£ 9 Analogic for Code Estimation and Detection

Analogic is a class of analog statistical signal processing circuits that dynamically solve an associated inference problem by locally propagating probabilities in a messagepassing algorithm [29] [15]. In this thesis, we study an exemplary embodiment of analogic called Noise-Locked Loop(NLL) which is a pseudo-random code estimation system. The previous work shows NLL can perform direct-sequence spread-spectrum acquisition and tracking functionality and promises orders-of-magnitude win over digital implementations [29]. Most of the research [30] [2] [3] has been focused on the simulation and implementation of probability representation NLL derived from exact form message-passing algorithms. We propose an approximate message-passing algorithm for NLL in loglikelihood ratio(LLR) representation and have constructed its analogic implementation. The new approximate NLL gives shorter acquisition time comparing to the exact form NLL. The approximate message-passing algorithm makes it possible to construct analogic which is almost temperature independent. This is very useful in the design of robust large-scale analogic networks. Generalized belief propagation(GBP) has been proposed to improve the computational accuracy of Belief Propagation [31] [32] [33]. The application of GBP to NLL promises significantly improvement of the synchronization performance. However, there is no report on circuit implementation. In this thesis, we propose analogic circuits to implement the basic computations in GBP, which can be used to construct general GBP systems. Finally we propose a novel current-mode signal restoration circuit which will be important in scaling analogic to large networks. Thesis Supervisor: Neil Gershenfeld Title: Associate Professor -. . < .& .' ... :-4 ; .. e : .. ' . ' ::e ' ''--:-1--t '---:-'~ '.-n " 'i 1 W :, i'oi:= w M ' da: | s s -. i e < y n . .: -. . . . .. .. .. ,. -. , , . ,. . , ,,; r, : G eNV-ii R Wk'i W Nl r ' l -i -~ ;r. ', .z::: . w. . . .;. , . -. : .,., 0 i, k , $ ' ' 0 -' i' -n < M :, :--; -S.. , . ,, 3, s-. c 4. , -r -:a -.. ;w , m-