We suggest a theory for a deformable and sliding charge density wave (CDW) in the Hall bar geometry for the quantum limit when the carriers in remnant small pockets are concentrated at lowest Landau levels (LL) forming a fractionally ($ u<1$) filled quantum Hall state. The gigantic polarizability of the CDW allows for a strong redistribution of electronic densities up to a complete charge segregation when all carriers occupy, with the maximum filling, a fraction $ u$ of the chain length - thus forming the integer quantum Hall state, while leaving the fraction $(1- u)$ of the chain length unoccupied. The electric field in charged regions easily exceeds the pinning threshold of the CDW, then the depinning propagates into the nominally pinned central region via sharp domain walls. Resulting picture is that of compensated collective and normal pulsing counter-currents driven by the Hall voltage. This scenario is illustrated by numerical modeling for nonstationary distributions of the current and the electric field. This picture can interpret experiments in mesa-junctions showing depinning by the Hall voltage and the generation of voltage-controlled high frequency oscillations (Yu.I. Latyshev, P. Monceau, A.A. Sinchenko, et al, presented at ECRYS-2011, unpublished).
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