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Distributed storage systems and associated storage codes can efficiently store a large amount of data while ensuring that data is retrievable in case of node failure. The study of such systems, particularly the design of storage codes over finite fields, assumes that the physical channel through which the nodes communicate is error-free. This is not always the case, for example, in a wireless storage system. We study the probability that a subpacket is repaired incorrectly during node repair in a distributed storage system, in which the nodes communicate over an AWGN or Rayleigh fading channels. The asymptotic probability (as SNR increases) that a node is repaired incorrectly is shown to be completely determined by the repair locality of the DSS and the symbol error rate of the wireless channel. Lastly, we propose some design criteria for physical layer coding in this scenario, and use it to compute optimally rotated QAM constellations for use in wireless distributed storage systems.
In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper. By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based on the numerical computations, the average flatness factor not only bounds but also orders correctly the performance of different lattices.
Three transmission schemes over a new type of multiple-access channel (MAC) model with inter-source communication links are proposed and investigated in this paper. This new channel model is well motivated by, e.g., wireless distributed storage networks, where communication to repair a lost node takes place from helper nodes to a repairing node over a wireless channel. Since in many wireless networks nodes can come and go in an arbitrary manner, there must be an inherent capability of inter-node communication between every pair of nodes. Assuming that communication is possible between every pair of helper nodes, the newly proposed schemes are based on various smart time-sharing and relaying strategies. In other words, certain helper nodes will be regarded as relays, thereby converting the conventional uncooperative multiple-access channel to a multiple-access relay channel (MARC). The diversity-multiplexing gain tradeoff (DMT) of the system together with efficient sphere-decodability and low structural complexity in terms of the number of antennas required at each end is used as the main design objectives. While the optimal DMT for the new channel model is fully open, it is shown that the proposed schemes outperform the DMT of the simple time-sharing protocol and, in some cases, even the optimal uncooperative MAC DMT. While using a wireless distributed storage network as a motivating example throughout the paper, the MAC transmission techniques proposed here are completely general and as such applicable to any MAC communication with inter-source communication links.
The Compute-and-Forward relaying strategy aims to achieve high computation rates by decoding linear combinations of transmitted messages at intermediate relays. However, if the involved relays independently choose which combinations of the messages to decode, there is no guarantee that the overall system of linear equations is solvable at the destination. In this article it is shown that, for a Gaussian fading channel model with two transmitters and two relays, always choosing the combination that maximizes the computation rate often leads to a case where the original messages cannot be recovered. It is further shown that by limiting the relays to select from carefully designed sets of equations, a solvable system can be guaranteed while maintaining high computation rates. The proposed method has a constant computational complexity and requires no information exchange between the relays.
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as in the SISO case are derived. Further, explicit coset codes for Rayleigh fading MIMO wiretap channels are designed. In particular, it is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet our design criteria perform better than scalar multiples of the code lattice for the same parameters.
Abstract Au-Kline syndrome (AKS) is a neurodevelopmental disorder associated with multiple malformations and a characteristic facial gestalt. The first individuals ascertained carried de novo loss-of-function (LoF) variants in HNRNPK. Here, we report 32 individuals with AKS (26 previously unpublished), including 13 with de novo missense variants. We propose new clinical diagnostic criteria for AKS that differentiate it from the clinically overlapping Kabuki syndrome and describe a significant phenotypic expansion to include individuals with missense variants who present with subtle facial features and few or no malformations. Many gene-specific DNA methylation (DNAm) signatures have been identified for neurodevelopmental syndromes. Because HNRNPK has roles in chromatin and epigenetic regulation, we hypothesized that pathogenic variants in HNRNPK may be associated with a specific DNAm signature. Here, we report a unique DNAm signature for AKS due to LoF HNRNPK variants, distinct from controls and Kabuki syndrome. This DNAm signature is also identified in some individuals with de novo HNRNPK missense variants, confirming their pathogenicity and the phenotypic expansion of AKS to include more subtle phenotypes. Furthermore, we report that some individuals with missense variants have an “intermediate” DNAm signature that parallels their milder clinical presentation, suggesting the presence of an epi-genotype phenotype correlation. In summary, the AKS DNAm signature may help elucidate the underlying pathophysiology of AKS. This DNAm signature also effectively supported clinical syndrome delineation and is a valuable aid for variant interpretation in individuals where a clinical diagnosis of AKS is unclear, particularly for mild presentations.