Decoding Error - Correction Codes Utilizing Bit - Error Probability Estimates

The main purpose of this dissertation is to estimate the individual bit-error probabilities of binary symbols or codewords while they are 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) Quadratic Residue (QR) code by 41.3% and 22.2% respectively, compared with other decoding algorithms. Another example is erasure decoding of Reed-Solomon (RS) 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 error. Thus, the decoder only needs to calculate the amplitudes of