Consider the rate R = 1/2, convolutional code with the systematic encoding matrix G(D) = XXXXXXXXXXD + D 2 + D 4 ) that is used to communicate over the binaryinput, 8-ary output DMC with transition...

Consider the rate R = 1/2, convolutional code with the systematic encoding matrix G(D) = (1 1 + D + D²
+ D⁴
) that is used to communicate over the binaryinput, 8-ary output DMC with transition probabilities P(r | v) given by the following table:

Suppose that after the information symbols and a tail of four dummy zeros have been encoded, the four “known” (systematic encoder!) zeros in the encoded tail are deleted before transmission. The sequence
 received.

a) How many information symbols were encoded? b) After an appropriate choice of integer metrics, use the stack algorithm to decode r.