These convolutional codes are usually represented in octal form. For example, the [171, 133] code, the two generator sequences for this code are 1111001 and 1011011, which are the binary representation of the octal numbers 171 and 133 respectively. Based on the codes given in Table 1, perform the followings:

1) Draw the shift-register encoder diagram for each of the codes. 2) For the [12 15] code, construct the state transition table, then draw the state diagram and trellis diagram (up to level 4). 3) Indicate on the trellis diagram obtained in 2), the path for the message 1011 and write down the codeword produced.

Constraint Length Code Rate 4 [54] 5 1/2 2/3 1/2 5 5 6 1/3 1/4 1/2 1/2 1/2 1/2 Generator Sequences (Octal representation) [12 15) [23 35 0; 0 5 13] [35 23] [37 33 25] [37 33 25 23] (51 73] [171 133] [371 247) (753 561] 7 8 9 Constraint Length Code Rate 4 [54] 5 1/2 2/3 1/2 5 5 6 1/3 1/4 1/2 1/2 1/2 1/2 Generator Sequences (Octal representation) [12 15) [23 35 0; 0 5 13] [35 23] [37 33 25] [37 33 25 23] (51 73] [171 133] [371 247) (753 561] 7 8 9