Device-to-Device (D2D) assisted coded caching is a promising approach to improve the communication efficiency over networks. However, the basic D2D coded caching scheme requires a subpacketization size that increases exponentially with the number of users. This is infeasible since the file size needs to be extremely large in the server. It is desirable to design a scheme that achieves a small subpacketization size while keeping the rate low. Recently, D2D placement delivery array (DPDA) was proposed to address the high subpacketization issue of D2D coded caching. This paper investigates the design of DPDA from the perspectives of linear algebraic and additive combinatorics. It is shown that a linear subspace possessing certain property can be employed in the design of DPDA. Based on this, a new D2D coded caching scheme with a subquadratic subpacketization size is derived through shortening the binary Reed-Muller codes. In order to obtain a D2D coded caching scheme with a linear subpacketization size, a new combinatorial structure called proper disjoint 3-term arithmetic progression (3-AP) free set is further introduced, and a deterministic algorithm for constructing it is provided with a polynomial complexity. Both the theoretical and numerical results reveal that the proposed schemes have a superior performance in terms of subpacketization size or transmission rate.

Symmetric multilevel diversity coding (SMDC) is a multi-source coding problem where the independent sources are ordered according to their importance. Prior work demonstrated thatsuperposition coding, where sources are encoded independently, is optimal. This paper investigates the(L,s)sliding secure SMDC problem, whereLrepresents the number of encoders andsis the security threshold. The security requirement dictates that each sourceXαmust be kept perfectly secure if no more than α –sencoders are accessible. The problem is specialized to the(L,s)multilevel secret sharingproblem when the firsts – 1sources are constants. Fors= 1, the two problems coincide, and we show that superposition coding is optimal. The rate regions for the(L,s)=(3,2)problems are characterized, which implies that superposition coding is suboptimal for the general case. The core insight for achieving lower rates through joint encoding is leveraging less important sources likeXα–1as secret keys for more important sources likeXα. Based on this idea, we propose a joint coding scheme that achieves the minimum sum rate of the general(L,s)multilevel secret sharing problem. Moreover, a pseudo-superposition coding scheme is proposed to achieve the minimum sum rate of the general sliding secure SMDC problem, which uses superposition coding for thessets of sourcesX1, X2,..., Xs–1, (Xs,Xs+1,XL)and joint coding amongXs,Xs+1,XL.

We propose in this paper to enhance the 5G low-density parity-check (LDPC) codes by transmitting the codewords in a block Markov superposition transmission (BMST) manner, resulting in a class of spatially coupled LDPC codes. We present a generalized extrinsic information transfer (EXIT) chart for performance analysis, showing that the decoding thresholds can be improved by increasing the memory size (coupled width)$m$. However, for m > 1, the receiver requires a relatively large window size for the sliding window decoding (SWD) algorithm, potentially causing unacceptable decoding latency. To address this issue, we propose an adaptive sliding window decoding (ASWD) algorithm, in which the decoding window size depends on the decoding state of the BMST system. The proposed EXIT chart analysis can also effectively guide the setting of the maximum decoding window in the ASWD algorithm, as well as the setting of the superposition fractions for the BMST-5G-LDPC system. Simulation results show that: 1) the ASWD algorithm can effectively reduce the average decoding window size in the medium to high signal-to-noise ratio (SNR) region, without the performance loss compared to the conventional SWD algorithm; 2) the proposed BMST-5G-LDPC code can achieve about 0.4, 0.5 and 1.7 dB performance gains compared to the 5G LDPC code over the AWGN channel, the fast fading channel, and the quasi-static block fading channel, respectively.

In remote or high-demand wireless cellular networks, efficient data collection from ground users (GUs) with fixed infrastructure poses a significant challenge. Unmanned aerial vehicles (UAVs) have emerged as a promising solution due to their flexible deployment and cost-effectiveness. This paper focuses on a UAV-aided wireless cellular communication system comprising a UAV and multiple adjacent GUs, where the mission of the UAV is to collect data from these GUs. The objective is to minimize UAV propulsion energy consumption while ensuring fair data uploading among all GUs. Due to the non-convex and intractable nature of the above problem, we propose a novel real-time waypoint localization method based on the parallel projection method from a geometric perspective. By enhancing the projection process, this approach achieves energy-efficient and fair data collection, along with an efficient trajectory design algorithm. Further, considering the scenario of densely distributed GUs in large-scale areas, a GU-clustering algorithm is proposed based on Mean Shift. Additionally, this paper categorizes GUs into homogeneous and heterogeneous scenarios and designs distinct trajectory designing algorithms to accommodate diverse real-world situations. Simulations and comparisons validate the effectiveness and efficiency of the proposed algorithms in tackling the UAV trajectory design challenges.

Federated learning (FL), as a distributed machine learning paradigm with privacy protection, has garnered significant attention since it prevents the exchange of raw local data. However, FL remains vulnerable to poisoning attacks, including data contamination and gradient manipulation. Moreover, attackers may launch individual or collusive attacks, complicating the identification of malicious clients. To address these challenges, we propose a universal poisoning defense framework incorporating three key strategies. First, we decouple client identities from gradients through anonymous obfuscation and enhance privacy with differential noise injection. Second, we detect potential detect potential collusive attackers via a joint similarity-based approach. Third, we apply an iterative low rank approximation-based anomaly detection to amplify discrepancies between benign and malicious clients and progressively filter out attackers. We theoretically demonstrate that anonymous obfuscation can enhance the privacy protection capability of differential privacy. Additionally, experimental results further validate that our scheme is comparable to or outperforms state-of-the-art defense methods against a variety of data and model poisoning attacks.

Symmetric multilevel diversity coding (SMDC) is a multi-source coding problem where the independent sources are ordered according to their importance. It was shown that sepa-rately encoding independent sources, referred to as superposition coding, is optimal. In this paper, an (L, s) sliding secure SMDC problem is considered, where$L$is the number of encoders and$s$is the security threshold, which means that each source$X$ais kept perfectly secure if no more than a -$s$encoders are accessible. It is shown that superposition coding is optimal for$s$= 1. The rate region for (L, s) = (3, 2) is characterized, which implies the suboptimality of superposition coding for the general problem. The main idea that joint coding can reduce rates is that we can use the previous source X a -1 as the secret key of X a. Based on this idea, a pseudo-superposition coding scheme is proposed to achieve the minimum sum rate, which uses superposition for the$s$sets of sources Xl, X2,‥ Xs-1, (Xs, Xs+1,”, XL). and joint encoding among Xs, Xs+1,”, XL.

Federated learning is a machine learning framework that facilitates training a shared model from distributed clients. However, challenges persist in optimizing communication efficiency. In this paper, we focus on hierarchical federated learning and model its global aggregation as a network function computation problem, where the central server desires to compute the arithmetic sum of the clients' gradients. Inspired by network coding, we propose two Coded Hierarchical Federated Learning (CHFL) approaches to enhance communication efficiency. The first approach, Separated CHFL (S-CHFL), involves transmitting divided segments separately to relays using a greedy algorithm. We establish the upper and lower bounds of the computing rate, showing that S-CHFL can achieve perfect balance in reverse combination network and reach the upper bound in certain networks. The second approach is Mixed CHFL (M-CHFL) where divided segments are mixed into linear combinations for transmission. We show that M-CHFL may be more efficient when data comes from a sufficiently large alphabet and analyze its upper bound for the computing rate.

To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The proposed method initially employs truncation to mitigate the impact of long-tail noise, followed by a non-uniform quantization of the post-truncation gradients based on their statistical characteristics. We provide a comprehensive convergence analysis of the quantized distributed SGD, establishing theoretical guarantees for its performance. Furthermore, by minimizing the convergence error, we derive optimal closed-form solutions for the truncation threshold and non-uniform quantization levels under given communication constraints. Both theoretical insights and extensive experimental evaluations demonstrate that our proposed algorithm outperforms existing quantization schemes, striking a superior balance between communication efficiency and convergence performance.

For current and future wireless communication networks, accurate Channel State Information (CSI) is pivotal for delivering high-quality services for countless devices. Traditional Channel Estimation (CE) methods grapple with channel aging, leading to inaccuracies. In contrast, we obtain the precise CSI by predicting channels based on neural networks, which have outstanding performance in feature extraction, data generation and prediction. Centralized Learning (CL) methods impose high demands on computational resources, storage and communication overhead. Moreover, it poses a risk to user data privacy. Consequently, we propose a Federated Learning-based Long Short Term Memory (FL-LSTM) Neural Network for real-time CSI prediction. We validate our model on the simulation dataset and measurement datasets. Simulation results show that our approach can predict the CSI data effectively, and its prediction performance approximates to Centralized Learning-based Long Short Term Memory (CL-LSTM) Neural Network. In addition, the global model is capable of generalization, which can be transferred to a new base station (BS) to accelerate the convergence of the local model and reduce the prediction error.

In this paper, we integrate the 5G low-density parity-check (LDPC) coded modulation systems with hybrid shaping, where the centroid-based geometric shaping is implemented to remedy the performance loss of the many-to-one probabilistic shaping. Taking into account the fact that the 5G parity-check matrices have an uneven density in different parts, we elaborately design a simple row-column interleaver for the bit-interleaved coded modulation with iterative decoding (BICM-ID) system to allocate the ambiguous bits caused by the many-to-one mapping to the sparser parity part, resulting in the hybrid shaping for BICM-ID (HS-BICM-ID) system. Numerical results have shown that the HS-BICM-ID can obtain shaping gains of about 0.5 dB and 1.4 dB compared to the constant composition distribution matching (CCDM) shaping and the geometric shaping, respectively, while it can obtain a shaping gain of about 1.7 dB compared to the scheme with uniform input. Our work has also shown that, at low and moderate spectral efficiency, the presented hybrid shaping can achieve a significant shaping gain and effectively remedy the performance loss of dyadic many-to-one probabilistic shaping.

Coded caching is an effective technique to reduce the data transmission load by exploiting the cache contents across the network. However, most coded caching schemes are designed for static networks that consist of only a placement phase and a delivery phase. In practice, a network maybe dynamic with multiple rounds of placement and delivery phases, and the number of users within the network may vary. In these dynamic networks, a conventional coded caching scheme may lead to the undesired updates at the existing users’ cache contents. This paper proposes a centralized coded caching scheme for dynamic networks that can support multiple rounds with newly joining users. It prevents cache contents of the existing users from being updated, extending the service duration of cache devices. Further recognizing the need of information security in coded caching, the considered dynamic networks are featured by two constraints: 1) the library files must be kept secure from a wiretapper who has access to the shared link; 2) any subset of users cannot obtain information from the demands of other users. This consideration leads to another dynamic coded caching scheme that ensures information security. It is shown that the proposed schemes can yield a small subpacketization level and achieve a good rate-memory tradeoff.

Coded caching is an effective technique to reduce the data transmission load by exploiting the cache contents across the network. However, most coded caching schemes are designed for static networks that consist of only a placement phase and a delivery phase among a constant number of users. In practice, a network maybe dynamic with multiple rounds of placement and delivery phases, and the number of users may vary. In such dynamic networks, a conventional coded caching scheme may lead to the undesired content updates at the users’ cache, which is caused by the newly joining users. This paper proposes a centralized coded caching scheme for dynamic networks that can support multiple rounds and accommodate the newly joining users during this process. It prevents cache contents of the existing users from being updated. It is shown that the proposed scheme can yield a reduced subpacketization level and achieve a good rate-memory tradeoff.

To address the potential traffic congestion in urban transportation systems, an intelligent dynamic Route Guidance System (RGS) is proposed, which calculates the road weights with real-time traffic flow predictions using the reinforcement learning method. Additionally, a training strategy is proposed for the Road Agents (RAs), which optimizes RA through interaction with the traffic environment. The effectiveness of the proposed method is verified through simulation on the Urban Mobility Simulation (SUMO) platform, and it is shown that the proposed method performs well in complex and changing urban traffic environments with different driver participation rates. Therefore, it provides a feasible solution to the congestion problem and will push forward the development of intelligent transportation systems.

The integration of sensing and communication (ISAC) using millimeter-wave (mmWave) attracted significant attentions recently in the research on Internet of Vehicles (IoV). While the ISAC technique offers advantages with increased bandwidth and improved time-frequency resolution, it encounters challenges in achieving accurate beam alignments, especially in highly dynamic scenarios. To enhance the accuracy of narrow beam alignment while mitigating the overhead in vehicular networks, this paper proposes an improved predictive beam tracking scheme based on the transceiver division structure and the bistatic radar theory. Specifically, the proposed scheme utilizes the ISAC echo signals to measure the vehicles' states and adopts an unscented Kalman filter (UKF) to reduce the overhead while ensuring the quality of service (QoS) in complicated road conditions. Simulation results show that the proposed scheme improves the prediction accuracy of angle of departure (AoD), which consequently ensures higher achievable communication rates in the IoV context.

In large-scale parallel computing systems, machines and the network suffer from non-negligible faults, often leading to system crashes. The traditional method to increase reliability is to restart the failed jobs. To avoid unnecessary time wasted on reboots, we propose an optimal scheduling strategy to enable fault-tolerant reliable computation to protect the integrity of computation. Specifically, we determine the optimal redundancy-failure rate tradeoff to incorporate redundancy into parallel computing units running multiple-precision arithmetics, like the Chinese Remainder Theorem, that are useful for applications such as asymmetric cryptography and fast integer multiplication. Inspired by network coding in distributed storage for disk failures, we propose coding matrices to strategically map partial computation to available computing units, so that the central unit can reliably reconstruct the results of any failed machine without recalculations to yield the final correct computation output. We propose optimization-based algorithms to efficiently construct the optimal coding matrices subject to fault tolerance specifications. Performance evaluation demonstrates that the optimal scheduling effectively reduces the overall running time of parallel computing while resisting wide-ranging failure rates.

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is important to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design of PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, four new coded caching schemes with a linear subpacketization level and a relatively small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.

Unmanned Aerial Vehicles (UAVs) can be used as aerial base stations for data collection in next-generation wireless networks due to their high adaptability and maneuverability. This paper investigates the scenario where multiple UAVs cooperatively fly over heterogeneous ground users (GUs) and collect data without a central controller. With the consideration of signal-to-interference-and-noise ratio (SINR) and fairness among users, we jointly optimize the trajectories of UAVs and the GUs associations to maximize the total throughput and energy efficiency. We formulate the long-term optimization problem as a decentralized partially observed Markov decision processes (DEC-POMDP) and derive an approach combining the coalition formation game (CFG) and multi-agent deep reinforcement learning (MADRL). We first formulate the discrete association scheduling problem as a non-cooperative theoretical game and use the CFG algorithm to achieve a decentralized scheme converging to Nash equilibrium (NE). Then, a MARL-based technique is developed to optimize the trajectories and energy consumption continuously in a centralized-training but decentralized-execution manner. Simulation results demonstrate that the proposed algorithm outperforms the commonly used schemes in the literature, regarding the fair throughput and energy consumption in a distributed manner.

Coded caching is an effective technique to utilize multicasting opportunities to reduce the data transmission load in cached networks. In such a scheme, each file in the data center or library is usually divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. Recently, a combinatorial structure called placement delivery array (PDA) was proposed as an effective tool to design coded caching schemes with a low subpacketization level. This paper proposes a novel PDA construction by selecting proper orthogonal arrays (POAs). It generalizes the existing construction, making it suitable to the scenario with a more flexible memory size. Based on the proposed PDA construction, a new coded caching scheme with the coded placement is further proposed. It is shown that the proposed schemes can yield a lower subpacketization level or transmission rate over the benchmark schemes.

Coded caching is an emerging technique to reduce the data transmission load during the peak-traffic times. In such a scheme, each file in the data center or library is divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user’s cache. However, the implementation complexity of this scheme increases with the number of packets. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. Recently, a combinatorial structure called placement delivery array (PDA) was proposed as an effective tool to design coded caching schemes with a relatively low subpacketization level. This paper proposes a novel PDA construction by selecting proper orthogonal arrays (POAs), which generalizes the existing construction but with a more flexible memory size. Based on the proposed PDA construction, an effective transform is further proposed to enable a coded caching scheme to achieve a smaller subpacketization level. Moreover, two new coded caching schemes with the coded placement are derived. It is shown that the proposed schemes can yield a lower subpacketization level or transmission rate over the benchmark schemes.

We propose an optimal scheduling strategy to enable fault-tolerant reliable computation to protect the integrity of computation. Specifically, we determine the optimal redundancy-failure rate tradeoff to incorporate redundancy into parallel computing units running multiple-precision arithmetic that are useful for applications such as asymmetric cryptography and fast integer multiplication. Inspired by network coding, we propose coding matrices to strategically map partial computation to available computing units, so that the central unit can reliably reconstruct the results of any failed machine without recalculations to yield the final correct computation output. We propose optimization-based algorithms to efficiently construct the optimal coding matrices subject to fault tolerance specifications. Performance evaluation demonstrates that the optimal scheduling effectively reduces the overall running time of parallel computing while resisting wide-ranging failure rates.

With the explosive development of big data, it is necessary to sort the data according to their importance or priorities. The sources with different importance levels can be modeled by the multilevel diversity coding systems (MDCS). Another trend in future communication networks, say 5G wireless networks and Internet of Things, is that users may obtain their data from all available sources, even from devices belonging to other users. Then, the privacy of data becomes a crucial issue. In a recent work by Li et al., the secure asymmetric MDCS (S-AMDCS) with wiretap channels was investigated, where the wiretapped messages do not leak any information about the sources (i.e. perfect secrecy). It was shown that superposition (source-separate coding) is not optimal for the general S-AMDCS and the exact full secure rate region was proved for a class of S-AMDCS. In addition, a bound on the key size of the secure rate region was provided as well. As a further step on the SAMDCS problem, this paper mainly focuses on the key size characterization. Specifically, the constraints on the key size of superposition secure rate region are proved and a counterexample is found to show that the bound on the key size of the exact secure rate region provided by Li et al. is not tight. In contrast, tight necessary and sufficient constraints on the secrecy key size of the counterexample, which is the four-encoder S-AMDCS, are proved.

The partially collaborative repair of multiple node failures in distributed storage systems is investigated. An exact-repair code is constructed using a bilinear form, which achieves the minimum-bandwidth partially collaborative repair (MBPCR) point. When the storage capacity is minimum, the problem of repairing multi-node failures using a Maximum Distance Separable (MDS) array code is also investigated. The minimum-storage partially collaborative repair (MSPCR) problem with same number of repairing and reconstruction nodes has been studied before. In this paper, the scenario where the number of repairing nodes is greater than that of reconstruction nodes and the storage capacity is already minimal for partial collaboration is considered. An MDS array code is constructed, which asymptotically achieves the MSPCR point. Further, we show that the given code construction could not always have a regular collaborative structure.

The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a target function, of which the inputs are generated at multiple source nodes. The edges in the network are assumed to be error-free and have limited capacity. The nodes in the network are assumed to have unbounded computing capability and be able to perform network coding. The computing rate of a network code that can compute the target function over the network is the average number of times that the target function is computed with zero error for one use of the network. In this paper, we obtain an improved upper bound on the computing capacity, which is applicable to arbitrary target functions and arbitrary network topologies. This improved upper bound not only is an enhancement of the previous upper bounds but also is the first tight upper bound on the computing capacity for computing an arithmetic sum over a certain non-tree network, which has been widely studied in the literature. We also introduce a multi-dimensional array approach that facilitates evaluation of the improved upper bound. Furthermore, we apply this bound to the problem of computing a vector-linear function over a network. With this bound, we are not only able to enhance a previous result on computing a vector-linear function over a network but also simplify the proof significantly. Finally, we prove that for computing the binary maximum function over the reverse butterfly network, our improved upper bound is not achievable. This result establishes that in general our improved upper bound is non-achievable, but whether it is asymptotically achievable or not remains open.

The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a target function, of which the inputs are generated at multiple source nodes. The computing rate of a network code that can compute the target function over the network is the average number of times that the target function is computed with zero error for one use of the network. In this paper, we obtain an improved upper bound on the computing capacity, which is applicable to arbitrary target functions and arbitrary network topologies. By applying this bound to the problem of computing a vector-linear function over a network, we are able to not only enhance a previous result on computing a vector-linear function over a network but also simplify the proof significantly. Finally, we prove that for computing the binary maximum function over the reverse butterfly network, our improved upper bound is not achievable. This result establishes that in general our improved upper bound is non achievable, but whether it is asymptotically achievable or not remains open.

The following model of network function computation in directed acyclic networks is considered: A sink node desires to compute correctly a target function with all possible inputs of the function generated at multiple source nodes. The network links have limited capacity and are error-free. The intermediate network nodes perform network coding without any computation bound. The computing rate is measured by the average number of times that the target function can be computed for one use of the network. Guang, Yang and Li recently proposed a general upper bound on the computing capacity that is tight for all the instances of the problem with known computing capacity in literature. In this paper, we show that their upper bound is not tight in general by explicitly characterizing the computing capacity of an example. Our technique can be extended to characterize upper bounds on the computing capacity of a general instance of the network function computing problem.

In the future communication applications, users may obtain their messages that have different importance levels distributively from several available sources, such as distributed storage or even devices belonging to other users. This scenario is the best modeled by the multilevel diversity coding systems (MDCS). To achieve perfect (information-theoretic) secrecy against wiretap channels, this paper investigates the fundamental limits on the secure rate region of the asymmetric MDCS (AMDCS), which include the symmetric case as a special case. Threshold perfect secrecy is added to the AMDCS model. The eavesdropper may have access to any one but not more than one subset of the channels but know nothing about the sources, as long as the size of the subset is not above the security level. The question of whether superposition (source separation) coding is optimal for such an AMDCS with threshold perfect secrecy is answered. A class of secure AMDCS (S-AMDCS) with an arbitrary number of encoders is solved, and it is shown that linear codes are optimal for this class of instances. However, in contrast with the secure symmetric MDCS, superposition is shown to be not optimal for S-AMDCS in general. In addition, necessary conditions on the existence of a secrecy key are determined as a design guideline.

Random linear network coding (RLNC) is a promising network coding solution when the network topology information is not fully available to all the nodes. However, in practice, nodes have partial knowledge of the network topology information. Motivated by this, we investigate the performance of RLNC and obtain different upper bounds on the failure probability of RLNC for the network constrained by different partial network topology information. These upper bounds not only improve the existing ones in the literature, but also show that the partial network topology information can bring benefits to the performance analysis of RLNC. On the other hand, it is observed that if more network topology information can be utilized, tighter upper bounds can be obtained, as expected. The upper bounds on two classical networks are compared for demonstration. To obtain a deeper understanding about the performance of RLNC, the asymptotic behavior of RLNC as the field size goes to infinity is also investigated.

Batched sparse (BATS) code is a promising technology for reliable end-to-end transmission in multi-hop wireless networks. One main research topic for BATS code is how to design an optimal inner code that is typically random linear network code. In this paper, this issue is focus on the number of transmissions from an end-to-end perspective. The problem is formulated as a mixed integer nonlinear programming (MINLP) problem with the objective of minimizing the total number of transmissions from source to destination. Subsequently, the inherent properties of inner codes are exploited to relax the integer restrictions by the means of the regularized incomplete beta function. As a result, a new nonlinear programming (NLP) problem is constructed. Solving the NLP problem provides a valid lower bound on the optimal solution, and, hence, is used as the performance measure for our heuristic. Furthermore, a centralized approximation approach is developed to solve our MINLP problem efficiently. The numerical results demonstrate that all solutions developed in the paper are near-optimal with a guaranteed performance bound.

Whether superposition (source separation) Is optimal for the asymmetric multilevel diversity coding systems (AMDCS) with perfect secrecy is answered in this paper by studying a non-trivial example. Threshold perfect secrecy is added to the AMDCS model. The eavesdropper may have access to any one but not more than one subset of the channels but can get nothing about the sources, as long as the size of the subset is not above the security level. The secure AMDCS (S-AMDCS) with five sources, four encoders and security level two is solved and it is shown that linear codes are optimal for this instance. However, in contrast with the secure symmetric multilevel diversity coding systems (S-SMDCS), superposition is shown to be not optimal for S-AMDCS in general from this counterexample.

In conventional distributed storage exact repair problems, all sources are reconstructed when the decoder has access to a certain number of encoders (disks). So, the underlying reconstruction network is equivalent to a single-source problem. This paper considers a variant of the exact repair problem, where the underlying reconstruction network is the independent distributed source coding problem, a type of multi-source problem. As the first non-trivial case with two sources and three encoders, the storage-repair tradeoff regions are proved for all the 33 instances, and it is shown that binary codes are optimal.

The rate regions of multilevel diversity coding systems (MDCSs), a sub-class of the broader family of multi-source multi-sink networks with special structure, are investigated in a systematic way. We enumerate all non-isomorphic MDCS instances with at most three sources and four encoders. Then, the exact rate region of every one of these more than 7000 instances is proven via computations showing that the Shannon outer bound matches with a custom constructed linear code-based inner bound. Results gained from these computations are summarized in key statistics involving aspects, such as the sufficiency of scalar binary codes, the necessary size of vector binary codes, and so on. Also, it is shown how to construct the codes for an achievability proof. Based on this large repository of rate regions, a series of results about general MDCS cases of arbitrary size that they inspired is introduced and proved. In particular, a series of embedding operations that preserve the property of sufficiency of scalar or vector codes is presented. The utility of these operations is demonstrated by boiling the thousands of MDCS instances for which scalar binary (superposition) codes are insufficient down to 12 (26) forbidden the smallest embedded MDCS instances.instances.

Recent algorithmic developments have enabled computers to automatically determine and prove the capacity regions of small hypergraph networks under network coding. A structural theory relating network coding problems of different sizes is developed to make the best use of this newfound computational capability. A formal notion of network minimality is developed, which removes components of a network coding problem that are inessential to its core complexity. Equivalence between different network coding problems under relabeling is formalized via group actions, an algorithm which can directly list single representatives from each equivalence class of minimal networks up to a prescribed network size is presented. This algorithm, together with rate region software, is leveraged to create a database containing the rate regions for all minimal network coding problems with five or fewer sources and edges, a collection of 744119 equivalence classes representing more than 9 million networks. In order to best learn from this database, and to leverage it to infer rate regions and their characteristics of networks at scale, a hierarchy between different network coding problems is created with a new theory of combinations and embedding operators.

The network function computation in directed acyclic networks is investigated in this paper. In such a network, a sink node desires to correctly compute a target function, of which all inputs are generated at multiple source nodes. The network links are assumed to be error-free and have limited capacity. The intermediate nodes can perform network coding. The computing rate of a network code is measured by the average number of times that the target function can be computed for one use of the network. In the paper, by using a cut-set partition approach to refine the equivalence classes associated with the inputs of the target function, a general upper bound on the network computing capacity is obtained, which is applicable to arbitrary target functions and network topologies. It is shown that this new upper bound is in general strictly better than the best existing one proposed by Huang, Tan and Yang.

We propose algorithms for finding extreme rays of rate regions achievable with vector linear codes over finite fields Fq, q ∈ {2, 3, 4} for which there are known forbidden minors for matroid representability. We use the idea of single element extensions (SEEs) of matroids and enumeration of non-isomorphic matroids using SEEs, to first propose an algorithm to obtain lists of all non-isomorphic matroids representable over a given finite field.We modify this algorithm to produce only the list of all non-isomorphic connected matroids representable over the given finite field. We then integrate the process of testing which matroids in a list of matroids form valid linear network codes for a given network within matroid enumeration. We name this algorithm, which essentially builds all matroids that form valid network codes for a given network from scratch, as network-constrained matroid enumeration.

Wireless data gathering networks are often tasked to gather correlated data under severe energy constraints. The use of simple channel codes with source-channel decoding can potentially provide good performance with low energy consumption. Here we consider progressive coding in multi-hop networks, where an intermediate node decodes its received noisy codewords. The estimated information is concatenated with the node's own information word and encoded; the resulting progressively-encoded codeword is then transmitted to the next node. In non-progressive coding, the node simply forwards the received noisy codewords along with its own encoded data. Here we compare the performance of two codes with low decoding complexity, Repeat-Accumulate (RA) and Low-Density Parity-Check (LDPC) codes, in combination with two progressive coding schemes. Progressive channel coding uses only channel decoding at the intermediate node, while progressive source-channel coding uses source-channel decoding, exploiting the probabilistic dependency of the information words (caused by the correlation structure of the data) jointly with the deterministic dependency induced by channel coding. Two decoding schemes are considered at the data center: channel decoding only and iterative source-channel decoding. In simulation experiments, we consider a line network topology with systematic RA and LDPC coding. Results show that progressive coding performs better than non-progressive coding, and RA codes perform better with lower computational complexity than LDPC codes, both for channel-decoding-only and iterative source-channel decoding.