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Multiset Combinatorial Gray Codes With Application to Proximity Sensor Networks
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DOI：10.1109/TIT.2025.3646470.png)
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Abstract
En 中文
We investigate coding schemes that map source symbols into multisets of an alphabet. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over proximity sensor networks. We define a multiset combinatorial Gray code as a multiset code with fixed multiset cardinality that possesses combinatorial Gray code characteristic. For source codes that are organized as a grid, namely an integer lattice, we propose a solution by first constructing a mapping from the grid to the set of symbols, which we referred to as colors. The codes are then defined as the images of rectangular blocks in the grid of fixed dimensions. We refer to the mapping as a color mapping and the code as a color multiset code. We propose the idea of product multiset code that enables us to construct codes for high dimensional grids based on 1-dimensional (1D) grids. We provide a detailed analysis of color multiset codes on 1D grids, focusing on codes that require the minimal number of colors. To illustrate the application of such a coding scheme, we consider an object tracking problem on 2D grids and show its efficiency, which comes from exploiting transmission parallelism. Some numerical results are presented to conclude the paper.
Keywords:
Codes
Image color analysis
Symbols
Reflective binary codes
Object tracking
Color
Lattices
Decoding
Zinc
Source coding
Multiset code
combinatorial Gray code
de Bruijin sequences
universal cycles
object tracking
Journal
I
IF:
2.9
Papers:
317
Citations:
0