Analysis of the Distribution of the Number of Correctable Erasures for Turbo Codes with DRP Interleavers

This paper investigates the maximum likelihood (ML) performance of turbo codes employing dithered relative prime (DRP) interleavers for the erasure channel. The performance is analysed by determining the distribution of correctable erasures based on the weight distribution of the code. A degradation from optimal maximum distance separable (MDS) performance or MDS shortfall is defined and determined for DRP and S-random interleavers. It is shown that the MDS shortfall is less than 4 bits on average for short turbo codes and is reduced to less than 3 bits by using DRP interleavers. The ML decoder error rate performance is determined for the turbo codes and compared to the best known linear code of the same block length and code rate, and also compared to a hypothetical binary MDS code. Given the constraints of turbo codes the DRP interleaver is shown to have good performance and is considerably better than the S-random interleaver turbo code.