Consider the rate R = 1/2, memory m = 2 convolutional encoding matrix G(D) = (1 + D + D 2 1 + D 2 ). a) Draw the complete code tree for length ` = 3 and tail m = 2. b) Find the Fano metrics for a BSC...

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

a) Draw the complete code tree for length ` = 3 and tail m = 2.

b) Find the Fano metrics for a BSC with crossover probability = 0.045, that is, R = R0 = 1/2.

c) Use the stack algorithm to decode the received sequence r = 00 01 10 00 00. How many computations are needed?

d) Repeat (c) with the Fano algorithm with threshold increment ∆ = 4.

e) Are the decisions in (c) and (d) maximum-likelihood?