  We provide a method for designing an optimal index assignment for scalar
K-description coding. The method stems from a construction of translated scalar
lattices, which provides a performance advantage by exploiting a so-called
staggered gain. Interestingly, generation of the optimal index assignment is
based on a lattice in K-1 dimensional space. The use of the K-1 dimensional
lattice facilitates analytic insight into the performance and eliminates the
need for a greedy optimization of the index assignment. It is shown that that
the optimal index assignment is not unique. This is illustrated for the
two-description case, where a periodic index assignment is selected from
possible optimal assignments and described in detail. The new index assignment
is applied to design of a K-description quantizer, which is found to outperform
a reference K-description quantizer at high rates. The performance advantage
due to the staggered gain increases with increasing redundancy among the
descriptions.
