Instantly decodable network codes for cooperative index coding problem over general topologies

In this paper, we study the problem of distributing a real-time video sequence to a group of partially connected cooperative wireless devices using instantly decodable network coding (IDNC). In such a scenario, the coding conflicts occur to service multiple devices with an immediately decodable packet, and the transmission conflicts occur from simultaneous transmissions of multiple devices. To avoid these conflicts, we introduce a novel IDNC graph that represents all feasible coding and transmission conflict-free decisions in one unified framework. Moreover, a real-time video sequence has a hard deadline and unequal importance of video packets. Using these video characteristics and the new IDNC graph, we formulate the problem of minimizing the mean video distortion before the deadline as a finite horizon Markov decision process (MDP) problem. However, the backward induction algorithm that finds the optimal policy of the MDP formulation has high modeling and computational complexities. To reduce these complexities, we further design a two-stage maximal independent set selection algorithm, which can efficiently reduce the mean video distortion before the deadline. Simulation results over a real video sequence show that our proposed IDNC algorithms improve the received video quality compared with the existing IDNC algorithms.

Instantly decodable network coding (IDNC) reduces the completion delay of packet retransmission for multicast services in wireless point-to-multipoint (PMP) networks. Compared with multicast services, multiple unicast services may be more common in PMP networks. Reducing completion delay using IDNC for multiple unicast services is still an open problem. According to the construction features of IDNC, we find that if some unicast retransmissions are combined as a retransmission group, IDNC benefits from network coding (NC) considerably, which increases retransmission efficiency. Based on this observation, we study the total completion delay of all these unicast transmissions with intersession NC. In this paper, we provide an intersession insight into the IDNC method. Specifically, we propose a framework that contains 1) a general solution to this minimum completion delay (MCD) problem, which is modeled as a bin-packing problem, and 2) a lower bound of completion delay for the MCD solution. Additionally, we provide a high-efficiency greedy algorithm to solve the MCD problem with low computational complexity. Simulation results demonstrate that the proposed method saves almost 43% retransmissions in PMP networks and makes 87.5% retransmission packets benefit from the NC transmission.

Most of Wireless Sensor Networks (WSNs) are usually deployed in hostile environments where the communications conditions are not stable and not reliable. Hence, there is a need to design an effective distributed schemes to enable the sensors cooperating in order to recover the sensed data. In this paper, we establish a novel cooperative data exchange (CDE) scheme using instantly decodable network coding (IDNC) across the sensor nodes. We model the problem using the cooperative game theory in partition form. We develop also a distributed merge-and-split algorithm in order to form dynamically coalitions that maximize their utilities in terms of both energy consumption and IDNC delay experienced by all sensors. Indeed, the proposed algorithm enables these sensors to self-organize into stable clustered network structure where all sensors do not have incentives to change the cluster he is part of. Simulation results show that our cooperative scheme allows nodes not only to reduce the energy consumption, but also the IDNC completion time.

In this paper, we propose a scheme of wireless multimedia network coded broadcast retransmission, based on Device-to-Device (D2D) communications, in which there are network coding conflicts and transmission conflicts between multiple terminal devices. For this reason, a novel instantly decodable network coding (IDNC) graph is constructed, where all the feasible coding and non-transmission collision cases are shown in the graph. Based on the constructed IDNC graph, we design the optimal broadcast strategy for batch transmission and sliding window transmission, and propose a heuristic maximum weight network coding selection algorithm (MWSA-NC) to reduce the complexity of the optimal search algorithm. The simulation results show that compared to the traditional scheme, the proposed algorithm can greatly improve the throughput of the system, reduce decoding latency and reduce video stream distortion.

We are concerned with designing feedback-based adaptive Instantly Decodable Network Coding (IDNC) schemes with the aim of minimizing retransmission times in wireless multicast and broadcast scenarios. In this paper, we first analyze the multiple factors influencing the transmission times and give the quantitative formula. Meantime, we introduce the concept of Cache-based Instantly Decodable Network Coding (C-IDNC) that the correctly received undecodable retransmission packets are waited in the cache for a future network decoding opportunity rather than delete. Then, we formulate the retransmission times minimization problem as an max-weight search problem and propose efficient algorithms for finding its optimal solution. Further, we propose a heuristic algorithms with worst case linear execution complexity based on sorting and iteration. Simulation results show that our proposed algorithms significantly reduce the IDNC retransmission times compared to previous works.

The traditional instantly decodable network coding (IDNC) schemes discard the non-instantly decodable packets (NIDPs), which results in the loss of useful information. In this letter, we consider a network coding scheme named as buffered instantly decodable network coding (B-IDNC) where each receiving node can cache the NIDPs containing two unreceived packets for subsequent network decoding, and give a decoding algorithm by utilizing the maximum decoding clique. The maximum decoding clique is defined as a subset of vertices in the IDNC graph, which can be decoded together. We approximate the average packet decoding delay minimization problem as the maximum weight encoding clique problem, and a heuristic algorithm named as maximum decoding clique based maximum weight vertex (MDC-MWV) searching algorithm is proposed to solve the approximated problem. Simulation results show that our proposed algorithm can reduce the average packet decoding delay compared with the conventional IDNC schemes.

This paper considers a heterogeneous network architecture wherein devices use two wireless interfaces to receive packets from the base station and to transmit or receive packets from other devices concurrently. For such a network architecture, this paper focuses on time-critical and order-constrained applications that require quick and reliable in-order decoding of the packets. This paper first introduces the dual delivery delay as a measure of degradation compared with the optimal in-order packet delivery to the devices. It then addresses the minimum delivery delay problem using instantly decodable network coding (IDNC). In particular, the dual interface IDNC graph is constructed to represent all feasible coding opportunities and conflict-free transmissions. Subsequently, the minimum delivery delay problem is shown to be equivalent to a maximum weight independent set selection problem over the dual interface IDNC graph. Simulation results demonstrate that the proposed IDNC algorithm effectively reduces the delivery delay as compared with the existing network coding algorithms. Especially, for a layered video transmission, the proposed solution provides a sequential delivering of video layers to individual devices.

The paper deals with a soft topological space which is dened over an initial universe set U with a xed set of parameters E . The main goal is to point out that any soft topological space is homeomorphic to a topological space $( E \times U, \tau )$ where $\tau$ is an arbitrary topology on the product $E \times U$ , consequently many soft topological notions and results can be derived from general topology. Furthermore, in many papers some notions are introduced by dierent ways and it would be good to give a unied approach for a transfer of topological notions to a soft set theory and to create a bridge between general topology and soft set theory.

In this paper, we investigate the use of instantly decodable network coding (IDNC) for improving two fundamental performance metrics, namely, the completion time (as a measure of throughput) and mean decoding delay, in multicast cooperative data exchange (CDE) systems, where a group of geographically close clients cooperate with each other to obtain their missing packets. Here, an IDNC scheme is used for the transmissions across these clients. We utilize the stochastic shortest path (SSP) technique to study the minimum mean completion time problem. However, since finding the optimum solution is intractable, we use the obtained formulation to draw some theoretical guidelines to heuristically find solutions that can efficiently reduce the completion time. Second, we formulate the minimum mean decoding delay problem as selecting the appropriate maximal clique over well-structured graphs at the clients, and in order to reduce its complexity, we propose a simple heuristic algorithm for it. The effectiveness of our proposed algorithms is verified through extensive simulations and comparisons with existing techniques.

This paper considers the problem of reducing the broadcast delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In D2D-enabled networks, devices help hasten the recovery of the lost packets of devices in their transmission range by sending network coded packets. To solve the problem, the different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. The joint optimization problem over the set of transmitting devices and the packet combinations of each is formulated. Due to the high complexity of finding the optimal solution, this paper focuses on cooperation without interference between the transmitting users. The optimal solution, in such interference-less scenario, is expressed using a graph theory approach by introducing the cooperation graph. Extensive simulations compare the decoding delay experienced in the Point to Multi-Point (PMP), the fully connected D2D (FC-D2D) and the more practical partially connected D2D (PC-D2D) configurations and suggest that the PC-D2D outperforms the FC-D2D in all situations and provides an enormous gain for poorly connected networks.

This paper investigates the delay minimization problem for instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In D2D enabled systems, users cooperate to recover all their missing packets. The paper proposes a game theoretic framework as a tool for improving the distributed solution by overcoming the need for a central controller or additional signaling in the system. The session is modeled by self-interested players in a non-cooperative potential game. The utility functions are designed so as increasing individual payoff results in a collective behavior which achieves both a desirable system performance in a shared network environment and the Nash equilibrium. Three games are developed whose first reduces the completion time, the second the maximum decoding delay and the third the sum decoding delay. The paper, further, improves the formulations by including a punishment policy upon collision occurrence so as to achieve the Nash bargaining solution. Learning algorithms are proposed for systems with complete and incomplete information, and for the imperfect feedback scenario. Numerical results suggest that the proposed game-theoretical formulation provides appreciable performance gain against the conventional point-to-multipoint (PMP), especially for reliable user-to-user channels.

We address the problem of joint path selection and rate allocation in multipath wireless streaming, in order to optimize a media specific quality of service. We leverage on the existence of multiple parallel wireless services, in order to enhance the received video quality at a wireless client. An optimization problem is proposed, aimed at minimizing a video distortion metric based on sequence-dependent parameters, and transmission channel characteristics, for a given wireless network infrastructure. Even if joint optimal path selection and rate allocation is in general an NP complete problem, an in-depth analysis of the media distortion evolution allows defining a low complexity optimal streaming strategy, under reasonable network assumptions. In particular, we show that a greedy allocation of rates along paths with increasing error probability leads to an optimal solution. We argue that a network path should not be chosen for transmission, unless all other available paths with lower error probability have been chosen. Moreover, the chosen paths should be used at their maximum end-to-end bandwidth. These results are demonstrated for both independent network paths, and non-disjoint channel segments, in generic network topologies. Simulation results showed that the optimal rate allocation carefully trades off total encoding/transmission rate, with the end-to-end transmission error probability and the number of chosen paths. In many cases, the optimal rate allocation provides more than 20% improvement in received video quality, compared to heuristic-based algorithms.

Stochastic network link transmission model

Recently, various pipeline parallelism strategies are proposed to tackle the scalability problem of training a large DNN model on a distributed system. However, most of the works focus on pipeline scheduling while lacking a general methodology to handle network partitioning and mapping to distributed systems with heterogeneous interconnection. In this work, we propose an efficient design flow, named Parmesan, to map the training of a large DNN onto a system with general device topology to maximize the throughput. Parmesan works in an end-to-end manner and solves the whole optimization problem in two phases. The first phase aims at producing well-balanced partitions, and the second phase works towards placing the DNN on devices connected by an arbitrary topology network, considering the heterogeneity of the interconnection bandwidth. We show that Parmesan speeds up the pipeline training throughput on systems with different GPU topologies and is able to handle the mapping problem for heterogeneously interconnected architectures. We believe our proposed general device topology mapping algorithm will provide valuable information for architecture designers and assist them in designing a more DNN-friendly architecture.

A dynamic disequilibrium interregional commodity flow model