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Consider the generator polynomial for a (15, 11) cyclic code defined by g(p)=p¹+p+1 a) Assume that the generator polynomial is directly used to encode the input information bits to ob- tain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is the input information polynomial. Find the first three rows of the equivalent generator matrix for the encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient. b) Still assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword. How many bit errors in the codeword can this code correct? c) Now assume that the encoder is required to produce systematic codewords using the generator poly- nomial. Find the first three rows of the equivalent generator matrix for the systematic encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient.

Consider the generator polynomial for a (15, 11) cyclic code defined by g(p)=p¹+p+1 a) Assume that the generator polynomial is directly used to encode the input information bits to ob- tain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is the input information polynomial. Find the first three rows of the equivalent generator matrix for the encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient. b) Still assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword. How many bit errors in the codeword can this code correct? c) Now assume that the encoder is required to produce systematic codewords using the generator poly- nomial. Find the first three rows of the equivalent generator matrix for the systematic encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Consider the generator polynomial for a (15, 11) cyclic code defined by g(p)=p¹+p+1 a) Assume that the generator polynomial is directly used to encode the input information bits to ob- tain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is the input information polynomial. Find the first three rows of the equivalent generator matrix for the encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient. b) Still assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword. How many bit errors in the codeword can this code correct? c) Now assume that the encoder is required to produce systematic codewords using the generator poly- nomial. Find the first three rows of the equivalent generator matrix for the systematic encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient.
Transcribed Image Text:Consider the generator polynomial for a (15, 11) cyclic code defined by g(p)=p¹+p+1 a) Assume that the generator polynomial is directly used to encode the input information bits to ob- tain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is the input information polynomial. Find the first three rows of the equivalent generator matrix for the encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient. b) Still assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword. How many bit errors in the codeword can this code correct? c) Now assume that the encoder is required to produce systematic codewords using the generator poly- nomial. Find the first three rows of the equivalent generator matrix for the systematic encoder. You don't need to present the entire generator matrix, just the first three rows are sufficient.
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