Index Codes with Minimum Locality for Three Receiver Unicast Problems

An index code for a broadcast channel with receiver side information is locally decodable if every receiver can decode its demand using only a subset of the codeword symbols transmitted by the sender instead of observing the entire codeword. Local decodability in index coding improves the error performance when used in wireless broadcast channels, reduces the receiver complexity and improves privacy in index coding. The locality of an index code is the ratio of the number of codeword symbols used by each receiver to the number message symbols demanded by the receiver. Prior work on locality in index coding have considered only single unicast and singleuniprior problems, and the optimal trade-off between broadcast rate and locality is known only for a few cases. In this paper we identify the optimal broadcast rate (including among non-linear codes) for all three receiver unicast problems when the locality is equal to the minimum possible value, i.e., equal to one. The index code that achieves this optimal rate is based on a clique covering technique and is well known. The main contribution of this paper is in providing tight converse results by relating locality to broadcast rate, and showing that this known index coding scheme is optimal when locality is equal to one. Towards this we derive several structural properties of the side information graphs of three receiver unicast problems, and combine them with information theoretic arguments to arrive at a converse

Locally Decodable Index Codes

An index code for broadcast channel with receiver side information is locally decodable if each receiver can decode its demand by observing only a subset of the transmitted codeword symbols instead of the entire codeword. Local decodability in index coding is known to reduce receiver complexity, improve user privacy and decrease decoding error probability in wireless fading channels. Conventional index coding solutions assume that the receivers observe the entire codeword, and as a result, for these codes the number of codeword symbols queried by a user per decoded message symbol, which we refer to as locality, could be large. In this paper, we pose the index coding problem as that of minimizing the broadcast rate for a given value of locality (or vice versa) and designing codes that achieve the optimal trade-off between locality and rate. We identify the optimal broadcast rate corresponding to the minimum possible value of locality for all single unicast problems. We present new structural properties of index codes which allow us to characterize the optimal trade-off achieved by: vector linear codes when the side information graph is a directed cycle; and scalar linear codes when the minrank of the side information graph is one less than the order of the problem. We also identify the optimal trade-off among all codes, including non-linear codes, when the side information graph is a directed 3-cycle. Finally, we present techniques to design locally decodable index codes for arbitrary single unicast problems and arbitrary values of locality.Comment: Accepted for publication in the IEEE Transactions on Information Theory. Parts of this manuscript were presented at IEEE ISIT 2018 and IEEE ISIT 2019. This arXiv manuscript subsumes the contents of arXiv:1801.03895 and arXiv:1901.0590

Instantly Decodable Network Coding: From Point to Multi-Point to Device-to-Device Communications

The network coding paradigm enhances transmission efficiency by combining information flows and has drawn significant attention in information theory, networking, communications and data storage. Instantly decodable network coding (IDNC), a subclass of network coding, has demonstrated its ability to improve the quality of service of time critical applications thanks to its attractive properties, namely the throughput enhancement, delay reduction, simple XOR-based encoding and decoding, and small coefficient overhead. Nonetheless, for point to multi-point (PMP) networks, IDNC cannot guarantee the decoding of a specific new packet at individual devices in each transmission. Furthermore, for device-to-device (D2D) networks, the transmitting devices may possess only a subset of packets, which can be used to form coded packets. These challenges require the optimization of IDNC algorithms to be suitable for different application requirements and network configurations. In this thesis, we first study a scalable live video broadcast over a wireless PMP network, where the devices receive video packets from a base station. Such layered live video has a hard deadline and imposes a decoding order on the video layers. We design two prioritized IDNC algorithms that provide a high level of priority to the most important video layer before considering additional video layers in coding decisions. These prioritized algorithms are shown to increase the number of decoded video layers at the devices compared to the existing network coding schemes. We then study video distribution over a partially connected D2D network, where a group of devices cooperate with each other to recover their missing video content. We introduce a cooperation aware IDNC graph that defines all feasible coding and transmission conflictfree decisions. Using this graph, we propose an IDNC solution that avoids coding and transmission conflicts, and meets the hard deadline for high importance video packets. It is demonstrated that the proposed solution delivers an improved video quality to the devices compared to the video and cooperation oblivious coding schemes. We also consider a heterogeneous network wherein devices use two wireless interfaces to receive packets from the base station and another device concurrently. For such network, we are interested in applications with reliable in-order packet delivery requirements. We represent all feasible coding opportunities and conflict-free transmissions using a dual interface IDNC graph. We select a maximal independent set over the graph by considering dual interfaces of individual devices, in-order delivery requirements of packets and lossy channel conditions. This graph based solution is shown to reduce the in-order delivery delay compared to the existing network coding schemes. Finally, we consider a D2D network with a group of devices experiencing heterogeneous channel capacities. For such cooperative scenarios, we address the problem of minimizing the completion time required for recovering all missing packets at the devices using IDNC and physical layer rate adaptation. Our proposed IDNC algorithm balances between the adopted transmission rate and the number of targeted devices that can successfully receive the transmitted packet. We show that the proposed rate aware IDNC algorithm reduces the completion time compared to the rate oblivious coding scheme

Signal design for Multiple-Antenna Systems and Wireless Networks

This dissertation is concerned with the signal design problems for Multiple Input and Multiple Output (MIMO) antenna systems and wireless networks. Three related but distinct problems are considered.The first problem considered is the design of space time codes for MIMO systems in the case when neither the transmitter nor the receiver knows the channel. We present the theoretical concept of communicating over block fading channel using Layered Unitary Space Time Codes (LUSTC), where the input signal is formed as a product of a series of unitary matrices with corresponding dimensionality. We show the channel capacity using isotropically distributed (i.d.) input signaling and optimal decoding can be achieved by layered i.d. signaling scheme along with a low complexity successive decoding. The closed form layered channel capacity is obtained, which serves as a design guideline for practical LUSTC. In the design of LUSTC, a successive design method is applied to leverage the problem of optimizing over lots of parameters.The feedback of channel state information (CSI) to the transmitter in MIMO systems is known to increase the forward channel capacity. A suboptimal power allocation scheme for MIMO systems is then proposed for limited rate feedback of CSI. We find that the capacity loss of this simple scheme is rather small compared to the optimal water-filling solution. This knowledge is applied for the design of the feedback codebook. In the codebook design, a generalized Lloyd algorithm is employed, in which the computation of the centroid is formulated as an optimization problem and solved optimally. Numerical results show that the proposed codebook design outperforms the existing algorithms in the literature.While it is not feasible to deploy multiple antennas in a wireless node due to the space limitation, user cooperation is an alternative to increase performance of the wireless networks. To this end, a coded user cooperation scheme is considered in the dissertation, which is shown to be equivalent to a coding scheme with the encoding done in a distributive manner. Utilizing the coding theoretic bound and simulation results, we show that the coded user cooperation scheme has great advantage over the non-cooperative scheme

Locally Decodable Index Codes

An index code for broadcast channel with receiver side information is locally decodable if each receiver can decode its demand by observing only a subset of the transmitted codeword symbols instead of the entire codeword. Local decodability in index coding is known to reduce receiver complexity, improve user privacy and decrease decoding error probability in wireless fading channels. Conventional index coding solutions assume that the receivers observe the entire codeword, and as a result, for these codes the number of codeword symbols queried by a user per decoded message symbol, which we refer to as locality, could be large. In this paper, we pose the index coding problem as that of minimizing the broadcast rate for a given value of locality (or vice versa) and designing codes that achieve the optimal trade-off between locality and rate. We identify the optimal broadcast rate corresponding to the minimum possible value of locality for all single unicast problems. We present new structural properties of index codes which allow us to characterize the optimal trade-off achieved by: vector linear codes when the side information graph is a directed cycle; and scalar linear codes when the minrank of the side information graph is one less than the order of the problem. We also identify the optimal trade-off among all codes, including non-linear codes, when the side information graph is a directed 3-cycle. Finally, we present techniques to design locally decodable index codes for arbitrary single unicast problems and arbitrary values of locality

Higher-rank Transmit Beamforming Using Space Time Block Coding

With the rapid development of wireless communications, there has been a massive growth in the number of wireless communications users and progressively more new high data rate wireless services will emerge. With these developments taking place, wireless spectral resources are becoming much more scarce and precious. As a result, research on spectrally efficient transmission techniques for current and future communication networks attracts considerable interest. As a promising multi-antenna communication technique, transmit beamforming is widely recognized as being able to improve the capacity of wireless systems without requiring additional spectral resources. In conventional (rank-one) beamforming, each user is served by a single beamformer. For certain transmit beamforming applications, the beamforming performance may be poor if the degrees of freedom in the conventional beamformer design become insufficient. The scope of this thesis is to address the beamforming performance degradation problems induced by the insufficient degrees of freedom in the beamformer design in certain practical scenarios. In this thesis, a fundamentally new idea of higher-rank (>1) transmit beamforming is proposed to improve the beamforming performance. Instead of a single beamformer assigned to each user, multiple beamformers are designed and correspondingly the degrees of freedom in the beamformer design are multiplied, i.e., the increase of the degrees of freedom consists in the increase of the number of design variables. To implement higher-rank beamforming, the central idea is to combine beamforming with different space time block coding (STBC) techniques. Conventionally, STBCs are used to exploit the transmit diversity resulting from the independent fading for different transmit antennas. However, the use of STBCs in the higher-rank beamforming approaches is not for the sake of transmit diversity, but for the sake of design diversity in the sense of degrees of freedom in the beamformer design. The single-group multicast beamforming problem of broadcasting the same information to all users is firstly considered in the thesis. It is assumed that the transmitter knows the instantaneous channel state information (CSI) which describes the short-term channel conditions of a communication link and can be estimated in modern communication systems. In the conventional approach, a single beamforming weight vector is designed to steer the common information to all users. In the case of a large number of users, the performance of the conventional approach usually degrades severely due to the limited degrees of freedom offered by a single beamformer. In order to mitigate this drawback, a rank-two beamforming approach is proposed in which two independent beamforming weight vectors are designed. In the rank-two beamforming approach, single-group multicast beamforming is combined with the two dimentional Alamouti STBC, and each user is simultaneously served with two Alamouti coded symbols from two beamformers. The degrees of freedom in the beamformer design are doubled and significant performance improvement is achieved. The multi-group multicast beamforming problem of transmitting the same information to users in the same group while transmitting independent information to users in different groups, is studied next in the thesis, also assuming that instantaneous CSI is available at the transmitter. The rank-two beamforming approach, originally devised for single-group multicasting networks that are free of multiuser interference, is extended to multi-group multicasting networks, where multiuser interference represents a major challenge. By combining multi-group multicast beamforming with Alamouti STBC, two independent beamforming weight vectors are assigned to each user and the degrees of freedom in the beamformer design are doubled resulting in drastically improved beamforming performance. Then, the multiuser downlink beamforming problem of delivering independent information to different users with additional shaping constraints is investigated in the thesis, also assuming instantaneous CSI at the transmitter. Additional shaping constraints are used to incorporate a variety of requirements in diverse applications. When the number of shaping constraints is large, the degrees of freedom in the beamformer design can be rather deficient. In order to address this problem, a general rank beamforming approach is proposed in which multiuser downlink beamforming is combined with high dimensional (>2) real-valued orthogonal space time block coding (OSTBC). In the general rank beamforming approach, the number of beamforming weight vectors for each user and the associated degrees of freedom in the beamformer design are multiplied by up to eight times, which lead to significantly increased flexibility for the beamformer design. Since instantaneous CSI can be difficult to acquire in certain scenarios, the use of statistical CSI describing the long-term statistical characteristics of the channel can be more practical in these scenarios. The rank-two beamformer designs based on instantaneous CSI can be straightforwardly applied in the case of statistical CSI. However, it is impossible to extend the general rank beamforming approach for the multiuser downlink beamforming problem with additional shaping constraints based on instantaneous CSI to the case of statistical CSI straightforwardly. Therefore, multiuser downlink beamforming with additional shaping constraints using statistical CSI at the transmitter is then studied and an alternative general rank beamforming approach is proposed in the thesis. In the general rank beamforming approach using statistical CSI, multiuser downlink beamforming is combined with quasi-orthogonal space time block coding (QOSTBC). The increased number of beamforming weight vectors and the associated degrees of freedom are much beyond the limits that can be achieved by Alamouti STBC in the beamformer design. Simulation results demonstrate that the proposed higher-rank transmit beamforming approaches can achieve significantly improved performance as compared to the existing approaches

Strategic Location Planning for Broadband Access Networks under Cooperative Transmission

To achieve a cost-effective network deployment, employing state-of-art technical advances provides a practical and effective way to enhance system performance and quality of service provisioning. Cooperative transmission has been recognized as one of the most effective paradigms to achieve higher system performance in terms of lower bit-error rate, higher throughput, larger coverage, more efficient energy utilization, and higher network reliability. This dissertation studies the location planning for the deployment of broadband access networks and explores the great potential of cooperative transmission in the context of single-cell cooperative relaying and multi-cell cooperative transmission, respectively. The placement problem is investigated in two categories of network deployment environment, i.e., an existing wireless access network and a perspective broadband access network, respectively. In an existing wireless access network, to solve some practical problems such as the requirements of capacity enhancement and coverage extension, relay stations (RSs) are introduced in the network architecture. We propose two optimization frameworks with the design objectives of maximizing cell capacity and minimizing number of RSs for deployment, respectively. Mathematical formulations are provided to precisely capture the characteristics of the placement problems. The corresponding solution algorithms are developed to obtain the optimal (or near-optimal) results in polynomial time. Numerical analysis and case studies are conducted to validate the performance benefits due to RS placement and the computation efficiency of the proposed algorithms. To deploy a new metropolitan-area broadband access network, we explore the integration of passive optical network (PON) and wireless cooperative networks (WCN) under the multi-cell cooperative transmission technology. An optimization framework is provided to solve the problem of dimensioning and site planning. The issues of node placement, BS-user association, wireless bandwidth and power breakdown assignment are jointly considered in a single stage to achieve better performance. We also propose a solution to the complex optimization problem based on decomposition and linear approximation. Numerical analysis and case studies are conducted to verify the proposed framework. The results demonstrate the performance gains and economic benefits. Given a set of network parameters, the proposed optimization frameworks and solutions proposed in this dissertation can provide design guidelines for practical network deployment and cost estimations. And the constructed broadband access networks show a more cost-effective deployment by taking advantage of the cooperative transmission technology