Improved bounds for the rate loss of multiresolution source codes

We present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering an M-resolution code, the rate loss at the ith resolution with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), where R/sub i/ is the rate achievable by the MRSC at stage i. This rate loss describes the performance degradation of the MRSC compared to the best single-resolution code with the same distortion. For two-resolution source codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (L/sub 1/=0); (iii) when the rate loss at the second resolution is 0 (L/sub 2/=0). The work of Lastras and Berger (see ibid., vol.47, p.918-26, Mar. 2001) gives constant upper bounds for the rate loss of an arbitrary memoryless source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D/sub 2/ approaches 0. We focus on the squared error distortion measure and (a) prove that for scenario (iii) L/sub 1/<1.1610 for all D/sub 2/