Improved bounds for the rate loss of multi-resolution source codes

In this paper, we present new bounds for the rate loss of multi-resolution source codes. Consider an M-resolution code with ith-resolution rate and distortion R_i and D_i. The ith-resolution rate loss, defined as L_i=R_i-R(D_i), describes the performance degradation of the multi-resolution code compared to the best single-resolution code with the same distortion. For 2-resolution codes, there are three scenarios of particular interest: (i) both resolutions are equally important; (ii) the rate loss at the first resolution is 0; (iii) the rate loss at the second resolution is 0. Lastras and Berger (see IEEE Trans. Inform. Theory, vol.47, no.3, p.918-26, March 2001) give constant upper bounds for the rate loss of an arbitrary i.i.d. source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D₂→0. In this paper, we: (a) prove that L₂ ⩽1.1610 for all D₂<D₁ in scenario (iii); (b) tighten the Lastras-Berger bound from L₁⩽1 to L₁⩽0.7250 in scenario (ii); (c) tighten the Lastras-Berger bound from 0.5 to 0.3801 in scenario (i); and (d) generalize the bound for scenario () to M-resolution codes