Multiple Access Algorithms Without Feedback Using Combinatorial Designs

A new class of multiple access algorithms for systems without feedback is introduced and analyzed. A finite population of users is assumed, where each user transmits a packet
R
times within the next
N
time slots (and all packets have an equal length of one slot). To improve the performance achieved by randomly selecting these
R
slots, user codes are invoked such that any two users will only transmit simultaneously in at most one slot, i.e., 2-(
N
,
R
, 1) designs. We argue that in most cases, the set of user codes can be generated easily using cyclic designs and provide a method to select
T
user codes from the set of user codes
S_N,R
in case the user population consists of
T<|S_N,R|
users. We further demonstrate how larger populations, with
T>|S_N,R|
, can still benefit from these user codes in two different manners. Closed formulas that express the success probability of a packet are provided for all population setups. Finally, a comparison with the random selection strategy demonstrates the performance gain realized by the new multiple access algorithms and some engineering rules to optimize the performance are provided.