| With the rapid development and wide deployment of M2M (Machine to Machine), Mesh, Ad-hoc and other types of decentralized random wireless communication systems, there are more demands on powerful FEC (Forward Error Correction Codes) with short length recently. Due to its error correction(EC) capability, Turbo codes with short length has been applied to a variety of communication protocols. Turbo codes can be modified to obtain CTC(Convolutional Turbo Codes) which is a type of 4-ary Turbo codes with short length. CTC has been applied widely because of its error correction capability.In order to evaluate the theoretical performance of the Turbo codes rapidly in engineering and scientific research, we can utilize the distance spectrum of Turbo codes to obtain the theoretical performance. It is the main content of this paper to analyze the theoretical performance of multi-ary Turbo codes based on distance spectrum.The introduction of this paper presents the background, significance,domestic and foreign research status and the main research content. In the second part of this paper, the theoretical performance analysis algorithm of tail-biting (TB) binary and duo-binary RSC codes are proposed. In this part, we first review the FAST algorithm, and then modify the FAST algorithm to calculate the distance spectrum (DS) of the duo-binary RSC code. Union bound is calculated based on the distance spectrum. The analysis on the error correction performances of RSC and duo-binary RSC are verified by Monte Carlo simulations, and the results show the analysis greatly matches the simulation results.In the third part, the theoretical performance analysis of Turbo codes and CTC is proposed. Firstly, the encoding and decoding structures of TB Turbo codes and CTC are reviewed. Then the DS calculation of Turbo codes and 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 Turbo codes and CTC can be analyzed on the base of union bound and pairwise error probability (PEP) techniques. Finally, the BEP analyses of Turbo codes and CTC are verified by Monte Carlo simulations. Both the analyses of simulation and theoretical performance curves show that CTC outperforms Turbo codes.In the forth section, the performance analysis is applied to serial concatenated convolutional code and hybrid concatenated convolutional code.The modified FAST algorithm is used to derive the distance spectrum of component encoders of binary and duo-binary SCCC and HCCC, and then the DS calculation of binary and duo-binary SCCC and HCCC with dual TB technique under the concept of uniform interleaver is presented. The methods to calculate BEP and DS are verified by simulations. Likewise, the duo-binary SCCC and HCCC codes perform better than their binary coding. |
