Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Convergence Analysis of Turbo Decoding of Serially Concatenated Block Codes and Product Codes Amir Krause | EURASIP Journal on Applied Signal Processing 2005 6 795-807 2005 Hindawi Publishing Corporation Convergence Analysis of Turbo Decoding of Serially Concatenated Block Codes and Product Codes Amir Krause Department of Electrical Engineering-Systems Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Email amirkrause@ Assaf Sella Department of Electrical Engineering-Systems Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Email asella@ Yair Be ery Department of Electrical Engineering-Systems Tel-Aviv University Ramat Aviv 69978 Tel-Aviv Israel Email ybeery@ Received 30 September 2003 Revised 16 August 2004 The geometric interpretation of turbo decoding has founded a framework and provided tools for the analysis of parallel-concatenated codes decoding. In this paper we extend this analytical basis for the decoding of serially concatenated codes and focus on serially concatenated product codes SCPC . product codes with checks on checks . For this case at least one of the component . rows columns decoders should calculate the extrinsic information not only for the information bits but also for the check bits. We refer to such a component decoder as a serial decoding module SDM . We extend the framework accordingly and derive the update equations for a general turbo decoder of SCPC and the expressions for the main analysis tools the Jacobian and stability matrices. We explore the stability of the SDM. Specifically for high SNR we prove that the maximal eigenvalue of the SDM s stability matrix approaches d - 1 where d is the minimum Hamming distance of the component code. Hence for practical codes the SDM is unstable. Further we analyze the two turbo decoding schemes proposed by Benedetto and Pyndiah by deriving the corresponding update equations and by demonstrating the structure of their stability matrices for the repetition code and an SCPC code with 2 X 2 information bits. Simulation results for the Hamming 7 4 3 1 2 and
