6,498 research outputs found
Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise
to optimal frequency-hopping sequences and optimal comma-free codes. New
constructions for PCDPs, based on almost difference sets and cyclic difference
matrices, are given. These produce new infinite families of optimal PCDPs (and
hence optimal frequency-hopping sequences and optimal comma-free codes). The
existence problem for optimal PCDPs in , with base blocks
of size three, is also solved for all .Comment: to appear in IEEE Transactions on Information Theor
Optimal and near-optimal frequency-hopping sequences based on Gaussian period
Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequency-hopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs
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