Consider the rate R = 1/2, memory m = 1, systematic encoding matrix G(D) = XXXXXXXXXXD). a) Draw the length ` = 5 trellis. b) Suppose that the encoder is used to communicate over a BSC with crossover...

Consider the rate R = 1/2, memory m = 1, systematic encoding matrix G(D) = (1 1 + D).

a) Draw the length ` = 5 trellis.

b) Suppose that the encoder is used to communicate over a BSC with crossover probability
 Use the Viterbi algorithm to decode the received sequence r = 10 01 11 11 11 11.

c) How many channel errors have occurred if the optimal path corresponds to the transmitted sequence?