The analysis and design of windowed Fourier frame based multiple description source coding schemes

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, although this number can be reduced to three or two by using time-shift or frequency-shift division schemes. The encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index. The distortion on each channel is analyzed using the Zak transform. For the optimal windows, explicit representation formulas are obtained and nonlocalization results are proved. Asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two