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

✍ Scribed by Yutaka Kobayashi; Masaya Fujisawa; Shojiro Sakata

Book ID
101294853
Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
251 KB
Volume
83
Category
Article
ISSN
1042-0967

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✦ Synopsis

Generalized minimum-distance decoding (GMD) is realized by iterating simultaneous erasure-error correction while varying the erasure pattern. Simultaneous erasureerror 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.

πŸ“œ SIMILAR VOLUMES

On Multisequence Shift Register Synthesi
On Multisequence Shift Register Synthesis and Generalized-Minimum-Distance Decoding of Reed-Solomon Codes
✍ N. Kamiya πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 618 KB

In this paper. it is shown that the problem of generalized-minimum-distance (GMD) decoding of Reed-Solomon (RS) codes can be reduced to the problem of multisequence shift register synthesis, and a simple algorithm is presented that yields a solution for this problem by finding, for \(k=1,2, \ldots\)