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In order to prevent the capacitive crosstalk in on-chip buses, several typesof capacitive crosstalk avoidance codes have been devised. These codes aredesigned to prohibit transition patterns prone to the capacity crosstalk fromany consecutive two words transmitted to on-chip buses. This paper provides arigorous analysis on the asymptotic rate of (p,q)-transition free wordsequences under the assumption that coding is based on a pair of a statefulencoder and a stateless decoder. The symbols p and q represent k-bit transitionpatterns that should not be appeared in any consecutive two words at the sameadjacent k-bit positions. It is proved that the maximum rate of the sequencesequals to the subgraph domatic number of (p,q)-transition free graph. Based onthe theoretical results on the subgraph domatic partition problem, a pair oflower and upper bounds on the asymptotic rate is derived. We also present thatthe asymptotic rate 0.8325 is achievable for the (10,01)-transition free wordsequences.

Bounds on Asymptotic Rate of Capacitive Crosstalk Avoidance Codes for On-chip Buses