On the rate loss of multiple description source codes

The rate loss of a multiresolution 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/). This paper generalizes the rate loss definition to multiple description source codes (MDSCs) and bounds the MDSC rate loss for arbitrary memoryless sources. For a two-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 joint rate loss associated with decoding the two descriptions together to achieve central distortion D/sub 0/ is measured either 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 for any memoryless source with variance /spl sigma//sup 2/, there exists a 2DSC for that source with L/sub 1//spl les/1/2 or L/sub 2//spl les/1/2 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 Gaussian source with variance /spl sigma//sup 2/.