Turbo Interleaving inside the cdma2000 and W-CDMA Mobile Communication Systems: A Tutorial

Fabio G. Guerrero* Electrical and Electronics Engineering School, Universidad del Valle, Cali, Colombia (South America). Ciudad Universitaria Meléndez, Calle 13 100-00, Edificio 355, Oficina 205, Cali, Colombia Phone: (572) 3392140 ext 109; Fax: (572) 3392140 ext 112 e-mail: fguerrer@univalle.edu.co

Maribell Sacanamboy Department of Computer Science Engineering, Universidad Javeriana, Cali, Colombia (South America). Calle 18 No. 118-250 Cali, Colombia Phone: (572) 321 8200 e-mail: msacanamboy@puj.edu.co

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Abstract In this paper a discussion of the detailed operation of the interleavers used by the turbo codes defined on the telecommunications standards cdma2000 (3GPP2 C.S0024-B V2.0) and W-CDMA (3GPP TS 25.212 V7.4.0) is presented. Differences in the approach used by each turbo interleaver as well as dispersion analysis and frequency analysis are also discussed. Two examples are presented to illustrate the complete interleaving process defined by each standard. These two interleaving approaches are also representative for other communications standards.

Keywords: Turbo coding, cdma2000, W-CDMA, 3G, interleaving, digital communications.

1. Introduction Near one decade ago the IMT2000 initiative of the International Telecommunication Union identified five base station-mobile station air interfaces for the third-generation mobile communications systems (3G). It seems clear at the present however that the two technologies that will be dominating the global market of third generation mobile communications systems are cdma2000 and W-CDMA [1].
   The salient feature of third generation mobile communications systems is its high capacity for transmitting information over the system data channels. By 1997 IMT2000 defined in Recommendation ITU-R M.1225 test data rates of 2048 kbit/s, 144 kbit/s and 64 kbit/s for indoors, pedestrian and vehicular traffic respectively [2] for purposes of evaluating the third-generation technologies. As expected, the continuing evolution of mobile technologies has left behind these values with much higher speeds. For instance, the Ultra Mobile BroadbandTM (UMBTM) air interface specification [3] is intended to deliver downlink and uplink data rates of 288 Mbit/s and 75 Mbit/s respectively using a bandwidth of 20 MHz.
   To offer these high data rates with access terminals increasingly both small and functional it is imperative to work at the limit of efficiency in data transmission. As it is well known in 1948 C. E. Shannon proved that the fundamental limit of digital transmission on channels with white noise is given by the classic channel capacity formula C = W log2 (1 + S / N), where C is the capacity in bit/s, W is the channel bandwidth in Hz, and S/N is the signal to noise ratio at the receiver.
   However, finding an error correction system able to achieve this limit meant extensive research for several decades. After more than forty years of research the concept of turbo coding developed by Claude Berrou and Alain Glavieux [4] finally proved that it was possible to reach the limit of channel capacity with an encoding scheme that could be constructed in practice. While turbo coding is not the only technique known to be able to attain the channel capacity limit [5] it is certainly the most commonly used channel coding technique for data channels in contemporary mobile communications systems.
   According to the inventors the turbo coding principle was born from the experimentation with the feedback concept applied to the error correcting problem using convolutional codes [6]. At the core of a turbo coding system there is a fundamental constitutive element called interleaver. An interleaver is a system that changes the positions of input data according to an established position permutation algorithm. Inside the turbo coding process the function of the interleaving block is to help in providing codes vectors with the highest possible level of randomness (ideally, independent vectors) [7] so that the resulting code resembles as close as possible the concept of random coding used by C . E. Shannon in [8] to prove the channel capacity theorem. Therefore the interleaver is a fundamental element for the performance of a turbo code [9].
   The understanding of interleaving is a subject of high interest to the specification of physical layers for both wired and wireless transmission technologies. The aim of this article is to show in detail how the turbo interleavers defined in the cdma2000 EV-DO Revision B (3GPP2 C.S0024-B V2.0) [10] and W-CDMA (3GPP TS 25.212 V7.6.0) [11] standards work, what are their main characteristics, and what are the design principles used by each one. This article has been written with a tutorial approach in mind. The article is organized as follows: Secti

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