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arXiv · 2506.15233

New Bounds and Constructions for Variable Packet-Error Coding

Xiangliang Kong·Xin Wang·Ron M. Roth·Itzhak Tamo
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Abstract

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.

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Xiangliang Kong, Xin Wang, Ron M. Roth, Itzhak Tamo. 2025-06-18. New Bounds and Constructions for Variable Packet-Error Coding. https://arxiv.org/abs/2506.15233

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