Consider a convolutional code with code rate R$=1/2,$ k$=1,$ and constraint length L$=3.$ The generators are $\_1=[100]$ and $\_2=[111].$ a$)$ Find the output for input $10100$ based on the trellis diagram of this convolutional code. b$)$ Suppose that the received sequence is $1110110010.$ Use the Viterbi algorithm to find the most likely transmitted data sequence. You should present the working steps using trellis diagram for encoding $($showing the encoding path$)$ and decoding $($showing the final survival path$)$ in your solution.