don't you sometimes just

R_A[k] |_{n_info} = E[ A[n] A[n-k]^* ]

= E[ A[n] A[n-k]^* | A[n] = 0 ] Pr[ A[n] = 0 ]
+ E[ A[n] A[n-k]^* | A[n] = 1 ] Pr[ A[n] = 1 ]

= E[ (-V)^2 delta[k] - V^2 delta[k-1] ] (1/2)
+ [ V^2 delta[k] - V^2 delta[k-1] ] (1/2)

= V^2 delta[k] - V^2 delta[k-1]