Forward collision resolution - A technique for random multiple-access to the adder channel

Consider M − HChoose P − T communications: T users or less, out of M potential users, are chosen at random to simultaneously transmit binary data over a common channel. A method for constructing codes that achieve error-free M − HChoose P − T communication over the noiseless Adder Channel (AC), at a nominal rate of 1/ T bits per channel symbol per active user, is described and an efficient decoding procedure is presented. The use of such codes is referred to as Forward Collision Resolution (FCR), as it enables correct decoding of collided messages without retransmissions. For any given T a code is available that yields a stable throughput arbitrarily close to 1 message/slot. Furthermore, if the occurrence of collisions is made known to the transmitters, such a throughput can be maintained for arbitrary T , T ≤ M as well. If such feedback is not available, and T is random, the probability of an unresolved collision is significantly smaller than the probability of a collision in an uncoded system, at comparable message-arrival and information rates. Haifa, December 10, 1992 ____________________________________ Parts of this paper were presented at the IT workshop at Bellagio, Italy, June 1987, under the title The Capacity of the Random Multiple-Access Channel is at least 1, Achievable by Forward Collision Resolution and at INFOCOM 89,under the title An Efficient Multiple-Access Method for the Binary Adder Channel. It incorporates work from the doctoral program of E. Plotnik.The work of I. Bar-David was supported by the Technion Fund for the Promotion of Research.