Broadcast Rate Research Articles

Rush skeletonweed (Chondrilla juncea) control and winter wheat injury with picloram applied in fallow

AbstractRush skeletonweed is an invasive weed in the winter wheat–fallow production regions of the inland Pacific Northwest. The objectives of this study were to determine the dose response of rush skeletonweed to picloram applied in the fall or spring of the fallow year with either a broadcast or weed-sensing sprayer, and to evaluate injury and grain yield in the subsequent winter wheat crop from these fallow treatments. Field studies were conducted between 2019 and 2022. Fall treatments were applied at one site in 2019, and one site in 2020. Spring treatments were applied at two sites in 2021. Four picloram herbicide rates (0, 140, 280, and 560 g ae ha−1), were applied with either a weed-sensing precision applicator or with a standard broadcast spray applicator. Rush skeletonweed densities in the wheat crop following fall-applied treatments declined with increasing picloram rates at both sites. Treatments applied with the weed-sensing sprayer achieved similar efficacy to broadcast treatments with an average of 37% and 26% of the broadcast rate applied. Spring-applied broadcast treatments resulted in reduced rush skeletonweed densities in wheat with increasing picloram rates. Picloram rate had no apparent effect on rush skeletonweed density when applied in the spring with a weed-sensing sprayer; however, the weed-sensing sprayer applied just 16% and 9% of the broadcast rate. Winter wheat grain yields were not reduced by fall picloram applications. Grain yields were not reduced by spring applications of picloram with the weed-sensing sprayer; however, grain yields were reduced by spring broadcast applications of picloram at both locations, and grain yields declined as the picloram rate increased. Applying picloram in the fall of the fallow phase with a weed-sensing sprayer provides effective and economical control of rush skeletonweed with a low risk for crop injury and yield loss in the following winter wheat crop.

Experimenting and Optimizing Design Parameters for a Pneumatic Hill-Drop Rapeseed Metering Device

The planter plate is the most important component of the pneumatic hill-drop seed metering system for rapeseed. The structural parameters of the planter plate are the primary determinants of rape planting. The key structural and operational parameters, such as the layout of the suction hole, its diameter, and its shape, were determined through theoretical analysis. Fluent is used to simulate the flow field of various types of suction holes, and the effect of suction hole shape on the change in the flow field of the suction chamber shell is analyzed. Under the same boundary conditions, the results indicate that the maximum velocity of the end face of the horn hole and the average pressure of the section are the highest. Using a high-speed camera, the effects of suction hole diameter and shape on seed filling performance were studied, and the results of Fluent simulation analysis were validated. The optimal seed metering device operating parameters were as follows: planter plate speed of 30–70 r/min and negative pressure of −2.5–−1.5 kPa. The influence of working negative pressure and the rotational speed of the planter plate on seed arrangement performance was studied within the optimal operating parameter range. In order to improve the performance of rational close planting in the seed planter, the multi-objective optimization design of working parameters and the verification test were also conducted. The results showed that with the best combination of working parameters, the empty broadcast rate does not go above 3%, the hole number qualified rate does not go below 96%, and the difference between them and the theoretical optimization result does not go above 5.5%.

Real-Time Precise DGNSS/INS Integrated Relative Positioning with High Output Rate and Low Broadcast Rate for Kinematic-to-Kinematic Applications

High-output-rate relative positions are required for high-speed safety-critical kinematic-to-kinematic applications such as pre-crash sensing and shipboard landing. We propose a real-time, high-output-rate relative positioning method based on the integration of a real time kinematic (RTK) differential global navigation satellite systems (DGNSS) relative positioning algorithm, carrier-phase-based tightly coupled GNSS/Inertial navigation system (TC-GNSS/INS) integration algorithm and polynomial prediction algorithm for position increment. We focus on the rarely studied issue that data broadcast rates and sampling rates have effects on the integrated relative positioning accuracy under different motion states of a moving base. A vehicle-to-vehicle field test with a frequently turning base demonstrates the advantages of the proposed method, such as low bit rate of broadcast data, high output rate of position solutions and excellent real-time tolerance of latency. The results show that compared with the 10-Hz output of sole RTK DGNSS relative positioning, the proposed method can provide centimeter-level-accuracy relative positions at an output rate of 125 Hz with a sampling rate of 1 Hz, and the bit rate can be reduced by 83.12%. A UAV-to-boat field test with straight-line-motion moving base is then carried out to validate the applicability of the proposed system for aircraft applications. The results show that the broadcast rate of position increments of the moving base can be further reduced.

Efficient Reinforcement Learning-Based Transmission Control for Mitigating Channel Congestion in 5G V2X Sidelink

Channel congestion has been an open challenge for vehicular networks due to the limited resource of communication channels. Explosion of channel access requests from a massive number of transmitter vehicles can exhaust bandwidth and then degrade transmission quality. The rapid drop of messages (because of the high bit error rate in the transmission congestion condition) can threaten the safety of connected vehicles. Maintaining congestion-free communications is then essential to improve the reliability for vehicular networks, including Cellular-V2X (C-V2X)-based cooperative intelligent transport systems and road-safety applications. In this work, we present a novel intelligent transmission control model, namely DEEPCUT, to automatically adjust the message broadcasting rate of a transmitter vehicle. DEEPCUT works based on a Double Deep Q-learning Networks with Prioritized Experience Relay framework. DEEPCUT encourages the transmitter vehicle to (1) reduce its broadcasting rate if the vehicle is maintaining a safe distance from its neighbors and (2) increase the rate if the vehicle is approaching the others at a high-risk distance, all done by using reward/punish strategies. The evaluation results show that DEEPCUT can cut up 16% redundant data while increasing 22% packet reception rate compared with baseline models, particularly in crowd vehicular communications. Our risk-based transmission control can be an excellent complement to address the congestion when the channel cannot satisfy every vehicle’s resource requests. At best, the risk assessment-based approach in our congestion control method can provide a novel material to enhance Decentralized Congestion Control (DCC) for 5G V2X sidelink in the coming specifications.

An Update-Based Maximum Column Distance Coding Scheme for Index Coding

In this paper, we propose a new scalar linear coding scheme for the index coding problem called update-based maximum column distance (UMCD) coding scheme. The central idea in each transmission is to code messages such that one of the receivers with the minimum size of side information is instantaneously eliminated from unsatisfied receivers. One main contribution of the paper is to prove that the other satisfied receivers can be identified after each transmission, using a polynomial-time algorithm solving the well-known maximum cardinality matching problem in graph theory. This leads to determining the total number of transmissions without knowing the coding coefficients. Once this number and what messages to transmit in each round are found, we then propose a method to determine all coding coefficients from a sufficiently large finite field. We provide concrete instances where the proposed UMCD coding scheme has a better broadcast performance compared to the most efficient existing coding schemes, including the recursive scheme (Arbabjolfaei and Kim, 2014) and the interlinked-cycle cover (ICC) scheme (Thapa <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2017). We prove that the proposed UMCD coding scheme performs at least as well as the MDS coding scheme in terms of broadcast rate. By characterizing two classes of index coding instances, we show that the gap between the broadcast rates of the recursive and ICC schemes and the UMCD scheme grows linearly with the number of messages. Then, we extend the UMCD coding scheme to its vector version by applying it as a basic coding block to solve the subinstances.

Pushing against the boundaries: Entertaining impoliteness and taboo discourse in the Egyptian TV showAbla Fahita

AbstractImpoliteness can be defined as the use of “communicative strategies” which are “designed to attack face, and thereby cause social conflict and disharmony” (Culpeper et al. 2003, 1564). The present study applies Jonathan Culpeper’s (2011a) model of “impoliteness” supplemented by the notions of jocular mockery, jocular abuse, and recipients’ responses (Bousfield 2008, 2010, Haugh and Bousfield 2012) to the Egyptian TV show Abla Fahita. Abla Fahita (Egyptian Arabic: أبلة فاهيتا‎ [ʾabla fāhīta]) is a puppet character that has regularly appeared on Egyptian television since 2011. The show is hugely popular and has been phenomenally successful, being watched on average by millions, according to the Egyptian Centre for Research on Public Opinion. It should be noted, however, that, due to the conservative nature of Egyptian culture, Abla Fahita and other similar TV shows are considered to violate Egyptian politeness standards radically. Hence, such shows have been condemned as degrading and of low moral standards and have been accused of causing a deterioration in the standards of Egyptian public taste. Despite all denunciations, Abla Fahita still enjoys a huge audience and dominates broadcast ratings. Part of the show’s popularity can be ascribed to its characteristic impoliteness, particularly Abla Fahita’s off-beat expressions in mocking her guests and her use of sexual innuendo, which is seen as entertaining by many viewers. The study, which reveals thatAbla Fahitaemploys what can be called a humorous-impoliteness formula to entertain viewers, is an attempt to apply contemporary Impoliteness Theory across cultures, and to Colloquial Egyptian Arabic in particular.

Using internal context to detect automotive controller area network attacks

The rise in data use within cars has led to concerns about their cybersecurity. The Controller Area Network (CAN) enables communication between components core to the car’s safety and performance, and has been demonstrated to be particularly vulnerable to hacking and malicious cyber-intrusion. CAN intrusion detection systems have been envisaged. Signatures of known attacks might be used for detection, but this method holds many limitations. Although some attacks might change packet broadcast rates or add unknown packets onto the network, attacks that have little or no effect on these, yet can alter the packet data, have also been devised. We therefore test three novelty detection methods (Local Outlier Factor, Compound Classifier and One-Class Support Vector Machine) that might identify an attack based solely on anomalies in CAN packet field data-values. The methods compare values across a cluster of CAN packets broadcast from different control units, so potentially could identify an attacked control unit even when its subsequent fabricated payload data-values remain plausible. We test the methods on data from two different makes of car across a range of manipulation magnitudes, reflecting the unpredictability of attacks. Different training regimes are tested, enabling us to assess validity across journeys. We also consider the processes needed to determine the CAN fields that might be included in the intrusion detection cluster, and present algorithms for automating those processes.

Theoretical Broadcast Rate Optimization for V2V Communications at Intersection

Cooperative vehicle safety (CVS) systems have been receiving significant attention as key enablers of important intelligent transportation system (ITS) applications, such as cooperative collision warning, emergency braking, and auto driving. In CVS systems, vehicles periodically broadcast short packets that include various types of vehicular information, e.g., position and speed. In this paper, we propose an optimization method for the broadcast rate in vehicle-to-vehicle (V2V) broadcast communications at an intersection based on theoretical analysis. We consider a model in which the locations of vehicles are modeled separately as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">queuing</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">running</i> segments and derive key performance metrics of V2V broadcast communications through a stochastic geometry approach. We develop <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-form</i> approximate formulas for the theoretical expressions because they are mathematically intractable. Based on approximate analysis, we optimize the broadcast rate such that the interference at an intersection is mitigated and the overall performance of V2V communications is maximized. Because of the closed-form approximation, the optimal rate can be used as a guideline for a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real-time</i> control-method, which cannot be achieved through time-consuming simulations. We evaluate our method through numerical examples and demonstrate its effectiveness.

Risk-Based Transmission Control for Mitigating Network Congestion in Vehicle-to- Everything Communications

Vehicle-to-Everything (V2X) communication technologies and High-definition (HD) maps are essential to improve the safety of vehicles in areas with limited visibility. V2X- enabled vehicles use periodic beacon messages to update each other on their moving state (position, velocity, heading). However, due to the limited resources of V2X wireless channels, the explosion of data pouring into the network (e.g., from a crowded group of connected vehicles) can exhaust bandwidth and cause severe network congestion. Consequently, the rapid drop of sharing messages can threaten the safety of connected vehicles due to lost tracking. In this work, we present an efficient risk-based transmission control model, namely RTC+, to automatically control the time interval for broadcasting beacon messages of the connected vehicles in V2X networks. RTC+ works at the application layer to minimize interference with algorithms in the low layers (e.g., MAC). Two new algorithms are proposed in RTC+. The first one is RiskSCAN, a robust risk management algorithm to check and determine whether a vehicle suffers the risk of a potential collision with its neighbors. The second is RateCONTR, an adaptive broadcasting rate control to adjust the time interval of sharing messages, particularly when bandwidth is limited to serve all channel requests. The evaluation results show that RTC+ can significantly increase 25% of packet delivery rate while mitigating the collision threats compared with the default time interval in current vehicular network settings.

Broadcast Approach for the Information Bottleneck Channel

This work considers a layered coding approach for efficient transmission of data over a wireless block fading channel without transmitter channel state information (CSI), which is connected to a limited capacity reliable link, known as the bottleneck channel. Two main approaches are considered, the first is an oblivious approach, where the sampled noisy observations are compressed and transmitted over the bottleneck channel without having any knowledge of the original information codebook. The second approach is a non-oblivious decode-forward (DF) relay where the sampled noisy data is decoded, and whatever is successfully decoded is reliably transmitted over the bottleneck channel. The bottleneck channel from relay to destination has a fixed capacity $C$ . We examine also the case where the channel capacity can dynamically change due to variable loads on the backhaul link. The broadcast approach is analyzed for cases that only the relay knows the available capacity for next block, and for the case that neither source nor relay know the capacity per block, only its capacity distribution. Fortunately, it is possible to analytically describe in closed form expressions, the optimal continuous layering power distribution which maximizes the average achievable rate. Numerical results demonstrate the achievable broadcast rates.

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.

Capacity Theorems for Distributed Index Coding

In index coding, a server broadcasts multiple messages to their respective receivers, each with some side information that can be utilized to reduce the amount of communication from the server. Distributed index coding is an extension of index coding in which the messages are broadcast from multiple servers, each storing different subsets of the messages. In this paper, the optimal tradeoff among the message rates and the server broadcast rates, which is defined formally as the capacity region, is studied for a general distributed index coding problem. Inner and outer bounds on the capacity region are established that have matching sum-rates for all 218 non-isomorphic four-message problems with equal link capacities for all the links from servers to receivers. The proposed inner bound is built on a distributed composite coding scheme that outperforms the existing schemes by incorporating more flexible decoding configurations and enhanced fractional rate allocations into two-stage composite coding, a scheme that was originally introduced for centralized index coding. The proposed outer bound is built on the polymatroidal axioms of entropy, as well as functional dependences such as the $\rm{fd}$-separation introduced by the multi-server nature of the problem. This outer bound utilizes general groupings of servers with different levels of granularity, which allows a natural tradeoff between computational complexity and tightness of the bound, and includes and improves upon all existing outer bounds for distributed index coding. Specific features of the proposed inner and outer bounds are demonstrated through concrete examples with four or five messages.

Rate response of select grass weeds to pinoxaden

AbstractPinoxaden is a POST acetyl coenzyme A carboxylase (ACCase) inhibitor in the phenylpyrazolin chemical family and is labelled for turfgrass use at broadcast rates of 35.5 to 71 g ai ha−1and spot spray rates of 156 to 310 g ai ha−1. A greenhouse rate-response study was conducted to characterize the efficacy of pinoxaden against common grassy weeds. Weed species examined in this study were yellow foxtail, southern sandbur, annual bluegrass, roughstalk bluegrass, large crabgrass, dallisgrass, bahiagrass, goosegrass, and perennial ryegrass. Nonlinear regressions were modelled to determine visible injury rates (the application rate at which 50% of the weed species were injured and the 90% [I90] rate) and weight reduction rates (the application rate at which there was a 50% reduction in fresh weight and 90% reduction [WR90]) for each weed species. Only annual bluegrass, bahiagrass, and goosegrass had visible injury I90values greater than the maximum labelled spot spray rate of 310 g ai ha−1. Annual bluegrass, bahiagrass, southern sandbur, and goosegrass all had WR90values greater than the maximum labelled spot spray rate of 310 g ai ha−1. Results from this study indicate that the evaluated weed species can be ranked, according to visible injury I90values, from most to least susceptible: perennial ryegrass &gt; yellow foxtail &gt; dallisgrass &gt; large crabgrass &gt; southern sandbur &gt; roughstalk bluegrass &gt; bahiagrass &gt; goosegrass &gt; annual bluegrass.

The characteristics of videos on demand for television programs and the determinants of their viewing patterns: Evidence from the Korean IPTV market

Korea's video-on-demand (VOD) market is led by pay TV service providers, especially internet protocol television (IPTV) service providers, and VODs for television programs (TV-VOD) represent the largest share of VOD in the country. TV-VOD is therefore of strategic importance to providers in terms of their current sales share and future growth. Focusing on the time-shift characteristics of TV-VOD and the serial complementarity of television programs, this study examines how various factors such as the characteristics of paid vs. free VOD services, and the average and variance of broadcast ratings affect VOD viewing patterns. An empirical analysis was conducted using data for TV-VODs of all television programs broadcast by major Korean broadcasters in 2015. The key findings are as follows: (1) There is an inverted-U shape relationship between broadcast ratings and TV-VOD views. This implies that there exists a positive window effect between the original broadcast and TV-VOD, with an exceptional substitution effect in segments with very high ratings. (2) Even if the average ratings are similar, there are more VOD views for programs that have a large fluctuation in ratings between episodes, mainly due to serial complementarity. (3) In terms of the distribution of VOD views over time, the initial concentration is higher in paid VOD packages and dramas, which implies that immediate decay appears for TV-VOD content because of subscriber preferences for novelty and the serial nature of drama shows. The study concludes with various implications for VOD service providers and policy makers.

Non-Orthogonal Unicast and Broadcast Transmission via Joint Beamforming and LDM in Cellular Networks

Limited bandwidth resources and higher energy efficiency requirements motivate incorporating multicast and broadcast transmission into the next-generation cellular network architectures, particularly for multimedia streaming applications. Layered division multiplexing (LDM), a form of non-orthogonal multiple access (NOMA), can potentially improve unicast throughput and broadcast coverage with respect to traditional orthogonal frequency division multiplexing (FDM) or time division multiplexing (TDM), by simultaneously using the same frequency and time resources for multiple unicast or broadcast transmissions. In this paper, the performance of LDM-based unicast and broadcast transmission in a cellular network is studied by assuming a single frequency network (SFN) operation for the broadcast layer, while allowing arbitrarily clustered cooperation among the base stations (BSs) for the transmission of unicast data streams. Beamforming and power allocation between unicast and broadcast layers, the so-called injection level in the LDM literature, are optimized with the aim of minimizing the sum-power under constraints on the user-specific unicast rates and on the common broadcast rate. The effects of imperfect channel coding and imperfect channel state information (CSI) are also studied to gain insights into robust implementation in practical systems. The non-convex optimization problem is tackled by means of successive convex approximation (SCA) techniques. Performance upper bounds are also presented by means of the S-procedure followed by semidefinite relaxation (SDR). Finally, a dual decomposition-based solution is proposed to facilitate an efficient distributed implementation of LDM in each of the SCA subproblems, where the unicast beamforming vectors can be obtained locally by the cooperating BSs. Numerical results are presented, which show the tightness of the proposed bounds and hence the near-optimality of the proposed solutions.

On the Optimal Broadcast Rate of the Two-Sender Unicast Index Coding Problem With Fully-Participated Interactions

The problem of two-sender unicast index coding consists of two senders and a set of receivers. Each receiver demands a unique message not demanded by any other receiver and has a subset of messages as its side information. Every demanded message is available with at least one of the senders. The senders avail the knowledge of the side information at all the receivers to reduce the total number of transmissions required to satisfy the demands of all the receivers. The objective is to find the minimum total of number of transmissions per message length (known as the optimal broadcast rate with finite length messages) and its limiting value as the message length tends to infinity (called the optimal broadcast rate). Achievable broadcast rates are provided for a class of the two-sender unicast index coding problem based on a special graph coloring technique called two-sender graph coloring. This result illustrates the utility of graph products in the two-sender unicast index coding problem for the first time in the literature. For another class, achievable broadcast rates are provided based on the optimal broadcast rates of three single-sender sub-problems with finite message length. This employs a code construction for the two-sender unicast index coding problem using optimal codes (including non-linear codes) of the sub-problems. Optimal broadcast rates are provided for a special class of the TUICP for which only an upper bound was known prior to this work. The optimal broadcast rates presented in this work also consider non-linear coding schemes at the two senders.

Automatic Identification System based Fishing Trajectory Data Preprocessing Method using Map Reduce

Many countries use vessel monitoring system (VMS) data to monitor their fishery activities. However, VMS data is limited in terms of distinguishing operations involving illegal fishing gear. Recently introduced automatic identification system (AIS) data is advantageous for tracking fishing ship behaviors.AIS data include various types of information about a ship, such as its state of navigation and its broadcast rate on the radio channel. We interpolate AIS trajectory data with a regular time interval and extract the ship velocity and course change data for fishing ship gear classification. To simplify and condense the data, the course change index (CCI) and ship speed index (SSI) are applied to the ship velocity and course data. The proposed mapper combines CCIs and SSIs into key words, while the proposed reducer collects fishing ship gear type values that are of the same key.By using the proposed key-value dataset from the MapReduce procedure, we can classify fishing gear type. We evaluated the performance of the proposed model by using a test dataset. The results showed that the proposed model achieved 76.2% accuracy in the classification of fishing ship trajectories against the test dataset.

Linear Programming Approximations for Index Coding

Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interests since its introduction (by Birk and Kol, 1998). In short, the problem can be defined as follows: there is an input $P \triangleq (p_{1}, {\dots }, p_{n})$ , a set of $n$ clients who each desire a single entry $p_{i}$ of the input, and a broadcaster whose goal is to send as few messages as possible to all clients so that each one can recover its desired entry. Additionally, each client has some predetermined “side information,” corresponding to the certain entries of the input $P$ , which we represent as the “side information graph” $ \mathcal {G}$ . The graph $ \mathcal {G}$ has a vertex $v_{i}$ for client $i$ and a directed edge $(v_{i}, v_{j})$ , indicating that client $i$ knows the $j$ th entry of the input. Given a fixed side information graph $ \mathcal {G}$ , we are interested in determining or approximating the “broadcast rate” of index coding on the graph, i.e., the least number of messages the broadcaster can transmit so that every client recovers its desired information. The complexity of determining this broadcast rate in the most general case is open, and the best-known approximations are barely better than the trivial $O(n)$ -approximation corresponding to sending each client their information directly without performing any coding. Using index coding schemes based on linear programs (LPs), we take a two-pronged approach to approximating the broadcast rate. First, extending earlier work on planar graphs, we focus on approximating the broadcast rate for special graph families, such as graphs with the small chromatic number and disk graphs. In certain cases, we are able to show that simple LP-based schemes give constant-factor approximations of the broadcast rate, which seem extremely difficult to obtain in the general case. Second, we provide several LP-based schemes for the general case, which are not constant-factor approximations, but which strictly improve on the best-known schemes. These can be viewed as both a strengthening of the constant-factor approximations proven for special graph families (as these schemes strictly improve on those which we prove are good approximations), as well as another tool that can be used either in practice or in future theoretical analyses.

Structural Characteristics of Two-Sender Index Coding.

This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori, known as side-information, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called two-sender unicast index coding (TSUIC). The main goal is to find the shortest aggregate normalized codelength, which is expressed as the optimal broadcast rate. In this work, firstly, for a given TSUIC problem, we form three independent sub-problems each consisting of the only subset of the messages, based on whether the messages are available only in one of the senders or in both senders. Then, we express the optimal broadcast rate of the TSUIC problem as a function of the optimal broadcast rates of those independent sub-problems. In this way, we discover the structural characteristics of TSUIC. For the proofs of our results, we utilize confusion graphs and coding techniques used in single-sender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graph-coloring approach that is different from the normal graph coloring, which we call two-sender graph coloring, and propose a way of grouping the vertices to analyze the number of colors used. We further determine a class of TSUIC instances where a certain type of side-information can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders.

Optimal Linear Broadcast Rates of Some Two-Sender Unicast Index Coding Problems

The two-sender unicast index coding problem consists of two senders, each having a different set of messages. Some messages may be common to both the senders. Each receiver demands a unique message and has a subset of messages known as its side-information. The senders transmit coded messages by availing the knowledge of the side-information of all the receivers, such that all the receivers are able to decode their demands. The aim is to find the optimal aggregate number of coded transmissions per message length (also called the optimal broadcast rate with finite length messages), and its limiting value as the message length tends to infinity (also called the optimal broadcast rate). In this paper, only linear coding schemes are considered. Optimal linear broadcast rate for any finite message length and optimal linear broadcast rate for a basic class of the two-sender unicast index coding problem are established. Optimal code-constructions are also provided. These results are given in terms of the corresponding results of three independent single-sender sub-problems of the two-sender unicast index coding problem. Proof techniques used to obtain the results for the two-sender problem are shown to be useful in obtaining the results for some classes of the multi-sender unicast index coding problem.