Homework two: source coding theory and practice

Homework two: source coding theory and practice
1. What is the performance if we use the same structured dithered quantization binning scheme for
Wyner-Ziv coding on a non-Gaussian setting X = Y + N , where N is independent of Y , zero mean with
2 ? If we only know the variance of N satisfy a ≤ σ 2 ≤ b, then what are the parameters we
variance σN
2 is random and uniformly distributed over [a, b],
should choose in the quantization scheme? If we know σN
should we change strategy if we still want to minimize the expected distortion? The last question is not
necessarily answered in the lattice code context, and you don’t have to derive an exact answer.
2. Write a “new” achievable region for the multiple description problem by combining EGC coding
scheme and that by Zhang and Berger.
3. Discuss the inclusion relation among the EGC region, the simplified EGC region, Zhang and Berger’s
rate region and the region you give in problem 2.
4. Show the following is true: for any zero mean Gaussian U, V with given covariance matrix, you can
always write U = T0 + T1 and V = T0 + T2 where T0 , T1 , T2 are jointly Gaussian, such that the correlation
coefficient of T1 and T2 is either 1 or -1; T0 is independent of (T1 , T2 ).
5. For the lossless one-helper problem, show the following is an equivalent characterization
R1 ≥ H(X|U ),
R2 ≥ I(Y ; U |X),
R1 + R2 ≥ I(Y ; U ) + H(X|U ),
where U ↔ Y ↔ X.