Supplementary document for the paper “ Real - Time Streaming of Gauss - Markov Sources over Sliding Window Burst - Erasure Channels ” submitted to ISIT 2013

First note that for any ρ ∈ (0, 1) and x ∈ R the function f (x) = x − 1 2 log ρ 2m 2 2x + 2πe(1 − ρ 2m) (1) is an monotonically increasing function with respect to x, because f ′ (x) = 2πe(1 − ρ 2m) ρ 2m 2 2x + 2πe(1 − ρ 2m) > 0. (2) By applying Shannon's EPI we have. h(s b |f a) ≥ 1 2 log ρ 2m 2 2h(sa|fa) + 2πe(1 − ρ 2m) (3) and thus, h(s a |f a) − h(s b |f a) ≤ h(s a |f a) − 1 2 log ρ 2m 2 2h(sa|fa) + 2πe(1 − ρ 2m) (4) ≤ 1 2 log(2πer) − 1 2 log ρ 2m 2πer + 2πe(1 − ρ 2m) (5) = 1 2 log r 1 − (1 − r)ρ 2m (6) where (5) follows from the assumption that h(s a |f a) ≤ 1 2 log(ρ 2m 2πer) and the monotonicity property of f (x). Define p = L + B − 1 and consider a periodic erasure channel with period p where in kth period only the codewords f kp+L−B (k−1)p+L+1 are available and the rest of the codewords in that period is erased by the channel. Fig. 1 shows the kth period of the source model. Now consider the following inequality.