrome for a single error at each of the other bits. e. Suppose that at most one error occurs. Correct the received vector [010001] by syndrome decoding.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the following linear block code: Each codeword consists of 3 data bits and 3 parity check bits, i.e., [i,,i2,i3,PuP2, P3]- The parity check bits are defined by P1 = i1 + iz P2 = i1 + iz mod 2 P3 = i2 + iz mod 2 mod 2 a. Determine the generator matrix. b. List all the legitimate codewords. c. Determine the minimum distance. d. Suppose that a single error occurs at the first bit. Compute the syndrome. Similarly, compute the syndrome for a single error at each of the other bits. e. Suppose that at most one error occurs. Correct the received vector [010001] by syndrome decoding.
Transcribed Image Text:Consider the following linear block code: Each codeword consists of 3 data bits and 3 parity check bits, i.e., [i,,i2,i3,PuP2, P3]- The parity check bits are defined by P1 = i1 + iz P2 = i1 + iz mod 2 P3 = i2 + iz mod 2 mod 2 a. Determine the generator matrix. b. List all the legitimate codewords. c. Determine the minimum distance. d. Suppose that a single error occurs at the first bit. Compute the syndrome. Similarly, compute the syndrome for a single error at each of the other bits. e. Suppose that at most one error occurs. Correct the received vector [010001] by syndrome decoding.
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