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Unformatted text preview: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 3, MAY 1998 909 Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding Sergio Benedetto, Fellow, IEEE , Dariush Divsalar, Fellow, IEEE , Guido Montorsi, Member, IEEE , and Fabrizio Pollara, Member, IEEE Abstract— A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h I interleavers. We obtain upper bounds to the average maximum- likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding al- gorithm. Throughout the paper, extensive comparisons with par- allel concatenated convolutional codes known as “turbo codes” are performed, showing that the new scheme can offer superior performance. Index Terms— Concatenated codes, iterative decoding, serial concatenation, turbo codes. NOMENCLATURE CC Constituent Code. PCCC Parallel Concatenated Convolutional Code. PCBC Parallel Concatenated Block Code. SCC Serially Concatenated Code. SCBC Serially Concatenated Block Code. SCCC Serially Concatenated Convolutional Code. ML Maximum Likelihood. IOWEF Input–Output Weight-Enumerating Function. CWEF Conditional Weight-Enumerating Function. SISO Soft Input Soft Output module. SW-SISO Sliding Window—Soft Input Soft Output module. LLR Log-Likelihood Ratio. MAP Maximum a posteriori . Manuscript received July 26, 1996; revised November 1, 1997. This work was supported in part by NATO under Research Grant CRG 951208. The work of S. Benedetto and G. Montorsi was supported by Italian National Research Council (CNR) under “Progetto Finalizzato Trasporti (Prometheus),” by MURST (Progetto 40% “Comunicazioni con Mezzi Mobili”), and by Qualcomm. The research described in this paper was performed in part at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, under Contract with the National Aeronautics and Space Administration (NASA). The material in this paper was presented in part at the IEEE Inter- national Symposium on Information Theory, Ulm, Germany, June 29–July 4, 1997. S. Benedetto and G. Montorsi are with Dipartimento di Elettronica, Politec- nico di Torino, Italy. D. Divsalar and F. Pollara are with Jet Propulsion Laboratory, Pasadena, CA 91109 USA....
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