Abstract: Determining data availability is disclosed, including: performing a data availability challenge with respect to a claimer node to determine whether the claimer node stores at least some elements included in a base layer in a digital tree corresponding to a data entity; and publishing a first set of elements associated with the base layer of the digital tree and the data availability challenge. Furthermore, encoding auditing is disclosed, including: obtaining a first set of elements associated with a base layer of a digital tree corresponding to a data entity; and generating an encoding validity determination of the digital tree based at least in part on whether the first set of elements is usable to recover a second set of elements associated with the base layer of the digital tree.

Abstract: Verifying a set of remotely stored data is disclosed, including: requesting a first element corresponding to a first leaf in a base layer of a digital tree, wherein the digital tree corresponds to a set of remotely stored data; receiving the first element corresponding to the first leaf; and receiving a membership proof comprising a set of elements from one or more layers higher in the digital tree than the base layer of the digital tree, wherein the set of elements comprises a path from the first leaf to a root of the digital tree, wherein the set of elements is dependent on a plurality of additional leaves and wherein verification of the first element corresponding to the first leaf increases a level of confidence in an availability of the plurality of additional leaves.

Abstract: Verifying a set of remotely stored data is disclosed, including: requesting a first element corresponding to a first leaf in a base layer of a digital tree, wherein the digital tree corresponds to a set of remotely stored data; receiving the first element corresponding to the first leaf; and receiving a membership proof comprising a set of elements from one or more layers higher in the digital tree than the base layer of the digital tree, wherein the set of elements comprises a path from the first leaf to a root of the digital tree, wherein the set of elements is dependent on a plurality of additional leaves and wherein verification of the first element corresponding to the first leaf increases a level of confidence in an availability of the plurality of additional leaves.

Abstract: A method for calculating a given multivariate polynomial f(Xi) is provided. The multivariate polynomial f(Xi) is to be calculated for every Xi in a large dataset X=(X1, X2, . . . ; XK) in accordance with an S-resilient, A-secure, and T-private scheme where K is an integer enumerating the number of elements in the dataset X, S is the number of stragglers to be tolerated, A is the number of adversaries to be tolerated, and T is the number of colluding workers that to be tolerated. The method is implemented by a computer system that includes a master computing device and a plurality of worker computing devices. The working computing devices can include colluding workers, malicious computing devices, and straggler computing devices.

Abstract: A method for managing spectrum sharing in a wireless communication network includes identifying a set of users in the wireless communication network which shares a spectrum of communication, classifying the set of users into multiple subsets of users, and scheduling, within a given time slot, one subset of users among the multiple subsets of users to transmit and receive data at the same time so that the scheduled subset of users shares the spectrum of communication. The users in a subset are selected by comparing the desired channel strength with the sum of strengths of the strongest interference from that user and the strongest interference to that user, all values in dB scale.

Abstract: A method for controlling a first node transmitting a transmission message to a plurality of second nodes may be provided. The method includes dividing the transmission message into at least one sub-message, encoding the at least one sub-message to a data stream, determining a first transmission direction of the data stream toward at least one of the plurality of second nodes, based on a polynomial of a channel gain between the first node and the at least one of the plurality of second nodes, and transmitting the data stream to the at least one of the plurality of second nodes, based on the determined first transmission direction.

Abstract: A method and apparatus to control interference in a relay node are provided and include simultaneously receiving a symbol from source nodes, adjusting channel coefficients; and relaying the symbol to destination nodes with adjusted channel coefficients. The simultaneously receiving and the relaying are performed during a symbol transmission process between the source and destination nodes.

Abstract: A method and apparatus to control interference in a relay node are provided and include simultaneously receiving a symbol from source nodes, adjusting channel coefficients; and relaying the symbol to destination nodes with adjusted channel coefficients. The simultaneously receiving and the relaying are performed during a symbol transmission process between the source and destination nodes.

Abstract: A method for managing spectrum sharing in a wireless communication network includes identifying a set of users in the wireless communication network which shares a spectrum of communication, classifying the set of users into multiple subsets of users, and scheduling, within a given time slot, one subset of users among the multiple subsets of users to transmit and receive data at the same time so that the scheduled subset of users shares the spectrum of communication. The users in a subset are selected by comparing the desired channel strength with the sum of strengths of the strongest interference from that user and the strongest interference to that user, all values in dB scale.

Abstract: A method and apparatus to control interference in a relay node are provided and include simultaneously receiving a symbol from source nodes, adjusting channel coefficients; and relaying the symbol to destination nodes with adjusted channel coefficients. The simultaneously receiving and the relaying are performed during a symbol transmission process between the source and destination nodes.

Abstract: A method for controlling a first node transmitting a transmission message to a plurality of second nodes may be provided. The method includes dividing the transmission message into at least one sub-message, encoding the at least one sub-message to a data stream, determining a first transmission direction of the data stream toward at least one of the plurality of second nodes, based on a polynomial of a channel gain between the first node and the at least one of the plurality of second nodes, and transmitting the data stream to the at least one of the plurality of second nodes, based on the determined first transmission direction.