In this paper, we propose a novel reservation system to study partition information and its transmission over a noise-free Boolean multiaccess channel. The objective of transmission is not to restore the message, but to partition active users into distinct groups so that they can, subsequently, transmit their messages without collision. We first calculate (by mutual information) the amount of information needed for the partitioning without channel effects, and then propose two different coding schemes to obtain achievable transmission rates over the channel. The first one is the brute force method, where the codebook design is based on centralized source coding; the second method uses random coding, where the codebook is generated randomly and optimal Bayesian decoding is employed to reconstruct the partition. Both methods shed light on the internal structure of the partition problem. A novel formulation is proposed for the random coding scheme, in which a sequence of channel operations and interactions induces a hypergraph. The formulation intuitively describes the transmitted information in terms of a strong coloring of this hypergraph. An extended Fibonacci structure is constructed for the simple, but nontrivial, case with two active users. A comparison between these methods and group testing is conducted to demonstrate the potential of our approaches.
A selection problem is among the basic communication primitives in networks. In this problem at most k participating stations have to broadcast successfully their messages. This problem is especially important in packet radio networks, where simultaneous transmissions of many neighbors result in interference among delivered messages. This work focuses on a single-hop radio networks with n-stations, also called a multiple access channel, and considers both static and dynamic versions of the selection problem. We construct a family of efficient oblivious deterministic protocols based on selectors, one of them with selection time cO(klog(n k)), and the second explicit construction with selection time cO(k polylog n). The first construction matches the lower bound Ω(klog(n k)) on deterministic oblivious selection, while the second one is the first known explicit construction better than Θ(k2). In the dynamic case we introduce the model of dynamic requests, called k-streams, which generalizes the static model and the dynamic requests with at most k participants. We prove that each oblivious deterministic protocol has latency Ω(k2 log k), and on the other hand we prove the existence of the oblivious deterministic protocol with latency cO(k2log n). In view of the existence of the randomized oblivious protocol with expected latency cO(klog(n k)), this shows that randomization is substantially better than determinism for dynamic setting. Selection problem can be applied to implement other communication primitives --- we demonstrate it in the example of broadcast problem in multi-hop ad-hoc radio networks. In particular, we design an adaptive deterministic protocol broadcasting in time cO(nlog D) in every D-hop radio network of n-stations.   Group testing was first proposed for blood tests, but soon found its way to many industrial applications. Combinatorial group testing studies the combinatorial aspect of the problem and is particularly related to many topics in combinatorics, computer science and operations research. Recently, the idea of combinatorial group testing has been applied to experimental designs, coding, multiaccess computer communication, done library screening and other fields. This book attempts to cover the theory and applications of combinatorial group testing in one place.   The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new information-theoretic perspective on group testing problems. We formulate the group testing problem as a channel coding decoding problem and derive a single-letter characterization for the total number of tests used to identify the defective set. Although the focus of this paper is primarily on group testing, our main result is generally applicable to other compressive sensing models. Selective families, a weaker variant of superimposed codes [KS64, F92, 197, CR96], have been recently used to design Deterministic Distributed Broadcast (DDB) protocols for unknown radio networks (a radio network is said to be unknown when the nodes know nothing about the network but their own label) [CGGPR00, CGOR00]. We first provide a general almost tight lower bound on the size of selective families. Then, by reverting the selective families - DDB protocols connection, we exploit our lower bound to construct a family of “hard” radio networks (i.e. directed graphs). These networks yield an O(n log D) lower bound on the completion time of DDB protocols that is superlinear (in the size n of the network) even for very small maximum eccentricity D of the network, while all the previous lower bounds (e.g. O(D log n) [CGGPR00]) are superlinear only when D is almost linear. On the other hand, the previous upper bounds are all superlinear in n independently of the eccentricity D and the maximum in-degree d of the network. We introduce a broadcast technique that exploits selective families in a new way. Then, by combining selective families of almost optimal size with our new broadcast technique, we obtain an O(Dd log3 n) upper bound that we prove to be almost optimal when d = O(n D). This exponentially improves over the best known upper bound [CGR00) when D, d = O(polylogn). Furthermore, by comparing our deterministic upper bound with the best known randomized one [BGI87] we obtain a new, rather surprising insight into the real gap between deterministic and randomized protocols. It turns out that this gap is exponential (as discovered in [BGI87]), but only when the network has large maximum in-degree (i.e. d = O(na), for some constant a > O). We then look at the multibroadcast problem on unknown radio networks. A similar connection to that between selective families and (single) broadcast also holds between superimposed codes and multibroadcast. We in fact combine a variant of our (single) broadcast technique with superimposed codes of almost optimal size available in literature [EFF85, HS87, I97, CHI99]. This yields a multibroadcast protocol having completion time O(Dd2 log3 n). Finally, in order to determine the limits of our multibroadcast technique, we generalize (and improve) the best known lower bound [CR96] on the size of superimposed codes. The tree algorithm, a new basic protocol for accessing a satellite channel by a large number of independent users, is considered. Previous multi-accessing techniques suffered from long delays, low throughput and or congestion instabilities. The ALOHA algorithm, for example, when applied to the Poisson source model, has a maximum throughput of .37 packets slot and is unstable. The tree protocol, under similar conditions, is stable, has a maximum average throughput of .43 and has respectable delay properties. In this protocol, the sources are assigned to the leaves of a tree graph. Message contentions are resolved by systematically moving from node to node through the tree, trying to determine the branches containing the conflicting users. It is shown that the tree protocol is a generalization of TDMA and that an optimum dynamic tree adaptively changes from an essentially random access protocol in light traffic to TDMA in heavy traffic. A major result is that if q . the probability that a user has a packet to transmit, is greater than 1 2 , then TDMA and the optimum tree protocol axe the same. If, on the other hand, q , then the optimum tree protocol is more efficient than TDMA. The maximum average throughput of a system consisting of the optimum tree protocol and a finite number of users is one packet slot. The tree protocol may be applied either to a direct access system or to a demand assignment access system. Consequently, an example is presented comparing the average delay properties of tree and TDMA protocols when applied to direct access and to reservation access systems. A binary superimposed code consists of a set of code words whose digit-by-digit Boolean sums (1 + 1 = 1) enjoy a prescribed level of distinguishability. These codes find their main application in the representation of document attributes within an information retrieval system, but might also be used as a basis for channel assignments to relieve congestion in crowded communications bands. In this paper some basic properties of nonrandom codes of this family are presented, and formulas and bounds relating the principal code parameters are derived. Finally, there are described several such code families based upon (1) q -nary conventional error-correcting codes, (2) combinatorial arrangements, such as block designs and Latin squares, (3) a graphical construction, and (4) the parity-check matrices of standard binary error-correcting codes. 