On robustness of hybrid digital analog source-channel coding with bandwidth mismatch

The problem of lossy transmission of a Gaussian source over an AWGN bandwidth-mismatched broadcast channel with three receivers is addressed. The tradeoff between the distortion levels at the good and the bad receivers is tackled when the distortion at the median receiver is required to be optimal. The problem was proposed by Tian and Shamai (2008), who subsequently found in the work of Tian and Shamai (2011) remarkable achievability results for bandwidth expansion ratios κ which are integers or unit fractions, i.e., κ = 2, 1/3, 1/5, etc. Their result is extended here to all κ ≥ 2 and κ ≤ 1/2 by generalizing the hybrid digital/analog (HDA) scheme in the work of Wilson et al. (2010) to the case of bandwidth mismatch. Finally, novel schemes are proposed for 1/2 = κ ≤ 1 and 1 <; κ ≤ 2 achieving nontrivial tradeoffs.