Algebraic And Soft-Decision Decoding Of The (71,36,11) Quadratic Residue Code

In modern communication systems, channel coding is one of the important technologies to achieve reliable transmissions. With the rapid development of the channel coding technology, more and more good codes have been discovered by researchers. This thesis mainly focuses on the study of a good algebraic code, called quadratic residue(QR) codes.QR codes are a nice family of binary BCH codes whose code rates are greater than or equal to 1/2. They have very strict algebraic structure and generally have large minimum distances, thus most of the known QR codes have excellent error-correcting performance. However, except the widely used Hamming and Golay codes, other QR codes have not been employed in communication systems due to their high decoding complexity. This thesis studies on the algebraic and soft-decision decoding algorithm of the(71, 36, 11) QR code, and the main contributions are as follows:1. A modified algebraic decoding algorithm of the(71, 36, 11) QR code is proposed. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities and simplifies the judgment conditions corresponding to different number of errors. Compared with the previous algorithms, when the weight of the error pattern is 4 and 5, the proposed algorithm maintains the same performance and increases the decoding efficiency by 56.1% and 18.2%, respectively.2. The soft-decision decoding of the(71, 36, 11) QR code is implemented. Considering the soft decision decoding algorithm provides more coding gain than the algebraic decoding, this thesis achieves the soft-decision decoding of the(71, 36, 11) QR code by applying the Chase II algorithm and introducing the optimality sufficient conditions to terminate the Chase algorithm quickly.3. In view of the complexity of soft-decision decoding based on the Chase II algorithm, two new soft-decision decoding algorithms for the(71, 36, 11) QR code are developed. One of which is to reduce the error correction capability of the hard-decision decoder and change the flipping method of the Chase II algorithm, the other is to preset a flipping threshold T in the shift-search algorithm and use the Chase II algorithm to implement the soft-decision decoding. These two algorithms can reduce the storage space and achieve a better tradeoff between decoding performance and computational complexity.