A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding
The decoding of binary random linear codes for packet erasures relies on receivers collecting a sufficient number of error-free coded packets for the reconstruction of a transmitted message. Syndrome decoding (SD), which conforms to the broad definition of guessing random additive noise decoding (GR...
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IEEE
2025-01-01
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| Series: | IEEE Open Journal of the Communications Society |
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| Online Access: | https://ieeexplore.ieee.org/document/11026088/ |
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| author | Ioannis Chatzigeorgiou |
| author_facet | Ioannis Chatzigeorgiou |
| author_sort | Ioannis Chatzigeorgiou |
| collection | DOAJ |
| description | The decoding of binary random linear codes for packet erasures relies on receivers collecting a sufficient number of error-free coded packets for the reconstruction of a transmitted message. Syndrome decoding (SD), which conforms to the broad definition of guessing random additive noise decoding (GRAND), endeavors to repair partially-correct received coded packets – which would otherwise be discarded by the packet erasure decoder – and boost the probability of a receiver successfully recovering the transmitted message. This paper introduces a low-complexity variant of SD, dubbed single-error correcting SD (SEC-SD), and conducts an in-depth analysis of the success probability of packet erasure decoding aided by SEC-SD. The analysis leads to a practical lower bound on the success probability of packet erasure decoding complemented by SD, and provides guidance on how SEC-SD can be modified to potentially achieve a higher success probability than SD at a lower computational cost. |
| format | Article |
| id | doaj-art-2b2158cc7f3b4a0da0697237bd9aaff1 |
| institution | Kabale University |
| issn | 2644-125X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of the Communications Society |
| spelling | doaj-art-2b2158cc7f3b4a0da0697237bd9aaff12025-08-20T03:24:08ZengIEEEIEEE Open Journal of the Communications Society2644-125X2025-01-0164962497710.1109/OJCOMS.2025.357700711026088A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise DecodingIoannis Chatzigeorgiou0https://orcid.org/0000-0001-6802-3434School of Computing and Communications, Lancaster University, Lancaster, U.K.The decoding of binary random linear codes for packet erasures relies on receivers collecting a sufficient number of error-free coded packets for the reconstruction of a transmitted message. Syndrome decoding (SD), which conforms to the broad definition of guessing random additive noise decoding (GRAND), endeavors to repair partially-correct received coded packets – which would otherwise be discarded by the packet erasure decoder – and boost the probability of a receiver successfully recovering the transmitted message. This paper introduces a low-complexity variant of SD, dubbed single-error correcting SD (SEC-SD), and conducts an in-depth analysis of the success probability of packet erasure decoding aided by SEC-SD. The analysis leads to a practical lower bound on the success probability of packet erasure decoding complemented by SD, and provides guidance on how SEC-SD can be modified to potentially achieve a higher success probability than SD at a lower computational cost.https://ieeexplore.ieee.org/document/11026088/Network codingbinary codeslinear codesdecodingerror analysis |
| spellingShingle | Ioannis Chatzigeorgiou A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding IEEE Open Journal of the Communications Society Network coding binary codes linear codes decoding error analysis |
| title | A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding |
| title_full | A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding |
| title_fullStr | A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding |
| title_full_unstemmed | A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding |
| title_short | A Lower Bound on the Success Probability of Binary Random Linear Network Codes Aided by Noise Decoding |
| title_sort | lower bound on the success probability of binary random linear network codes aided by noise decoding |
| topic | Network coding binary codes linear codes decoding error analysis |
| url | https://ieeexplore.ieee.org/document/11026088/ |
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