Analysis On The Convergence Performance Of Turbo Codes With Short And Medium Frame Sizes

Because of the excellent performance, turbo codes have been widely used in many communication systems. In the past 20 years, many scholars have conducted extensive research on turbo code, including simplified decoding algorithms, the convergence analysis of iterative decoding, the design of turbo code, etc. Bit error rate (BER) chart of turbo code can be divided into three regions:the region of low Eb/N0 with negligible iterative BER reduction, the waterfall region and the BER floor region. The performance of BER floor region can be analyzed by using union bound, but the analysis of waterfall region lacks effective method while it is the most widely used. In addition, the complicated decoding complexity and high time latency also limit the application of turbo code.As an engineering tool for the convergence analysis of iterative decoding, the extrinsic information transfer (EXIT) chart is useful to predict the convergence threshold Eb/N0, where the waterfall region occurs in the BER curve of the infinite length turbo codes. But with decoding complexity and high time latency, in the practical communication systems the information length is limited to a small number of bits, e.g.,3G and the 3rd generation partnership project long term evolution (3GPP LTE) communication systems. On the other hand, the finite-length turbo codes have a gentle waterfall in the BER chart with a wide Eb/N0 region, and the convergence threshold is not meaningful in practice. EXIT band chart can be used to analyze the convergence characteristic of the finite length turbo code by simulating the open loop component decoder.The thesis gives a introduction of digital communication system and the history of channel encoding at first, the previous research work and outcome in turbo code, the research significance and the structure. Then, a brief introduction of the fundamental principle of turbo encoding and decoding is given, the BER performance analysis of turbo decoding of 3GPP LTE standard with different simulation parameters and different decoding algorithms is investigated. Next, EXIT band chart is derived for the probabilistic convergence performance of finite length turbo code, and the statistical properties of extrinsic information is included. Subsequently, the iterative decoding trajectories can also be predicted from EXIT band chart. EXIT band chart can be influenced by some factors. The EXIT band chart of different length turbo codes of 3GPP LTE standard are simulated while two bands are tangent, and their BER curves are showed.The asymmetric turbo codes performances are compared with symmetric turbo code. With proper selection of component codes, the asymmetric turbo code can show better performance in both waterfall region and error floor region simultaneously. So, in some cases asymmetric turbo code’s performance is better than symmetric turbo codes. This paper gives the component codes with the EXIT characteristics to design the asymmetric turbo code. The simulation results show the asymmetric turbo codes can perform better BER performance with reduced decoding complexity. Last, EXIT band chart can be used to analyze the decoding probabilistic convergence behavior of P1-NP2-Turbo code which have finite information length.