Inspired by group testing algorithms and the coded computation paradigm, we propose and analyze a novel multiple access scheme for detecting active users in large-scale networks. The scheme consists of a simple randomized detection algorithm that uses computation coding as intermediate steps for computing logical disjunction functions over the multiple access channel (MAC). First we show that given an efficient MAC code for disjunction computation the algorithm requires @math decision steps for detecting @math active users out of @math users. Subsequently we present a simple suboptimal code for a class of MACs with arbitrarily varying sub-gaussian noise that uniformly requires @math channel uses for solving the activity detection problem. This shows that even in the presence of noise an efficient detection of active users is possible. Our approach reveals that the true crux of the matter lies in constructing efficient codes for computing disjunctions over a MAC.
Computation over multiple-access channels, to the best of our knowledge, was first proposed for a special case in @cite_6 and later formalized for a more general setting in @cite_7 . A special case that has received much attention is the computation of the modulo sum of sources over multiple-access channels because it yields a more efficient approach to network coding which is called Physical Layer Network Coding @cite_3 . For the binary case, this can be viewed as computation coding for the logical Exclusive Or function. We, in contrast, need a computational channel code which computes logical disjunctions (or equivalently conjunctions).
@cite_3 @cite_7 @cite_6
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Multichannel communication in a wireless mesh network with routers having multiple radio interfaces significantly enhances the network capacity. Efficient channel assignment and routing is critical for realization of optimal throughput in such networks. In this paper, we investigate the problem of finding the largest number of links that can be activated simultaneously in a wireless mesh network subject to interference, radio and connectivity constraints. Our goal is to activate all such links and we present an interference aware channel assignment algorithm that realizes this goal. We show that the Link Interference Graph created by utilizing a frequently used interference model gives rise to a special class of graphs, known as overlapping double-disk (ODD) graphs. We prove that the Maximum Independent Set computation problem is NP-complete for this special class of graphs. We provide a Polynomial Time Approximation Scheme (PTAS) for computation of the Maximum Independent Set of an ODD graph. We use this PTAS to develop a channel assignment algorithm for a multiradio multichannel Wireless Mesh Network. We evaluate the performance of our channel assignment algorithm by comparing it with the optimal solution obtained by solving an integer linear program. Experimental results demonstrate that our channel assignment algorithm produces near optimal solution in almost all instances of the problem. In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference. We investigate channel-coded physical-layer network coding in a two-way relaying scenario, where the end nodes A and B choose their symbols, S_A and S_B, from a small non-binary field, F , and adopt a non-binary PSK modulation. The relay then directly decodes the network-coded combination aS_A+bS_B over F from the noisy received superimposed channel-encoded packets. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients (a,b). As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of (a,b). In this paper, we compare different mappings between F and the PSK constellation, and prove that many have identical performance in terms of frame error rate (FER). Moreover, we derive a lower bound on the performance of decoding the network-coded combinations. Simulation results show that if we adopt either i) concatenated Reed-Solomon and convolutional coding or ii) low-density parity check codes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the FER and, in particular, the ternary constellation has the best FER performance among all considered cases. The problem of reliably reconstructing a function of sources over a multiple-access channel (MAC) is considered. It is shown that there is no source-channel separation theorem even when the individual sources are independent. Joint source-channel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separation-based strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multiple-access channel with a joint source-channel lattice code. Finally, computation codes are used to determine the multicast capacity of finite-field multiple-access networks, thus linking them to network coding.