Decoding the (47,24,11) quadratic residue code using bit-error probability estimates

Abstract

A new algorithm is developed to facilitate faster decoding of the (47,24,11) Quadratic Residue (QR) code. This decoder, based on the idea first developed by Reed in a 1959 MIT Lincoln Laboratory Report, uses real channel data to estimate the individual bit-error probabilities in a received word. The algorithm then sequentially inverts the bits with the highest probability of error until one of the errors is canceled. The remaining errors are then corrected by the use of algebraic decoding techniques. This new algorithm, called the reliabilitysearch algorithm, is a complete decoder that significantly reduces the decoding complexity in terms of CPU time while maintaining the same bit-error rate (BER) performance. In fact, this algorithm is an appropriate modification to the algorithm developed by Chase. © 2009 IEEE.