Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel
The Gilbert-Varshamov (GV) lower bound is used to provide indications and prescriptions for the outer code coding parameters for a memory synchronisation model that focuses solely on the internal resynchronisation process. The binary and <inline-formula> <tex-math notation="LaTeX"...
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10024292/ |
| _version_ | 1797902244438343680 |
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| author | Shamin Achari Ling Cheng |
| author_facet | Shamin Achari Ling Cheng |
| author_sort | Shamin Achari |
| collection | DOAJ |
| description | The Gilbert-Varshamov (GV) lower bound is used to provide indications and prescriptions for the outer code coding parameters for a memory synchronisation model that focuses solely on the internal resynchronisation process. The binary and <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary GV bounds are utilised in this analysis to indicate parameters to remove the remaining substitution errors and provide a complete framework. Procedures and examples are provided to determine optimal outer code parameters for given inner-entropies and residual substitution errors produced during resynchronisation. In particular, using the non-binary GV bounds allows us to match the best alphabet size for given parameters. For the cases explored, a 16-ary GV bound provides the best results, with an (<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>) code of (120, 57, 37) being a possible outer code when the inner entropy is 0.1. Using GV bounds for outer code parameter considerations frees the system from using stringent codes and instead allows any outer code to be utilised to meet the required error correction needs. |
| first_indexed | 2024-04-10T09:14:38Z |
| format | Article |
| id | doaj.art-becbd09c3e27450a874501251ed411fa |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-10T09:14:38Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| spelling | doaj.art-becbd09c3e27450a874501251ed411fa2023-02-21T00:03:01ZengIEEEIEEE Access2169-35362023-01-01118324833110.1109/ACCESS.2023.323889910024292Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov ChannelShamin Achari0https://orcid.org/0000-0003-3914-4530Ling Cheng1https://orcid.org/0000-0001-7873-8206School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, South AfricaSchool of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, South AfricaThe Gilbert-Varshamov (GV) lower bound is used to provide indications and prescriptions for the outer code coding parameters for a memory synchronisation model that focuses solely on the internal resynchronisation process. The binary and <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary GV bounds are utilised in this analysis to indicate parameters to remove the remaining substitution errors and provide a complete framework. Procedures and examples are provided to determine optimal outer code parameters for given inner-entropies and residual substitution errors produced during resynchronisation. In particular, using the non-binary GV bounds allows us to match the best alphabet size for given parameters. For the cases explored, a 16-ary GV bound provides the best results, with an (<inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>) code of (120, 57, 37) being a possible outer code when the inner entropy is 0.1. Using GV bounds for outer code parameter considerations frees the system from using stringent codes and instead allows any outer code to be utilised to meet the required error correction needs.https://ieeexplore.ieee.org/document/10024292/Alphabet size matchingchannel boundsGilbert-Varshamov boundssynchronisation finite-state Markov channel |
| spellingShingle | Shamin Achari Ling Cheng Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel IEEE Access Alphabet size matching channel bounds Gilbert-Varshamov bounds synchronisation finite-state Markov channel |
| title | Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel |
| title_full | Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel |
| title_fullStr | Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel |
| title_full_unstemmed | Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel |
| title_short | Alphabet Size Matching Techniques Based on Non-Binary Gilbert-Varshamov Bounded Limits for Synchronization Finite State Markov Channel |
| title_sort | alphabet size matching techniques based on non binary gilbert varshamov bounded limits for synchronization finite state markov channel |
| topic | Alphabet size matching channel bounds Gilbert-Varshamov bounds synchronisation finite-state Markov channel |
| url | https://ieeexplore.ieee.org/document/10024292/ |
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