ABSTRACT
This chapter presents the simplification techniques and architectures for implementing the interpolation–-based Chase and generalized minimum distance (GMD) decoding. The interpolation–-based Chase decoder has been reduced by more than an order of magnitude. The Chase decoder requires much lower complexity to achieve similar performance as other popular algebraic soft–-decision decoding algorithms, such as the Kotter–-Vardy and bit–-level generalized minimum distance algorithms. The GMD decoding algorithm carries out multiple decoding trials with different erasure patterns. Before a point is interpolated, no constraint about this point has been added to the interpolation curves. Hence, it can be considered as an erased point. Accordingly, it was proposed in to adopt the interpolation–-based process to achieve one–-pass GMD decoding. Although systematic re–-encoding reduces the complexity of the Chase de–-coder. The overall process of the interpolation–-based GMD decoding is similar to that of the interpolation–-based Chase decoding.
