Tolga M. Duman

A Turbo Codes and Turbo Coded Modulation Systems: Analysis and Performance Bounds

May 15, 1998
2:00 PM
422 Snell Building

Abstract

The turbo coding technique, which was introduced in 1993, is nothing but a way of concatenating two simple convolutional codes in parallel to obtain an overall powerful code. This simple scheme offers an exceptional performance at very low signal to noise ratios. Although turbo codes have initially been proposed as parallel concatenation of two convolutional codes, other code concatenation methods such as serial or hybrid concatenation have also been developed. Furthermore, for applications where bandwidth is scarce, turbo codes can be used in conjunction with a coded modulation scheme to obtain ``turbo coded modulation'' as an alternative to trellis coded modulation or multi-level coding. There are various potential applications of the turbo coding principle in a number of areas such as deep-space communications, wireless data communications and magnetic recording channels.

In this dissertation, we study a number of important issues to provide a better understanding of turbo codes and turbo coded modulation systems. We deal with four main problems. We first study optimal power allocation for standard turbo codes. We describe a general power allocation rule based on a simple example, and show that considerable performance improvement is possible without increasing the decoding complexity or delay requirements of the system. We then derive a new upper bound on the bit error probability of standard turbo codes by using the Gallager bound instead of the usual union bound. This bound allows us to closely predict the performance of turbo codes for a range of signal to noise ratios at which the union bound diverges. The rest of the dissertation deals with turbo coded modulation systems. We develop a methodology to apply union bounds for the generic turbo coded modulation system for AWGN channels. We describe the methodology by studying a specific system, however, generalization of this technique to other systems is straightforward. In the last part of the dissertation, we extend these performance bounds to fading channels. Besides being the only methods of theoretical performance analysis for turbo coded modulation systems, these methods provide us with some very promising future research directions.

Thesis Committee:
Prof. M. Salehi (advisor)
Prof. D. Brady
Prof. J.G. Proakis
Prof. M. Stojanovic