Consider the rate R = 1/3 convolutional code with encoding matrix G(D) = XXXXXXXXXXD + D 2 1 + D 2 ) realized in controller canonical form. Prove the Costello bound for periodically time-varying, rate...

Consider the rate R = 1/3 convolutional code with encoding matrix G(D) = (1 1 + D + D²
1 + D²
) realized in controller canonical form.

Prove the Costello bound for periodically time-varying, rate R = b/c convolutional codes with polynomial, systematic generator matrices.