On the rate loss of multiple description source codes and additive successive refinement codes

The rate loss of a multi-resolution source code (MRSC) describes the difference between the rate needed to achieve distortion D/sub i/ in resolution i and the rate-distortion function R(D/sub i/). We generalize the rate loss definition and bound the rate losses of multiple description source codes (MDSCs) and additive MRSCs (AMRSCs). For a 2-description MDSC (2DSC), the rate loss of description i with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), i=1, 2, where R/sub i/ is the rate of the ith description; the rate loss associated with decoding the two descriptions together to achieve central distortion D/sub 0/ is measured as L/sub 0/=R/sub 1/+R/sub 2/-R(D/sub 0/) or as L/sub 12/=L/sub 1/+L/sub 2/. We show that given an arbitrary source with variance /spl sigma//sup 2/, there exists a 2DSC with L/sub 1//spl les/0.5 and (a) L/sub 0//spl les/1 if D/sub 0//spl les/D/sub 1/+D/sub 2/-/spl sigma//sup 2/, (b) L/sub 12//spl les/1 if 1/D/sub 0//spl les/1/D/sub 1/+1/D/sub 2/-1//spl sigma//sup 2/, (c) L/sub 0//spl les/L/sub G0/+1.5 and L/sub 12//spl les/L/sub G12/+1 otherwise, where L/sub G0/ and L/sub G12/ are the joint rate losses of a normal (0, /spl sigma//sup 2/) source. An AMRSC is an MRSC with the kth-resolution reconstruction equal to the sum of the first k side reproductions of an MDSC. We obtain one bound on the rate loss of an AMRSC.