Power Decoding Reed--Solomon Codes Up to the Johnson Radius
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| Titel: | Power Decoding Reed--Solomon Codes Up to the Johnson Radius |
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| Autoren: | Rosenkilde, Johan |
| Verlagsinformationen: | 2015-05-08 2017-12-07 |
| Publikationsart: | Electronic Resource |
| Abstract: | Power decoding, or "decoding using virtual interleaving" is a technique for decoding Reed--Solomon codes up to the Sudan radius. Since the method's inception, it has been an open question if it is possible to use this approach to decode up to the Johnson radius -- the decoding radius of the Guruswami--Sudan algorithm. In this paper we show that this can be done by incorporating a notion of multiplicities. As the original Power decoding, the proposed algorithm is a one-pass algorithm: decoding follows immediately from solving a shift-register type equation, which we show can be done in quasi-linear time. It is a "partial bounded-distance decoding algorithm" since it will fail to return a codeword for a few error patterns within its decoding radius; we investigate its failure behaviour theoretically as well as give simulation results. This is an extended version where we also show how the method can be made faster using the re-encoding technique or a syndrome formulation. Comment: Extended version of paper accepted for Advances in Mathematics of Communication. Results announced at ACCT-14 |
| Index Begriffe: | Computer Science - Information Theory, text |
| URL: | |
| Verfügbarkeit: | Open access content. Open access content |
| Other Numbers: | COO oai:arXiv.org:1505.02111 1106218115 |
| Originalquelle: | CORNELL UNIV From OAIster®, provided by the OCLC Cooperative. |
| Dokumentencode: | edsoai.on1106218115 |
| Datenbank: | OAIster |
Nájsť tento článok vo Web of Science | Abstract: | Power decoding, or "decoding using virtual interleaving" is a technique for decoding Reed--Solomon codes up to the Sudan radius. Since the method's inception, it has been an open question if it is possible to use this approach to decode up to the Johnson radius -- the decoding radius of the Guruswami--Sudan algorithm. In this paper we show that this can be done by incorporating a notion of multiplicities. As the original Power decoding, the proposed algorithm is a one-pass algorithm: decoding follows immediately from solving a shift-register type equation, which we show can be done in quasi-linear time. It is a "partial bounded-distance decoding algorithm" since it will fail to return a codeword for a few error patterns within its decoding radius; we investigate its failure behaviour theoretically as well as give simulation results. This is an extended version where we also show how the method can be made faster using the re-encoding technique or a syndrome formulation.<br />Comment: Extended version of paper accepted for Advances in Mathematics of Communication. Results announced at ACCT-14 |
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