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 (Eb/N0) of 1.9 dB, which is 0.4 dB higher than Eb/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.

Low complexity modified turbo codes (MTC) offer bit error rate performance close to Shannon's limit with significantly reduced decoding complexity. However, since interleavers used in turbo codes interleave bit positions in one-dimensional (1D) array, they cannot be used for MTC which encode information bits arranged in 2D array. Moreover, MTC use several interleavers which increase the memory requirement to store permutation patterns. Objective of this study is to design two-stage interleaver for MTC with low memory requirement, large values of column spreading factor and dispersion in the interleaved pattern. Expressions have been derived for limits on maximum values of spreading factor and dispersion for 2D information array. Simulation results show superior performance of MTC with two-stage interleavers than that with random interleavers at high bit energy to noise ratio. Moreover, analysis shows that two-stage interleaver requires 50% less memory storage than random interleaver. Proposed interleaver can also be used for turbo codes in which 1D information array is being used.

This paper proposes a new class of Turbo type codes referred to as Improved Low Complexity Hybrid Turbo Codes (ILCHTC). For low Bit Energy to Noise Ratio (Eb/No)ILCHTC shows better convergence of errors than that of Low Complexity Hybrid Turbo Code (LCHTC). Simulation results show that ILCHTC achieves Bit Error Rate (BER) of 10-5at Eb/Noof 1.9 dB, which is 0.4 dB more than that for Turbo Convolutional Codes (TCC). Analysis of ILCHTC and LCHTC decoders show that the number of computations reduce by a factor of two as compared to the computations of TCC decoder.