THE HADAMARD-TRANSFORM - A TOOL FOR INDEX ASSIGNMENT

We show that the channel distortion for maximum-entropy encoders, due to noise on a binary-symmetric channel, is minimized if the vector qua ntizer can be expressed as a linear transform of a hypercube, The inde x assignment problem is regarded as a problem of linearizing the vecto r quantizer, We define classes of index assignments with related prope rties, within which the best index assignment is found by sorting, not searching, Two powerful algorithms for assigning indices to the codev ectors of nonredundant coding systems are presented, One algorithm fin ds the optimal solution in terms of linearity, whereas the other finds a very good, but suboptimal, solution in a very short time.