TY - GEN
T1 - On the capacity of precision-resolution constrained systems
AU - Schwartz, Moshe
AU - Bruck, Jehoshua
PY - 2006/12/1
Y1 - 2006/12/1
N2 - 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 l's are separated by at least d O's, and there are no more than k consecutive O's anywhere in the stream. The motivation for this scheme comes from the fact that certain sensor characteristics restrict the minimum time between adjacent l's or else the two will be merged in the receiver, while a clock drift between transmitter and receiver may cause spurious O's or missing O'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 a way 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, α, θ)-PR, which turns out to be a simple extension of RLL, and the PR system with infinite-precision encoder, (∞, α, θ)-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 α, and the decoder resolution factor θ. 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.
AB - 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 l's are separated by at least d O's, and there are no more than k consecutive O's anywhere in the stream. The motivation for this scheme comes from the fact that certain sensor characteristics restrict the minimum time between adjacent l's or else the two will be merged in the receiver, while a clock drift between transmitter and receiver may cause spurious O's or missing O'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 a way 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, α, θ)-PR, which turns out to be a simple extension of RLL, and the PR system with infinite-precision encoder, (∞, α, θ)-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 α, and the decoder resolution factor θ. 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.
UR - http://www.scopus.com/inward/record.url?scp=39049116047&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2006.262110
DO - 10.1109/ISIT.2006.262110
M3 - Conference contribution
AN - SCOPUS:39049116047
SN - 1424405041
SN - 9781424405046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1462
EP - 1466
BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Y2 - 9 July 2006 through 14 July 2006
ER -