Soliton distribution


A soliton distribution is a type of discrete probability distribution that arises in the theory of erasure correcting codes, which use information redundancy to compensate for transmission errors manifesting as missing data. A paper by Luby introduced two forms of such distributions, the ideal soliton distribution and the robust soliton distribution.

Ideal distribution

The ideal soliton distribution is a probability distribution on the integers from 1 to K, where K is the single parameter of the distribution. The probability mass function is given by

Robust distribution

The robust form of distribution is defined by adding an extra set of values to the elements of mass function of the ideal soliton distribution and then standardising so that the values add up to 1. The extra set of values, t, are defined in terms of an additional real-valued parameter δ and c,. Define R as R=c ln. Then the values added to p, before the final standardisation, are
While the ideal soliton distribution has a mode at 2, the effect of the extra component in the robust distribution is to add an additional spike at the value M.