On higher order permutors for serially concatenated convolutional codes

A new parameter set for designing permutors is introduced. It is called the set of higher order separations and can be considered as a generalization of the well-known symbol separation (spreading factor). The respective permutor is called a higher order permutor and we show how such a permutor can be constructed. For a second-order permutor in a serially concatenated convolutional encoding scheme we give a lower bound on the minimum distance of the resulting overall code. The integers that determine the sufficiently large separations, i.e., the smallest separations for which the distance properties can be guaranteed, are derived from the active distances of the convolutional component encoders. Additionally, a growth rate of the minimum distance like O((d_free ^o)^{lfloorrho/2rfloor+1}) is proved for serially concatenated convolutional encoders with permutors having large separations of order rho