On parallel asynchronous communication codes

Abstract

A b~l r r~~l -I n a s y n c h r o n o u s b u s e s , t h e s e n d e r encodes a d a t a w o r d w i t h a c o d e w o r d f r o m a n u n o r d e r e d c o d e a n d t r a n s m i t s it o n t h e p a r a l l e l b u s lines. I n t h i s pap e r , some t r a n s m i s s i o n t i m e a n a l y s i s f o r t h e a b o v e parallel a s y n c h r o n o u s c o m m u n i c a t i o n scheme are p r e s e n t e d . It is proved that t h e average t r a n s m i s s i o n t i m e f o r a code w o r d is a s t r i c t l y increasing f u n c t i o n o f the weight, w , o f the c o d e w o r d a n d i t a p p r o a c h e s t h e w o r s t t r a n s m i s s i o n t i m e possible w h e n w goes to infinity. T h i s implies that the low w e i g h t c o d e s r e s u l t i n a f a s t e r i m p l e m e n t a t i o n o f the a b o v e c o m m u n i c a t i o n scheme.T h i s paper a l s o a n a l y z e s t h e t r a n s m i s s i o n t i m e p e r f o r m a n c e o f the r e c e n t l y introd u c e d p r o x i m i t y d e t e c t i n g codes; f u r t h e r , some efficient low c o n s t a n t w e i g h t code d e s i g n s are described.I n d e x terms: Asynchronous communication, delay-insensitive codes, unordered codes, constant weight codes, proximity detecting codes, low weight codes. Unordered codes [6], [3], [l], [2], are used to achieve parallel asynchronous communication in asynchronous busses in which the transmission time on each individual bus line may vary from line to line due to different shapes, lengths and physical states of the bus lines. Researchers in [6], (21, have modeled this communicationscheme as a situation in which the sender communicates with the receiver using n parallel tracks (the bus lines) by rolling marbles in the tracks. If the i-th component of the code word is a 1 then the sender rolls a marble in the i-th track of the bus. Because of the different topologies and physical states of the tracks, the amount of time a marble takes to travel from the source to the destination is unknown and may differ from track t o track or even from roll to roll. But it is non-negative and finite; namely, marbles eventually do arrive after they have been rolled onto a track. Since there is no clock telling the receiver when the code word has been received completely (namely, when all the l/marbles of the code word have reached the destination), the only way the receiver has to realize the complete reception of the code word is to make a membership test of the current word in the unordered code at the receiver end of the bus. For example, if the unordered code employed in the communication scheme is a constant weight w code of length n [4], the receiver can figure out the complete reception of the code word by checking, at the receiver end of the bus, that the current word has w 1's. Once complete reception is detected, the receiver sends an acknowledgment signal to the sender indicating that it is ready to receive the next code word.In the paper, we present some transmission time analysis for the above parall...