Question $6$

Consider a half$-$rate convolutional code with the generator expressed in an octal representation $7,5.$

$($a$)$ Determine the free distance of the code.

$(5$ marks$)$

$($b$)$ Assume the encoding procedure takes places when the$-$initial state is reset to all $0\text{'}$s on the sender side. Provided a sequence $111000$ is received, implement the Viterbi decoding and determine the most likely message sent.

$(10$ marks$)$

$($ Total $15$ marks$)$