Weighted-Hamming Metric for Parallel Channels
Sebastian Bitzer, Alberto Ravagnani, Violetta Weger
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The 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.
arXiv:2401.17801•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•1 citation