#### Aya2002

##### Advanced Member level 4

**convolutional encoder**

hi Friends,

i have this example and i want to understand it but i cant can some body help me please?

Example 2.1: A convolutional encoder has the following parameters:

G=[133 171]

R=1/2

K=7 (constraint length)

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

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 first digit is computed from i(x)•g1(x). The second digit is computed from i(x)•g2(x).

thus for i(x)=101=1+x^2,

first digit = (1+x^2)(1+x^2+x^3+x^5+x^6)=10 01 10 00 1

second digit=(1+x^2)(1+x+x^2+x^3+x^6)= 11 00 11 10 1

the encoder sequence is 11 01 00 10 11 01 01 00 11

my questions are:

1. the input i(x), in this example it was 101 (how?)

2. how the encoder sequence was calculated?

thanks