Schwartz, Moshe and Bruck, Jehoshua (2006) On the Capacity of PrecisionResolution Constrained Systems. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechPARADISE:2006.ETR073

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Abstract
Arguably, the most famous constrained system is the (d, k)RLL (RunLength Limited), in which a stream of bits obeys the constraint that every two 1's are separated by at least d 0's, and there are no more than k consecutive 0's anywhere in the stream. The motivation for this scheme comes from the fact that certain sensor characteristics restrict the minimum time between adjacent 1's or else the two will be merged in the receiver, while a clock drift between transmitter and receiver may cause spurious 0's or missing 0's at the receiver if too many appear consecutively. The intervalmodulation scheme introduced by Mukhtar and Bruck extends the RLL constraint and implicitly suggests a way of taking advantage of higherprecision clocks. Their work however, deals only with an encoder/decoder construction. In this work we introduce a more general framework which we call the precisionresolution (PR) constrained system. In PR systems, the encoder has precision constraints, while the decoder has resolution constraints. We examine the capacity of PR systems and show the gain in the presence of a highprecision encoder (thus, we place the PR system with integral encoder, (p=1,alpha,theta)PR, which turns out to be a simple extension of RLL, and the PR system with infiniteprecision encoder, (infinity,alpha,theta)PR, on two ends of a continuum). We derive an exact expression for their capacity in terms of the precision p, the minimal resolvable measurement at the decoder alpha, and the decoder resolution factor theta. In an analogy to the RLL terminology these are the clock precision, the minimal time between peaks, and the clock drift. Surprisingly, even with an infiniteprecision encoder, the capacity is finite.
Item Type:  Report or Paper (Technical Report) 

Additional Information:  This work was supported in part by the Caltech Lee Center for Advanced Networking and by NSF grant ANI0322475. Also available online: http://www.paradise.caltech.edu/papers/etr073.pdf 
Group:  Parallel and Distributed Systems Group 
Record Number:  CaltechPARADISE:2006.ETR073 
Persistent URL:  http://resolver.caltech.edu/CaltechPARADISE:2006.ETR073 
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ID Code:  26104 
Collection:  CaltechPARADISE 
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Deposited On:  22 Feb 2006 
Last Modified:  26 Dec 2012 13:53 
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