Writing on Dirty Paper with Resizing and its Application to Quasi-Static Fading Broadcast Channels

This paper studies a variant of the classical problem of ``writing on dirty paper'' in which the sum of the input and the interference, or dirt, is multiplied by a random variable that models resizing, known to the decoder but not to the encoder. The achievable rate of Costa's dirty paper coding (DPC) scheme is calculated and compared to the case of the decoder's also knowing the dirt. In the ergodic case, the corresponding rate loss vanishes asymptotically in the limits of both high and low signal-to-noise ratio (SNR), and is small at all finite SNR for typical distributions like Rayleigh, Rician, and Nakagami. In the quasi-static case, the DPC scheme is lossless at all SNR in terms of outage probability. Quasi-static fading broadcast channels (BC) without transmit channel state information (CSI) are investigated as an application of the robustness properties. It is shown that the DPC scheme leads to an outage achievable rate region that strictly dominates that of time division.Comment: To appear in IEEE International Symposium on Information Theory 200

High Yield Solvothermal Synthesis of Hexaniobate Based Nanocomposites via the Capture of Preformed Nanoparticles in Scrolled Nanosheets

The ability to encapsulate linear nanoparticle (NP) chains in scrolled nanosheets is an important advance in the formation of nanocomposites.These nanopeapods (NPPs) exhibit interesting properties that may not be achieved by individual entities. Consequently, to fully exploit the potential of NPPs, the fabrication of NPPs must focus on producing composites with unique combinations of morphologically uniform nanomaterials. Various methods can produce NPPs, but expanding these methods to a wide variety of material combinations can be difficult. Recent work in our group has resulted in the in situ formation of peapod-like structures based on chains of cobalt NPs. Building on this initial success, a more versatile approach has been developed that allows for the capture of a series of preformed NPs in NPP composites. In the following chapters, various synthetic approaches for NPPs of various material combinations will be presented and the key roles of various reaction parameters will be discussed. Also, uniform hexaniobate nanoscrolls were fabricated via a solvothermal method induced by heating up a mixture of TBAOH, hexaniobate crystallites, and oleylamine in toluene. The interlayer spacing of the nanoscrolls was easily tuned by varying the relative amount and chain lengths of the primary alkylamines. To fabricate NPPs, as-synthesized NPs were treated with hexaniobate crystallite in organic mixtures via solvothermal method. During solvothermal treatment, exfoliated hexaniobate nanosheets scroll around highly ordered chains of NPs to produce the target NPP structures in high yield. Reaction mixtures were held at an aging temperature for a few hours to fabricate various new NPPs (Fe3O4@hexaniobate, Ag@hexaniobate, Au@hexaniobate, Au-Fe3O4@hexaniobate, TiO2@hexaniobate, CdS@hexaniobate, CdSe@hexaniobate, and ZnS@hexaniobate). This versatile method was first developed for the fabrication of magnetic peapod nanocomposites with preformed nanoparticles (NPs). This approach is effectively demonstrated on a series of ferrite NPs (≤ 14 nm) where Fe3O4@hexaniobate NPPs are rapidly (~ 6 h) generated in high yield. When NP samples with different sizes are reacted, clear evidence for size selectivity is seen. Magnetic dipolar interactions between ferrite NPs within the Fe3O4@hexaniobate samples leads to a significant rise in coercivity, increasing almost four-fold relative to free particles. Other magnetic ferrites NPPs, MFe2O4@hexaniobate (M = Mn, Co, Ni), can also be prepared. This synthetic approach to nanopeapods is quite versatile and should be readily extendable to other, non-ferrite NPs or NP combinations so that cooperative properties can be exploited while the integrity of the NP assemblies is maintained. Further, this approach demonstrated selectivity by encapsulating NPs according to their size. The use of polydispersed NP systems is also possible and in this case, evidence for size and shape selectivity was observed. This behavior is significant in that it could be exploited in the purification of inhomogeneous NP samples. Other composite materials containing silver and gold NPs are accessible. Partially filled Fe3O4@hexaniobate NPPs were used as templates for the in situ growth of gold to produce the bi-functional Au- Fe3O4@hexaniobate NPPs. Encapsulation of Ag and Au NP chains with a hexaniobate nanoscroll was shifted the surface plasmon resonance to higher wavelengths. In these composites NPs can be incorporated to form NPP structures, decorated on nanosheets before scrolling, or attached to the surfaces of the nanoscrolls. The importance of this advancement is the promise it holds for the design and assembly of active nanocomposites. One can create important combinations of nanomaterials for potential applications in a variety of areas including catalysis, solar conversion, thermoelectrics, and multiferroics