# All sources are nearly successively refinable

## Abstract

Given an achievable quadruple (R1, R2, D1, D2) for progressive transmission, the rate loss at step i is defined as Li = Ri - R(Di). Let D1 and D2 be any two desired distortion levels (D2 < D1). It is shown that for an i.i.d. source and for squared error, an achievable quadruple can be found for which Li ≤ 1/2 bit/sample (a similar statement is proved for situations in which more than two steps are required). Moreover, an achievable quadruple can be found with L2 arbitrarily small and L1 ≤ 1/2 bit/sample if D2 is small enough. If an information-efficient description at D1 is required (i.e., L1 = 0), then there exists an achievable quadruple with L2 ≤ 1 bit/sample. The results are independent of both the source and the particular D1, D2 requirements and extend to any difference distortion measure. The techniques employed parallel Zamir's bounding of the rate loss in the Wyner-Ziv problem. Bounds for the rate loss in other multiterminal source coding problems also are given.