Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability
The paper presents a new scheme of cyclic codes suitable for the correction of burst errors. This is accomplished by the proper definition of their parity check polynomials in which the difference between orders of every two consecutive elements of the utilized polynomial is unique and in order of p...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9234436/ |
| _version_ | 1819120742952861696 |
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| author | Sina Vafi |
| author_facet | Sina Vafi |
| author_sort | Sina Vafi |
| collection | DOAJ |
| description | The paper presents a new scheme of cyclic codes suitable for the correction of burst errors. This is accomplished by the proper definition of their parity check polynomials in which the difference between orders of every two consecutive elements of the utilized polynomial is unique and in order of power of 2. In the proposed polynomials, the number of applied elements is much lower than their orders (or codes' lengths). This leads to represent codes as a class of low-density parity check (LDPC) codes, while they do not have any 4 cycle in their Tanner graphs. Considering the properties of the circulant matrix and structure of the defined polynomials, it is proven that codes have the optimum burst error-correcting capability. This is evident for short and long length codes. Moreover, it is shown that constructed codes can be combined with Fire codes and demonstrate cyclic codes that are applicable for the simultaneous correction of random and burst errors. |
| first_indexed | 2024-12-22T06:25:30Z |
| format | Article |
| id | doaj.art-4cd7147b18ed41068cfa4711aa9699cf |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T06:25:30Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-4cd7147b18ed41068cfa4711aa9699cf2022-12-21T18:35:51ZengIEEEIEEE Access2169-35362020-01-01819206519207210.1109/ACCESS.2020.30328379234436Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting CapabilitySina Vafi0https://orcid.org/0000-0002-7886-973XCollege of Engineering, IT and Environment, Charles Darwin University, Darwin, NT, AustraliaThe paper presents a new scheme of cyclic codes suitable for the correction of burst errors. This is accomplished by the proper definition of their parity check polynomials in which the difference between orders of every two consecutive elements of the utilized polynomial is unique and in order of power of 2. In the proposed polynomials, the number of applied elements is much lower than their orders (or codes' lengths). This leads to represent codes as a class of low-density parity check (LDPC) codes, while they do not have any 4 cycle in their Tanner graphs. Considering the properties of the circulant matrix and structure of the defined polynomials, it is proven that codes have the optimum burst error-correcting capability. This is evident for short and long length codes. Moreover, it is shown that constructed codes can be combined with Fire codes and demonstrate cyclic codes that are applicable for the simultaneous correction of random and burst errors.https://ieeexplore.ieee.org/document/9234436/Burst error correcting cyclic codescirculant parity check matrixlow density parity check (LDPC) codescompound channels |
| spellingShingle | Sina Vafi Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability IEEE Access Burst error correcting cyclic codes circulant parity check matrix low density parity check (LDPC) codes compound channels |
| title | Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability |
| title_full | Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability |
| title_fullStr | Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability |
| title_full_unstemmed | Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability |
| title_short | Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting Capability |
| title_sort | cyclic low density parity check codes with the optimum burst error correcting capability |
| topic | Burst error correcting cyclic codes circulant parity check matrix low density parity check (LDPC) codes compound channels |
| url | https://ieeexplore.ieee.org/document/9234436/ |
| work_keys_str_mv | AT sinavafi cycliclowdensityparitycheckcodeswiththeoptimumbursterrorcorrectingcapability |