Interleavers for turbo codes using permutation polynomials over integer rings

A class of deterministic interleavers for turbo codes (TCs) based on permutation polynomials over Z_N is introduced. The main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code. Moreover, since the interleaver can be generated by a few simple computations, storage of the interleaver tables can be avoided. By using the permutation polynomial-based interleavers, the design of the interleavers reduces to the selection of the coefficients of the polynomials. It is observed that the performance of the TCs using these permutation polynomial-based interleavers is usually dominated by a subset of input weight 2m error events. The minimum distance and its multiplicity (or the first few spectrum lines) of this subset are used as design criterion to select good permutation polynomials. A simple method to enumerate these error events for small m is presented. Searches for good interleavers are performed. The decoding performance of these interleavers is close to S-random interleavers for long frame sizes. For short frame sizes, the new interleavers outperform S-random interleavers.