The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-373

“Decoding Error Correction Codes Utilizing Bit Error Probability Estimates”

by Gregory Oleg Dubney

August 2005

The main purpose of this dissertation is to estimate the individual bit-error probabilities of a codeword while it is being received. It turns out that the bit-error probabilities are a function of the received-bit amplitudes and the channel noise power, both of which are assumed to be unknown a-priori at the receiver. In this study coherent detection is implemented with a Costas phase-locked loop receiver which facilitates the joint estimation of these two parameters, and as a consequence, the bit-error probabilities. The bit-error probability estimates make it possible to reduce the decoding complexity and improve the performance of various error-correction codes.One example is reliability-based decoding of cyclic codes. The traditional algebraic techniques to decode these codes up to true minimum distance are difficult and computationally complex. In the reliability-based decoding strategy, the bit-error probability estimates are utilized to cancel one error in the received word, and then a less complex algebraic decoding algorithm is used to correct the remaining errors. Simulation results show that the reliability search algorithm significantly reduces the decoding time of the (23, 12, 7) Golay code and the (47, 24, 11) QR code by 41.3% and 22.2%, respectively compared with other decoding algorithms. Another example is erasure decoding of Reed-Solomon codes. An erasure is a symbol error with its location known to the decoder. However, in current decoding procedures, the locations of the error symbols are unknown and must be estimated. Knowledge of the bit-error probabilities enable the decoder to determine the symbols that have the highest probability of being in error. Thus, the decoder only needs to calculate the amplitudes of these symbol erasures to decode the codeword. Simulation results show that correcting combinations of errors and erasures results in a slightly lower symbol-error probability compared with decoding errors only over an additive white Gaussian noise (AWGN) channel

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