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    The convolutional encoder

    I have this question: In the book "Introduction to CDMA Wireless Communications" by: Mosa Ali Abu-Rgheff, page 108 the following example;



    Example 2.11
    A convolutional encoder that provides the best error performance in satellite communication
    systems has the following parameters:

    G = [133 171]
    R = 1/2
    K = 7
    Determine the structure of the encoder.
    Solution
    The two octal number are converted to binary forms as:
    133=001 011 011=1 011 011
    171=001 111 001=1 111 001
    The generator polynomials are:

    g1(x) = 1 · (x^0) + 0 · (x^1) + 1 · (x^2) + 1 · (x^3) + 0 · (x^4) + 1 · (x^5) + 1 · (x^6)
    g2(x) = 1 · (x^0) + 1 · (x^1) + 1 · (x^2) + 1 · (x^3) + 0 · (x^4) + 0 · (x^5) + 1 · (x^6)

    Denote the input as i(x), the 1st digit is computed from i(x). g1(x). The 2nd digit is computed from i(x). g2(x).

    Thus for i(x)=101=1+x^2,
    1st digit=(1+x^2)(1+x^2 +x^3 +x^5 +x^6)=10 01 10 00 1
    2nd digit=(1+x^2)(1+x+x^2 +x^3 +x^6)=11 00 11 10 1

    The encoded sequence is 11 01 00 10 11 01 01 00 11

    My question is how the encoded sequence is 11 01 00 10 11 01 01 00 11 ?

    can i have a detailed procedure for this result?

    Many thanks

    Montadar

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    Re: The convolutional encoder

    Quote Originally Posted by Aya2002
    I have this question: In the book "Introduction to CDMA Wireless Communications" by: Mosa Ali Abu-Rgheff, page 108 the following example;



    Example 2.11
    A convolutional encoder that provides the best error performance in satellite communication
    systems has the following parameters:

    G = [133 171]
    R = 1/2
    K = 7
    Determine the structure of the encoder.
    Solution
    The two octal number are converted to binary forms as:
    133=001 011 011=1 011 011
    171=001 111 001=1 111 001
    The generator polynomials are:

    g1(x) = 1 · (x^0) + 0 · (x^1) + 1 · (x^2) + 1 · (x^3) + 0 · (x^4) + 1 · (x^5) + 1 · (x^6)
    g2(x) = 1 · (x^0) + 1 · (x^1) + 1 · (x^2) + 1 · (x^3) + 0 · (x^4) + 0 · (x^5) + 1 · (x^6)

    Denote the input as i(x), the 1st digit is computed from i(x). g1(x). The 2nd digit is computed from i(x). g2(x).

    Thus for i(x)=101=1+x^2,
    1st digit=(1+x^2)(1+x^2 +x^3 +x^5 +x^6)=10 01 10 00 1
    2nd digit=(1+x^2)(1+x+x^2 +x^3 +x^6)=11 00 11 10 1

    The encoded sequence is 11 01 00 10 11 01 01 00 11

    My question is how the encoded sequence is 11 01 00 10 11 01 01 00 11 ?

    can i have a detailed procedure for this result?

    Many thanks

    Montadar



    I have just replied you on the telecom_research group email, check it out. If you have more questions, I'll try to answer them as well


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