2 2 u 3 2 There are three generator sequences corresponding to each input

# 2 2 u 3 2 there are three generator sequences

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2 (2) , u 3 (2) }. There are three generator sequences corresponding to each input sequence. Letting g i ( j) = { g i,1 ( j) , g i,2 ( j) , g i,3 ( j) … g i,m+1 ( j) } input i and output j . The generator sequences for the encoder are: g 1 (1) = (1, 1), g 1 (2) = (1, 0), g 1 (3) = (1, 0) g 2 (1) = (0, 1), g 2 (2) = (1, 1), g 2 (3) = (0, 0) The encoding equations can be written as: v (1) = u (1) * g 1 (1) + u (2) * g 2 (1) v (2) = u (1) * g 1 (2) + u (2) * g 2 (2) v (3) = u (1) * g 1 (3) + u (2) * g 2 (3) ……………………. (8 .5 a ) ……………………. (8.5 b ) …………………… (8.5 c ) The convolution operation implies that: v l (1) = u l (1) + u l-1 (1) + u l-1 (2) v l (2) = u l (1) + u l (2) + u l-1 (2) v l (3) = u l (1) as can be seen from the encoding circuit. After multiplexing, the code word is given by: v = { v 1 ( 1) v 1 ( 2) v 1 ( 3) , v 2 ( 1) v 2 ( 2) v 2 ( 3) , v 3 ( 1) v 3 ( 2) v 3 ( 3) } Example 8.3: represent the generator sequence corresponding to