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VQ Design – Optimality Conditions

                Nearest Neighbor Condition

For a given codebook, C, the optimal regions {Ri: i=1,…,N} satisfy the condition:

                      Ri {x: d(x,yi) d(x,yj);  j}

   That is

                       Q(x)=yi only if d(x,yi) d(x,yj) j

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