NDLI: On the Capacity of Precision-Resolution Constrained Systems

Content Provider	IEEE Xplore Digital Library
Author	Schwartz, M. Bruck, J.
Copyright Year	2006
Description	Author affiliation: California Inst. of Technol., Pasadena, CA (Schwartz, M.; Bruck, J.)
Abstract	Arguably, the most famous constrained system is the (d, k)-RLL (run-length 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 interval-modulation scheme introduced by Mukhtar and Bruck extends the RLL constraint and implicitly suggests away of taking advantage of higher-precision clocks. Their work however, deals only with an encoder/decoder construction. In this work we introduce a more general framework which we call the precision-resolution (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 high-precision encoder (thus, we place the PR system with integral encoder, (p=1, alpha, thetas)-PR, which turns out to be a simple extension of RLL, and the PR system with infinite-precision encoder, (infin, alpha, thetas)-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 thetas. 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 infinite-precision encoder, the capacity is finite
Starting Page	1462
Ending Page	1466
File Size	199366
Page Count	5
File Format	PDF
ISBN	142440505X
DOI	10.1109/ISIT.2006.262110
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Decoding Clocks Time measurement Postal services Optical transmitters Context Holographic optical components Sensor phenomena and characterization Terminology Magnetic separation
Content Type	Text
Resource Type	Article

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