Question

IF I b. Consider convolutional encoder with constraint length=4. The connection vectors are given by 91 = (1 110), 92 = [0 11 1) and 93 = [1 1 0 1]. i. The encoder Diagram (3 Marks) ii. State Transition Table; and (5 Marks) iii. State diagram (5 Marks)

Answer 1

The answer is been attached below,

Given convolutional encoder with constraint length = 4 . Se k = 4. So every message bit effects the output bit forº 4 suciesive shifts- The output x will generate due to 91-[1110] momim2 x = The output x₂ will generate due to g2 = [o'lll] 22 = m, 6 m₂ m₂ The output x2 will generate due to 93-[1101] x₂ m #m A m3 cis Encoder Diagram mm2 m3 LY 220 23 ₃0/p sequence

x = m 0 m, o m2, 22= m,om2om3, x3 = m 0 m, o ma Make state table using the above equations -X-OR gate off is I for odd no. of ones state Transition Table Current state IP olp Next state m₂ m₂ m. 24, 262x3 m2m, m O a O 0 D b 0 I C o - - - - b = d e - C- f - d= O g h o o 1 b - - fa с d - - - O o O e g= - - - O f h=1 0 og h - -

can be written as Next stage status before shift status after -shifth m2 m₂ mm, m2 Just discard represent state after state (m₂ m₂ m) shift iem, mm) (ii) we can make state diagram using state transition table We use solid line for llp zero and we nee dashed line for ip bit 1. all 110 Tio ooo 0101 011/ 1100 fy 100 k- por Qoa 101 olo

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