Coding for delay-insensitive communication with partial synchronization

Assume that information is transmitted in parallel among many lines in such a way that an electrical transition represents a 1 and an absence of a transition represents a 0. The propagation delay in the wires varies and results in asynchronous reception. The challenge is to find an efficient communication scheme that will be delay-insensitive. One of the common solutions to this problem is to use a handshake mechanism. Namely, the transmitter sends the next vector only after getting an acknowledgment that the current vector was received. A natural question is: how does the receiver know that reception of the current vector is complete? This problem was solved by Verhoeff (1988) by using the so-called unordered codes. However, in practice, it is common that the communication lines are arranged in pairs (double-rail) such that the propagation delay on the lines within a pair is identical. In general, the lines can be arranged in groups (of size larger than 1) where transmission within a group is synchronized. The authors have created a few delay-insensitive schemes that take advantage of partial synchronization within groups. To achieve that, they have generalized to arbitrary alphabets the following known results: Sperner´s theorem on unordered sets, Henry-Knuth´s (Henry, 1982; Knuth, 1986) construction of balanced codes, and Berger´s (1961) construction of unordered codes. Finally, they have focused on practice, and constructed a code that uses double-rail channels but has the advantage that it is a rate ¾ code as opposed to the rate ½ double-rail code (that is the common code being used in real systems)