New Bounds and Constructions for Variable Packet-Error Coding
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911011666132992 |
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| author | Kong, Xiangliang Wang, Xin Roth, Ron M. Tamo, Itzhak |
| author_facet | Kong, Xiangliang Wang, Xin Roth, Ron M. Tamo, Itzhak |
| contents | In this paper, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes with dynamic error-correcting capabilities that adapt to varying numbers of errors. Specifically, we first provide several bounds on the rate--distortion trade-off for general variable packet-error coding schemes. Then, we present two explicit constructions of variable packet-error coding schemes. The first construction uses higher-order MDS codes and provides a coding scheme that achieves a better rate--distortion trade-off compared to known results for general parameter regimes. The second construction is based on a variant of the repetition code and yields a coding scheme with an optimal rate--distortion trade-off, with respect to our bound, for certain parameter regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Bounds and Constructions for Variable Packet-Error Coding Kong, Xiangliang Wang, Xin Roth, Ron M. Tamo, Itzhak Information Theory Combinatorics 94B25, 94B65 E.4 In this paper, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes with dynamic error-correcting capabilities that adapt to varying numbers of errors. Specifically, we first provide several bounds on the rate--distortion trade-off for general variable packet-error coding schemes. Then, we present two explicit constructions of variable packet-error coding schemes. The first construction uses higher-order MDS codes and provides a coding scheme that achieves a better rate--distortion trade-off compared to known results for general parameter regimes. The second construction is based on a variant of the repetition code and yields a coding scheme with an optimal rate--distortion trade-off, with respect to our bound, for certain parameter regimes. |
| title | New Bounds and Constructions for Variable Packet-Error Coding |
| topic | Information Theory Combinatorics 94B25, 94B65 E.4 |
| url | https://arxiv.org/abs/2506.15233 |