Consider the rate R = 1/2, memory m = 2 encoding matrix G(D) = (1 + D + D 2 1 + D 2 ). a) Draw the length ` = 4 trellis. b) Suppose that the encoder is used to communicate over a BSC with crossover...

Consider the rate R = 1/2, memory m = 2 encoding matrix G(D) = (1 + D + D²
1 + D²
).

a) Draw the length ` = 4 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 = 11 11 00 11 01 11.

c) Suppose that the information sequence is u = 1011. How many channel errors are corrected in (b)?