Design and Construction of Algebraic-Geometry Codes

点击翻译按钮获取中文摘要

Fast decoding algorithm is proposed, base on the Generalized Mimimum Distant decoding. This is obtained by completing Kotter's decoding algorithm. We introduce an auxiliary polynomial by which a perfect iterative decoding procedure is established. Hardware inplementations can be easily designed. The new decoding procedure can be thought as a reverse direction type of Welch-Berlekamp method. In the Welch-Berlekamp method, a time-consuming syndrome calculation is always required, whereas our wethod begins with a simple hard-decision decoding. Algebraic-Geometry codes can be also fastly decoded by generalizing our method.Furthermore, a new decoding procedure capable to the beyond BCH bound, is developed which needs a short computation time less then 1/6 times a conventional case, i.e., Blahut and Horiguchi method.