Fixed-slope universal lossy data compression

• Authors: En-hui Yang;Zhen Zhang;T. Berger
• Venue: IEEE Transactions on Information Theory
• Year: 2006

Corresponding to any lossless codeword length function l, three universal lossy data compression schemes are presented: one is with a fixed rate, another is with a fixed distortion, and a third is with a fixed slope. The former two universal lossy data compression schemes are the generalization of Yang-Kieffer's (see ibid., vol.42, no.1, p.239-45, 1995) results to the general case of any lossless codeword length function l, whereas the third is new. In the case of fixed-slope λ>0, our universal lossy data compression scheme works as follows: for any source sequence xn of length n, the encoder first searches for a reproduction sequence yn of length n which minimizes a cost function n-1l(yn)+λρn(xn, yn) over all reproduction sequences of length n, and then encodes xn into the binary codeword of length l(yn) associated with yn via the lossless codeword length function l, where ρn(xn, yn) is the distortion per sample between xn and yn. Under some mild assumptions on the lossless codeword length function l, it is shown that when this fixed-slope data compression scheme is applied to encode a stationary, ergodic source, the resulting encoding rate per sample and the distortion per sample converge with probability one to Rλ and Dλ, respectively, where (Dλ, Rλ) is the point on the rate distortion curve at which the slope of the rate distortion function is -λ. This result holds particularly for the arithmetic codeword length function and Lempel-Ziv codeword length function. The main advantage of this fixed-slope universal lossy data compression scheme over the fixed-rate (fixed-distortion) universal lossy data compression scheme lies in the fact that it converts the encoding problem to a search problem through a trellis and then permits one to use some sequential search algorithms to implement it. Simulation results show that this fixed-slope universal lossy data compression scheme, combined with a suitable search algorithm, is promising