turbo2c - William E. Ryan New Mexico State University Box...

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A Turbo Code Tutorial William E. Ryan New Mexico State University Box 30001 Dept. 3-O, Las Cruces, NM 88003 wryan@nmsu.edu Abstract | We give a tutorial exposition of turbo codes and the associated algorithms. Included are a simple derivation for the performance of turbo codes, and a straightforward presentation of the iterative de- coding algorithm. The derivations of both the per- formance estimate and the modi¯ed BCJR decoding algorithm are novel. The treatment is intended to be a launching point for further study in the ¯eld and, signi¯cantly, to provide su±cient information for the design of computer simulations. I. Introduction Turbo codes, ¯rst presented to the coding community in 1993 [1], represent the most important breakthrough in coding since Ungerboeck introduced trellis codes in 1982 [2]. Whereas Ungerboeck's work eventually led to coded modulation schemes capable of operation near capacity on bandlimited channels [3], the original turbo codes of- fer near-capacity performance for deep space and satellite channels. The invention of turbo codes involved reviv- ing some dormant concepts and algorithms, and combining them with some clever new ideas. Because the principles surrounding turbo codes are both uncommon and novel, it has been di±cult for the initiate to enter into the study of these codes. Complicating matters further is the fact that there exist now numerous papers on the topic so that there is no clear place to begin study of these codes. In this paper, we hope to address this problem by in- cluding in one paper an introduction to the study of turbo codes. We give a detailed description of the encoder and present a simple derivation of its performance in additive white Gaussian noise (AWGN). Particularly di±cult for the novice has been the understanding and simulation of the iterative decoding algorithm, and so we give a thorough description of the algorithm here. This paper borrows from some of the most prominent publications in the ¯eld [4]- [9], sometimes adding details that were omitted in those works. However, the general presentation and some of the derivations are novel. Our goal is a self-contained, simple introduction to turbo codes for those already knowledge- able in the ¯elds of algebraic and trellis codes. The paper is organized as follows. In the next section we present the structure of the encoder, which leads to an esti- mate of its performance. The subsequent section then de- scribes the iterative algorithm used to decode these codes. The treatment in each of these sections is meant to be su±ciently detailed so that one may with reasonable ease design a computer simulation of the encoder and decoder. II. The Encoder and Its Performance Fig. 1 depicts a standard turbo encoder. As seen in the ¯gure, a turbo encoder is consists of two binary rate 1/2 convolutional encoders separated by an N -bit interleaver or permuter, together with an optional puncturing mech- anism. Clearly, without the puncturer, the encoder is rate 1/3, mapping N data bits to 3 N code bits. We observe
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This note was uploaded on 03/20/2012 for the course EEL 6650 taught by Professor Shea during the Spring '12 term at University of Florida.

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turbo2c - William E. Ryan New Mexico State University Box...

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