Improved low complexity hybrid turbo codes and union bound analysis

Turbo convolutional codes (TCC) are excellent error correcting codes for wireless channels. However, TCC decoders require large decoding complexity. Moreover, complexity of TCC decoder does not reduce even if puncturing is used to change the coding rate. Modified turbo codes require lower decoding complexity than TCC as they use multiple concatenations of simple block codes and convolutional codes. Recently, a class of modified turbo codes called low complexity hybrid turbo codes (LCHTC) and improved low complexity hybrid turbo codes (ILCHTC) have been proposed. It has been shown that LCHTC and ILCHTC achieve bit error rate (BER) which is comparable to TCC and have much lower decoding complexity. Simulation results show that BER performance of ILCHTC is better than that of LCHTC. Rate-1/3 ILCHTC achieve BER of 10^-5 at bit energy-to-noise ratio (E_b/N₀) of 1.9 dB, which is 0.4 dB higher than E_b/N₀ for TCC adopted by third generation partnership project (3GPP). Moreover, ILCHTC and LCHTC decoders require half the number of computations as compared to those required for TCC decoder. In this study, union-bound analysis of ILCHTC is presented to investigate BER performance<;10^-6. For large interleaver lengths, analysis of theoretical union bound requires numerous computations. Therefore approximate analysis of union bound is derived from theoretical union bound. It is shown that the analysis of approximate union bound achieves reasonable accuracy. Moreover, approximate union bound can be evaluated with significantly less computational complexity than the theoretical union bound.