Aspects of List-of-Two Decoding
We study the problem of list decoding with focus on the case when we have a list size limited to two. Under this restriction we derive general lower bounds on the maximum possible size of a list-of-2-decodable code. We study the set of correctable error patterns in an attempt to obtain a characteriz...
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Linköpings universitet, Datatransmission
2006
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ndltd-UPSALLA1-oai-DiVA.org-liu-69192013-01-08T13:04:19ZAspects of List-of-Two DecodingengEriksson, JonasLinköpings universitet, DatatransmissionLinköpings universitet, Tekniska högskolanInstitutionen för systemteknik2006list decodingSudan's algorithmReed-Solomon codeDatatransmissionDatatransmissionWe study the problem of list decoding with focus on the case when we have a list size limited to two. Under this restriction we derive general lower bounds on the maximum possible size of a list-of-2-decodable code. We study the set of correctable error patterns in an attempt to obtain a characterization. For a special family of Reed-Solomon codes - which we identify and name 'class-I codes' - we give a weight-based characterization of the correctable error patterns under list-of-2 decoding. As a tool in this analysis we use the theoretical framework of Sudan's algorithm. The characterization is used in an exact calculation of the probability of transmission error in the symmetric channel when list-of-2 decoding is used. The results from the analysis and complementary simulations for QAM-systems show that a list-of-2 decoding gain of nearly 1 dB can be achieved. Further we study Sudan's algorithm for list decoding of Reed-Solomon codes for the special case of the class-I codes. For these codes algorithms are suggested for both the first and second step of Sudan's algorithm. Hardware solutions for both steps based on the derived algorithms are presented. Doctoral thesis, monographinfo:eu-repo/semantics/doctoralThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-6919urn:isbn:91-85497-49-5Linköping Studies in Science and Technology. Dissertations, 0345-7524 ; 1010application/pdfinfo:eu-repo/semantics/openAccess |
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language |
English |
format |
Doctoral Thesis |
sources |
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topic |
list decoding Sudan's algorithm Reed-Solomon code Datatransmission Datatransmission |
spellingShingle |
list decoding Sudan's algorithm Reed-Solomon code Datatransmission Datatransmission Eriksson, Jonas Aspects of List-of-Two Decoding |
description |
We study the problem of list decoding with focus on the case when we have a list size limited to two. Under this restriction we derive general lower bounds on the maximum possible size of a list-of-2-decodable code. We study the set of correctable error patterns in an attempt to obtain a characterization. For a special family of Reed-Solomon codes - which we identify and name 'class-I codes' - we give a weight-based characterization of the correctable error patterns under list-of-2 decoding. As a tool in this analysis we use the theoretical framework of Sudan's algorithm. The characterization is used in an exact calculation of the probability of transmission error in the symmetric channel when list-of-2 decoding is used. The results from the analysis and complementary simulations for QAM-systems show that a list-of-2 decoding gain of nearly 1 dB can be achieved. Further we study Sudan's algorithm for list decoding of Reed-Solomon codes for the special case of the class-I codes. For these codes algorithms are suggested for both the first and second step of Sudan's algorithm. Hardware solutions for both steps based on the derived algorithms are presented. |
author |
Eriksson, Jonas |
author_facet |
Eriksson, Jonas |
author_sort |
Eriksson, Jonas |
title |
Aspects of List-of-Two Decoding |
title_short |
Aspects of List-of-Two Decoding |
title_full |
Aspects of List-of-Two Decoding |
title_fullStr |
Aspects of List-of-Two Decoding |
title_full_unstemmed |
Aspects of List-of-Two Decoding |
title_sort |
aspects of list-of-two decoding |
publisher |
Linköpings universitet, Datatransmission |
publishDate |
2006 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-6919 http://nbn-resolving.de/urn:isbn:91-85497-49-5 |
work_keys_str_mv |
AT erikssonjonas aspectsoflistoftwodecoding |
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1716507574998663168 |