Asymptotical Analysis of Several Multiple Description Scenarios with L≥ 3 Descriptions

This work compares theoretically the performance of several representative practical multiple description (MD) frameworks with L ≥ 3 symmetric descriptions. The first scenario is the classic unequal erasure protection (UEP) scheme using a successively refinable code (SRC) and Reed-Solomon codes. The second scenario is an improvement upon UEP by applying domain partitioning and permuted Reed-Solomon codes. The third scenario uses a finer partitioning and erasure correction via repetition codes. Additionally, the MD lattice vector quantizer and another recent MD scheme are considered in the comparison. The aforementioned MD schemes are compared in terms of the expected squared error asymptotically achievable as the rate R of a description approaches ∞, assuming independent description losses. Our analysis reveals that the improvement of the second scenario upon the first one when R → ∞ can reach up to 1.68 dB, but it approaches 0 as the description loss rate p goes to 0 and L approaches ∞. Additionally, we find that the first two schemes outperform the third one with an unbounded gain when R → ∞, as p→ 0 or L → ∞. Further, we show that the first three scenarios achieve unbounded improvements over the other two as R → ∞ and p → 0. On the other hand, we point out that some of the results of our asymptotic analysis rely on strong assumptions and therefore an experimental validation is needed before applying them to practical situations.