Constrained shift-register synthesis: Fast GMD decoding of 1D algebraic codes

Abstract

Generalized minimum-distance decoding (GMD) is realized by iterating simultaneous erasure-error correction while varying the erasure pattern. Simultaneous erasure-error correction can be considered as a constrained (in regard to the erasure location ideal) shift-register synthesis problem. Then, various procedures can be derived as extensions of the BM algorithm, such as erasure preprocessing, erasure postprocessing, as well as intermediate types. In this approach, fast GMD decoding can be introduced naturally as an erasure postprocessing algorithm, up to the designed distance for one-dimensional algebraic code. The proposed method provides better theoretical insight as well as the advantage that the efficiency is somewhat improved compared to other similar methods. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(4): 71–80, 2000