We study the problem of cooperative localization of a large network of nodes in integer-coordinated unit disk graphs, a simplified but useful version of general random graph. Exploiting the property that the radius r sets clear cut on the connectivity of two nodes, we propose an essential philosophy that "no connectivity is also useful information just like the information being connected" in unit disk graphs. Exercising this philosophy, we show that the conventional network localization problem can be re-formulated to significantly reduce the search space, and that global rigidity, a necessary and sufficient condition for the existence of unique solution in general graphs, is no longer necessary. While the problem is still NP-hard, we show that a (depth-first) tree-search algorithm with memory O(N ) (N is the network size) can be developed, and for practical setups, the search complexity and speed is very manageable, and is magnitudes less than the conventional problem, especially when the graph is sparse or when only very limited anchor nodes are available.

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Writing process in hard disk drives (HDD) is affected from nonlinearity. Normally, nonlinearity is not easy to be avoided or removed since it is unexpected and caused by various sources. In this paper, we review a description of a nonlinearity behavior by using a Volterra model, and using a random binary number to generate an input data. The Volterra model can describe both linear and nonlinear parts of the readback signals in terms of the volterra equations. In addition, we propose to use an MMSE method to equalize the read-back signals with nonlinearity using various constraints before applying the Viterbi detector. For a 2nd-order Volterra model, the results show that the equalizer with 1 1 g = constraint gives the lowest MMSE values. Furthermore, as the nonlinearity level increases, the bit error rate (BER) performance degrades.

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