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arXiv · 2401.17801

Weighted-Hamming Metric for Parallel Channels

Sebastian Bitzer·Alberto Ravagnani·Violetta Weger
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Abstract

Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters.

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Sebastian Bitzer, Alberto Ravagnani, Violetta Weger. 2024-01-31. Weighted-Hamming Metric for Parallel Channels. https://arxiv.org/abs/2401.17801

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