maree
Newbie level 2
solution??
if any body has solution for these questions these questions are from book "wireless communication"
1) All Hamming codes have a minimum distance of 3. What is the error-correction and error-detection capability of a Hamming code?
2) The (15,11) Hamming code has generator polynomial g(X)=1+ X + X4. Determine if the codewords described by polynomials c1(X)=1+X+X3 +X7 and c2(X)=1+X3 +X5 +X6 are valid codewords for this generator polynomial. Also find the systematic form of this polynomial p(X)+ Xn−ku(X) that generates the codewords in systematic form.
3) The (7,4) cyclic Hamming code has a generator polynomial g(X)=1+ X2 + X3.
(a) Find the generator matrix for this code in systematic form.
(b) Find the parity check matrix for the code.
(c) Suppose the codeword C = [1011010] is transmitted through a channel and the corresponding received codeword is C = [1010011]. Find the syndrome polynomial associated with this received codeword.
(d) Find all possible received codewords such that for transmitted codeword C = [1011010], the received codeword has a syndrome polynomial of zero
if any body has solution for these questions these questions are from book "wireless communication"
1) All Hamming codes have a minimum distance of 3. What is the error-correction and error-detection capability of a Hamming code?
2) The (15,11) Hamming code has generator polynomial g(X)=1+ X + X4. Determine if the codewords described by polynomials c1(X)=1+X+X3 +X7 and c2(X)=1+X3 +X5 +X6 are valid codewords for this generator polynomial. Also find the systematic form of this polynomial p(X)+ Xn−ku(X) that generates the codewords in systematic form.
3) The (7,4) cyclic Hamming code has a generator polynomial g(X)=1+ X2 + X3.
(a) Find the generator matrix for this code in systematic form.
(b) Find the parity check matrix for the code.
(c) Suppose the codeword C = [1011010] is transmitted through a channel and the corresponding received codeword is C = [1010011]. Find the syndrome polynomial associated with this received codeword.
(d) Find all possible received codewords such that for transmitted codeword C = [1011010], the received codeword has a syndrome polynomial of zero