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This letter characterizes the optimal policies for bandwidth use and storage for the problem of distributed storage in Internet of Things (IoT) scenarios, where lost nodes cannot be replaced by new nodes as is typically assumed in Data Center and Cloud scenarios. We develop an information flow model that captures the overall process of data transmission between IoT devices, from the initial preparation stage (generating redundancy from the original data) to the different repair stages with fewer and fewer devices. Our numerical results show that in a system with 10 nodes, the proposed optimal scheme can save as much as 10.3 % of bandwidth use, and as much as 44 % storage use with respect to the closest suboptimal approach.

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The transmission behaviour of a distributed Bragg reector (DBR) with surface dielectric gratings on top and bottom is studied. The transmission shows a comb-like spectrum in the DBR band gap, which is explained in the Fano picture. The number density of the transmission peaks increases with increasing number of cells of the DBR, while the ratio of the average full width at half maximum to the corresponding average free spectral range, being only few percent for both transversal electric and magnetic waves, is almost invariant. The transmission peaks can be narrower than 0.1 nm and are fully separated from each other in certain wavebands. We further prove that the transmission combs are robust against randomness in the heights of the DBR layers. Therefore, the proposed structure is a candidate for an ultra-narrow-band multichannel filter or polarizer.

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