Gallager codes for CDMA applications

Abstract

In this thesis, we develop a new coding system for direct sequence code-division multiple access (DS-CDMA) that supports more multiple users than many previously reported DS-CDMA systems. The most important distinctive feature of this new approach is the use of powerful short frame Gallager codes for data error protection. These codes combine strong protection against multiple access interference (MAI) and channel noise with small data delays. This combination makes these Gallager codes an excellent choice as an error-protecting scheme in speech-oriented CDMA applications. We investigate the theoretical performance of Gallager codes with maximum-likelihood decoder and derive new block error probability bounds for short frame Gallager codes. We show that these bounds are smaller than block error probability bounds for many orthogonal and superorthogonal convolutional codes that were previously suggested for similar applications. We propose a new construction for Gallager codes that results in a significant performance improvement for short frame Gallager codes and hence makes them strong candidates for CDMA applications. We discuss low complexity iterative decoding algorithms (suboptimal a-posteriori probability (APP) algorithms) for Gallager codes. We show that the decoding complexity of Gallager codes obtained in the proposed construction is lower than the decoding complexity of turbo codes and other Gallager code constructions, a feature that leads to implementation of fast software-oriented decoders for Gallager codes. We also investigate decoder hardware implementation issues that exploit inherent parallelism of the decoding algorithm. We present simulation results for Gallager codes in additive white Gaussian noise (AWGN) and fading channels. We show that the strong performance of Gallager codes in AWGN channels successfully combats multiple access interference in CDMA systems. Gallager codes also exhibit good performance in fading channels making them particularly suitable for mobile environment. We conclude that Gallager codes are strong candidates for wireless CDMA systems that are emerging recently as a communication system of choice for the rapidly developing PCS market.