Transition table / matrix for convolutional encoder K=3 understandings (it used for RF transmitter FSK modulation)

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JimmyCho

Joined Aug 1, 2020
62
Im trying to understand convolutional encoder K=3 (K is number of D flip flops-registers), and I almost understand it but still confused about what's called transition matrix which in other words it means " what input value (0 or 1) would produce the next state, given the current state" So if we have K=3 which means 3 shift registers, there's 2^(K-1) possibilities which means there's 4 states as Im showing down: (it's in other words state machine) enter image description here





















And I fully understand it, and Im stuck on how do I built the correspond transition matrix for this state machine?
I've seen on the internet something weird that the transition table for convolutional encoder K=3 is:
transitionMatrix = [0 1 1 55; 0 0 1 1; 55 0 55 1; 55 0 55 1]; it was written that value 55 is value of STATE HISTORY . I didn't understand this matrix and how this matrix describe the state machine that I attached the photo above for convolutional encoder K=3
Could anyone please help me out for this?
I already did the state machine and I understand it, I didn't understand how do I build the transition matrix ..Im posting here in order to understand it and not just copying it or reading it from a book without knowing how do I implement it.
attaching down the hardware design of convolutional encoder K=3 (K is number of registers):

1605200912334.png
 
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