We propose a contention-based random-access protocol, designed for wireless networks where the number of users is not a priori known. The protocol operates in rounds divided into equal-duration slots, performing at the same time estimation of the number of users and resolution of their transmissions. The users independently access the wireless link on a slot basis with a predefined probability, resulting in a distribution of user transmissions over slots, based on which the estimation and contention resolution are performed. Specifically, the contention resolution is performed using successive interference cancellation which, coupled with the use of the optimized access probabilities, enables throughputs that are substantially higher than the traditional slotted ALOHA-like protocols. The key feature of the proposed protocol is that the round durations are not a priori set and they are terminated when the estimation contention-resolution performance reach the satisfactory levels.
In @cite_9 it was noted that the execution of SIC within the framed SA framework resembles the execution of the iterative belief-propagation (BP) decoding on erasure channel, enabling the application of theory and tools of codes-on-graphs. Following this insight, the author analyzed the convergence of the SIC using and-or tree arguments @cite_7 and obtained optimal repetition strategies in terms of maximizing throughput of the scheme. It was shown that the optimal repetition strategies follow the same guidelines used for encoding of left-irregular LDPC codes. In the asymptotic case when the number of users tends to infinity, both (logical) @math and @math tend to 1. Nevertheless, for the optimal performance, the number of slots in the frame is determined by the number of transmissions.
@cite_9 @cite_7
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Contention resolution diversity slotted ALOHA (CRDSA) is a simple but effective improvement of slotted ALOHA. CRDSA relies on MAC bursts repetition and on interference cancellation (IC), achieving a peak throughput T ≅ 0.55, whereas for slotted ALOHA T ≅ 0.37. In this paper we show that the IC process of CRDSA can be conveniently described by a bipartite graph, establishing a bridge between the IC process and the iterative erasure decoding of graph-based codes. Exploiting this analogy, we show how a high throughput can be achieved by selecting variable burst repetition rates according to given probability distributions, leading to irregular graphs. A framework for the probability distribution optimization is provided. Based on that, we propose a novel scheme, named irregular repetition slotted ALOHA, that can achieve a throughput T ≅ 0.97 for large frames and near to T ≅ 0.8 in practical implementations, resulting in a gain of 45 w.r.t. CRDSA. An analysis of the normalized efficiency is introduced, allowing performance comparisons under the constraint of equal average transmission power. Simulation results, including an IC mechanism described in the paper, substantiate the validity of the analysis and confirm the high efficiency of the proposed approach down to a signal-to-noise ratio as a low as Eb N0=2 dB. We introduce a new set of probabilistic analysis tools based on the analysis of And-Or trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, including random loss-resilient codes, solving random k-SAT formula using the pure literal rule, and the greedy algorithm for matchings in random graphs. In addition, these tools allow generalizations of these problems not previously analyzed to be analyzed in a straightforward manner. We illustrate our methodology on the three problems listed above