Distance spectrum calculation method for double binary turbo codes

With the rapid development and deployment of M2M, Mesh, ad-hoc and other types of decentralized random wireless communication systems, there are more demands on powerful forward error correction codes (FEC) with short length recently. Due to its error correction (EC) capability, convolutional TUrbo code (CTC) with short length has been applied widely. In this paper, the distance spectrum (DS), which can catch the EC performance efficiently, is studied for CTCs. Firstly the DS of tail-biting (TB) duo-binary recursive systematic convolutional codes (RSC) is calculated by the modified FAST algorithm, and then the DS calculation of CTC with dual TB technique under the concept of uniform interleaver is presented. Given the DS results, the bit error probability (BEP) performance of the CTC can be analyzed on the base of union bound and pairwise error probability (PEP) techniques. The analysis on the EC performance of CTC is verified by Monte Carlo simulations, and the results show the analysis greatly matches the simulation results.