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: Iterative Decoding of Concatenated Codes: A Tutorial Phillip A. Regalia | EURASIP Journal on Applied Signal Processing 2005 6 762-774 2005 Phillip A. Regalia Iterative Decoding of Concatenated Codes A Tutorial Phillip A. Regalia Departement Communications Images et Traitement de l Information Institut National des Telecommunications 91011 Evry Cedex France Department of Electrical Engineering and Computer Science Catholic University of America Washington DC 20064 USA Email phillip. regalia@ Received 29 September 2003 Revised 1 June 2004 The turbo decoding algorithm of a decade ago constituted a milestone in error-correction coding for digital communications and has inspired extensions to generalized receiver topologies including turbo equalization turbo synchronization and turbo CDMA among others. Despite an accrued understanding of iterative decoding over the years the turbo principle remains elusive to master analytically thereby inciting interest from researchers outside the communications domain. In this spirit we develop a tutorial presentation of iterative decoding for parallel and serial concatenated codes in terms hopefully accessible to a broader audience. We motivate iterative decoding as a computationally tractable attempt to approach maximum-likelihood decoding and characterize fixed points in terms of a consensus property between constituent decoders. We review how the decoding algorithm for both parallel and serial concatenated codes coincides with an alternating projection algorithm which allows one to identify conditions under which the algorithm indeed converges to a maximum-likelihood solution in terms of particular likelihood functions factoring into the product of their marginals. The presentation emphasizes a common framework applicable to both parallel and serial concatenated codes. Keywords and phrases iterative decoding maximum-likelihood decoding information geometry belief propagation. 1. INTRODUCTION The advent of the turbo decoding algorithm for parallel concatenated codes a decade ago 1 ranks among
