Abstract alphabet source coding theorem revisited: redundancy analysis

The problem of investigating how close the performance of the best nth order block code can be to the rate distortion limit is known as the redundancy problem of lossy source coding. The difference between the performance of a block code and the rate distortion limit is called the redundancy of the block code. We investigate the redundancy of nth order block coding in the case of abstract source and reproduction alphabets. We obtain results similar to the positive redundancy results of Zhang, Yang and Wei (see IEEE Trans. Inform. Theory, vol.43, no.1, p.71-91, 1997) on lossy source coding with finite alphabets.