Holographic coding by Walsh–Hadamard transformation of randomized and permuted data

Holographic coding has the very appealing property of obtaining partial information on the data from any part of the coded information. In the paper, holographic coding schemes based on the Walsh–Hadamard orthogonal codes are studied. It is proposed to randomize the data so that the coefficient of the Walsh–Hadamard code would be approximately uniform and thus ensure, with high probability, a monotonic gain of information. The data are xored with randomly chosen bits from random data that have been stored during a preprocessing stage or pseudorandom data produced by a pseudorandom generator. Statistical properties of the truncated sums of the Inverse Walsh–Hadamard Transformation (IWHT), taking into account the “white-noise nature” and the mentioned above holographic, is considered. Furthermore, an enhancement of the algorithm, based on random permutation and block coding is suggested. The results are compared to the Rate Distortion function and jpeg compression.