R. Balan et al., The analysis and design of windowed Fourier frame based multiple description source coding schemes, IEEE INFO T, 46(7), 2000, pp. 2491-2536
In this paper the windowed Fourier encoding-decoding scheme applied to the
multiple description compression problem is analyzed, In the general case,
four window functions are needed to define the encoder and decoder, althoug
h this number can be reduced to three or two by using time-shift or frequen
cy-shift division schemes. The encoding coefficients are next divided into
two groups according to the eveness of either modulation or translation ind
ex. The distortion on each channel is analyzed using the Zak transform. For
the optimal windows, explicit representation formulas are obtained and non
localization results are proved. Asymptotic formulas of the total distortio
n and transmission rate are established and the redundancy is shown to trad
e off between these two.