Architecture and Analysis for Next Generation Mobile Signal Processing.

Mobile devices have proliferated at a spectacular rate, with more than 3.3 billion active cell phones in the world. With sales totaling hundreds of billions every year, the mobile phone has arguably become the dominant computing platform, replacing the personal computer. Soon, improvements to today’s smart phones, such as high-bandwidth internet access, high-definition video processing, and human-centric interfaces that integrate voice recognition and video-conferencing will be commonplace. Cost effective and power efficient support for these applications will be required. Looking forward to the next generation of mobile computing, computation requirements will increase by one to three orders of magnitude due to higher data rates, increased complexity algorithms, and greater computation diversity but the power requirements will be just as stringent to ensure reasonable battery lifetimes. The design of the next generation of mobile platforms must address three critical challenges: efficiency, programmability, and adaptivity. The computational efficiency of existing solutions is inadequate and straightforward scaling by increasing the number of cores or the amount of data-level parallelism will not suffice. Programmability provides the opportunity for a single platform to support multiple applications and even multiple standards within each application domain. Programmability also provides: faster time to market as hardware and software development can proceed in parallel; the ability to fix bugs and add features after manufacturing; and, higher chip volumes as a single platform can support a family of mobile devices. Lastly, hardware adaptivity is necessary to maintain efficiency as the computational characteristics of the applications change. Current solutions are tailored specifically for wireless signal processing algorithms, but lose their efficiency when other application domains like high definition video are processed. This thesis addresses these challenges by presenting analysis of next generation mobile signal processing applications and proposing an advanced signal processing architecture to deal with the stringent requirements. An application-centric design approach is taken to design our architecture. First, a next generation wireless protocol and high definition video is analyzed and algorithmic characterizations discussed. From these characterizations, key architectural implications are presented, which form the basis for the advanced signal processor architecture, AnySP.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86344/1/mwoh_1.pd

Embedding multidimensional grids into optimal hypercubes

Let $G$ and $H$ be graphs, with $|V(H)|\geq |V(G)|$, and $f:V(G)\rightarrow V(H)$ a one to one map of their vertices. Let $dilation(f) = max\{ dist_{H}(f(x),f(y)): xy\in E(G) \}$, where $dist_{H}(v,w)$ is the distance between vertices $v$ and $w$ of $H$. Now let $B(G,H)$ = $min_{f}\{ dilation(f) \}$, over all such maps $f$. The parameter $B(G,H)$ is a generalization of the classic and well studied "bandwidth" of $G$, defined as $B(G,P(n))$, where $P(n)$ is the path on $n$ points and $n = |V(G)|$. Let $[a_{1}\times a_{2}\times \cdots \times a_{k} ]$ be the $k$-dimensional grid graph with integer values $1$ through $a_{i}$ in the $i$'th coordinate. In this paper, we study $B(G,H)$ in the case when $G = [a_{1}\times a_{2}\times \cdots \times a_{k} ]$ and $H$ is the hypercube $Q_{n}$ of dimension $n = \lceil log_{2}(|V(G)|) \rceil$, the hypercube of smallest dimension having at least as many points as $G$. Our main result is that $$B( [a_{1}\times a_{2}\times \cdots \times a_{k} ],Q_{n}) \le 3k,$$ provided $a_{i} \geq 2^{22}$ for each $1\le i\le k$. For such $G$, the bound $3k$ improves on the previous best upper bound $4k+O(1)$. Our methods include an application of Knuth's result on two-way rounding and of the existence of spanning regular cyclic caterpillars in the hypercube.Comment: 47 pages, 8 figure