Turbo codes have been the subject of much research in recent years, producing results very close to the theoretical limit set by Shannon. The codes have been successfully implemented in satellite and video conferencing systems and provision has been made in 3rd generation mobile systems. These codes have not been used for short frame systems due to the delay at the decoder. In this thesis, comprehensive comparisons of the two common decoding algorithms are made, with reference to short frames. The effects of increasing memory size of component codes, frame sizes, utilising puncturing and errors in channel estimation are investigated over AWGN and Rayleigh fading channels. The decoder systems are compared for complexity as well as for equal numbers of iterations. Results show that less complex decoder strategies produce good results for voice quality bit error rates. Investigations are also made into the effects of errors in signal-to-noise ratio estimation at the SOVA turbo decoder, showing this decoding algorithm to be more resilient than Log-MAP decoders in published literature. The decoders are also tested over channels displaying inter-symbol interference. Channels include a time-invariant channel and three ETSI standard time-varying channels simulating indoor, pedestrian and vehicular situations, upgraded for more realistic Doppler effect. To combat these types of channels, a derivative of turbo codes, turbo equalisation is often used. To keep receiver delay to a minimum, decision feedback equalisation is used here. Results show that the combination can produce improvements in decoded results with increasing turbo iterations where ISI is low, but that iterative improvements do not occur under harsh circumstances. The combination produces much superior results compared with codes on their own under even the most extreme circumstances.

Turbo codes are a recently discovered class of error correction codes that achieve near-Shannon limit performance. Because of their complexity and highly parallel nature, turbo-coded applications are well suited for configurable computing. Field-programmable gate arrays (FPGAs), which are the main building blocks of configurable computing machines (CCMs), allow users to design flexible hardware that is optimized for performance, speed, power consumption, and chip-area. This thesis presents the implementation and performance of an improved turbo decoder on a configurable computing platform. The design's performance and throughput are emphasized in light of its algorithmic improvements, and its flexibility is emphasized as it is ported to a newer, more efficient architecture with more hardware resources. Because this decoder will eventually become the error correction component of a software radio, the design must maintain a high data rate, interface easily with other modules, and conserve hardware resources for future research developments. / Master of Science

Error correction codes are a means of including redundancy in a stream of information bits to allow the detection and correction of symbol errors during transmission. The birth of error correction coding showed that Shannon's channel capacity could be achieved when transmitting information through a noisy channel. Turbo codes are a very powerful form of error correction codes that bring the performance of practical coding even closer to Shannon's theoretical specifications. Bit-error-rate (BER) performance and power dissipation are two important measures of performance used to characterize communication systems. Subject to the law of diminishing returns, as the resolution of the analog-to-digital converter (ADC) in the decoder increases, BER improves, but power dissipation increases. The number of decoding iterations has a similar effect on the BER performance and power dissipation of turbo coded systems. This is significant since turbo decoding is typically practiced in a fixed iterative manner, where all transmitted frames go through the same number of iterations. This is not always necessary since certain "good" frames would converge to their final bits within a few iterations, and other "bad" frames never do converge. In this thesis, we investigate the technical feasibility of adapting the resolution of the ADC in the decoder, and the number of decoding iterations, in order to obtain the best trade-off possible between BER performance and power dissipation in a communication system. With the aid of computer-aided simulations, this thesis investigates the performance and practical implementation issues associated with incorporating a variable resolution ADC into the decoder structure of turbo codes. The possibility of further power conservation resulting from reduced decoding computation is also investigated with the use of a recently developed iterative stopping criterion. / Master of Science

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One recent method to approach the capacity of a channel is Turbo Coding. However, a major concern with the implementation of a Turbo Code is the overall complexity and real-time throughput of the digital hardware system. The salient design problem of Turbo Coding is the iterative decoder, which must perform calculations over all possible states of the trellis. Complex computations such as exponentiations, logarithms and division are explored as part of this research to compare the complexity of the traditionally avoided maximum a-posteriori probability (MAP) decoder to that of the more widely accepted and simplified Logarithm based MAP decoder (LOG-MAP). This research considers the fine grained implementation and processing of MAP, LOG-MAP and a hybrid LOG-MAP-Log Likelihood Ratio (LLR) based Turbo Codes on a Xilinx Virtex 4 PGA. Verification of the Turbo Coding system performance is demonstrated on a Xilinx Virtex 4 ML402SX evaluation board with the EDA of the Xilinx System Generator utilizing hardware co-simulation. System throughput and bit error rate (BER) are the performance metrics that are evaluated as part of this research. An efficient system throughput is predicated by the parallel design of the decoder and BER is determined by data frame size, data word length and the number of decoding iterations. Furthermore, traditional and innovative stopping rules are evaluated as part of this research to facilitate the number of iterations required during decoding. / Engineering

No / Software radio and reconfigurable systems represent reconfigurable functionalities of the radio interface. Considering turbo decoding function in battery-powered devices like 3GPP mobile terminals, it would be desirable to choose the optimum decoding algorithm: SOVA in terms of latency, and log-MAP in terms of performance. In this paper it is shown that the two algorithms share common operations, making feasible a reconfigurable SOVA/log-MAP turbo decoder with increased efficiency. Moreover, an improvement in the performance of the reconfigurable architecture is also possible at minimum cost, by scaling the extrinsic information with a common factor. The implementation of the improved reconfigurable decoder within the 3GPP standard is also discussed, considering different scenarios. In each scenario various frame lengths are evaluated, while the four possible service classes are applied. In the case of AWGN channels, the optimum algorithm is proposed according to the desired quality of service of each class, which is determined from latency and performance constraints. Our analysis shows the potential utility of the reconfigurable decoder, since there is an optimum algorithm for most scenarios.

Turbo codes are a class of forward error correction (FEC) codes that offer energy efficiencies close to the limits predicted by information theory. The features of turbo codes include parallel code concatenation, recursive convolutional encoding, nonuniform interleaving, and an associated iterative decoding algorithm. Although the iterative decoding algorithm has been primarily used for the decoding of turbo codes, it represents a solution to a more general class of estimation problems that can be described as follows: a data set directly or indirectly drives the state transitions of two or more Markov processes; the output of one or more of the Markov processes is observed through noise; based on the observations, the original data set is estimated. This dissertation specifically describes the process of encoding and decoding turbo codes. In addition, a more general discussion of iterative decoding is presented. Then, several new applications of iterative decoding are proposed and investigated through computer simulation. The new applications solve two categories of problems: the detection of turbo codes over time-varying channels, and the distributed detection of coded multiple-access signals. Because turbo codes operate at low signal-to-noise ratios, the process of phase estimation and tracking becomes difficult to perform. Additionally, the turbo decoding algorithm requires precise estimates of the channel gain and noise variance. The first significant contribution of this dissertation is a study of several methods of channel estimation suitable specifically for turbo coded systems. The second significant contribution of this dissertation is a proposed method for jointly detecting coded multiple-access signals using observations from several locations, such as spatially separated base stations. The proposed system architecture draws from the concepts of macrodiversity combining, multiuser detection, and iterative decoding. Simulation results show that when the system is applied to the time division multiple-access cellular uplink, a significant improvement in system capacity results. / Ph. D.