Given the generator matrix 1 1 O 0 0 0 0 1 1 1 O O B 1 0 0 1 O 183 1 0 0 0 1 (a) Find H the parity-check matrix (b) The received vector are r [1100010], [1110110], [1110011]. Calculate the syndrome. Find the error vectors and hence, identify the error bits. (c) Find the transmitted code vectors Syndrome Error 001 011 101 BO pattern 0010000 0000100 0000001 1 0

Systems Architecture
7th Edition
ISBN:9781305080195
Author:Stephen D. Burd
Publisher:Stephen D. Burd
Chapter8: Data And Network Communication Technology
Section: Chapter Questions
Problem 25VE
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Given the generator matrix
1
1
0
0
Bo
21
0
1
1
1
3
1
0
1
O
#43
0
1
0
0
(a) Find H the parity-check matrix
(b) The received vector are r [1100010], [1110110],
[1110011]. Calculate the syndrome. Find the error
vectors and hence, identify the error bits.
(c) Find the transmitted code vectors
Syndrome Error
001
011
101
pattern
0010000
0000100
0000001
1
0
0
Transcribed Image Text:Given the generator matrix 1 1 0 0 Bo 21 0 1 1 1 3 1 0 1 O #43 0 1 0 0 (a) Find H the parity-check matrix (b) The received vector are r [1100010], [1110110], [1110011]. Calculate the syndrome. Find the error vectors and hence, identify the error bits. (c) Find the transmitted code vectors Syndrome Error 001 011 101 pattern 0010000 0000100 0000001 1 0 0
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