Index Coding Research Articles

Index Coding in Vehicle to Vehicle Communication

Vehicle to Vehicle (V2V) communication phase is an integral part of collaborative message dissemination in vehicular ad-hoc networks (VANETs). In this work, we apply index coding techniques to reduce the number of transmissions required for data exchange. The index coding problem has a sender, which tries to meet the demands of several receivers in a minimum number of transmissions. All these receivers have some prior knowledge of the messages, known as the side-information. In this work, we consider a particular case of the index coding problem, where multiple nodes want to share information among them. Under this set up, lower bound on the number of transmissions is established when the cardinality of side-information is the same. An optimal solution to achieve the bound in a special case of VANET scenario is presented. For this special case, we consider the link between the nodes to be error-prone, and in this setting, we construct optimal linear error correcting index codes.

Task-Based Solutions to Embedded Index Coding

In the index coding problem a sender holds a message $x \in \{0,1\}^{n}$ and wishes to broadcast information to $n$ receivers in a way that enables the $i$ th receiver to retrieve the $i$ th bit $x_{i}$ . Every receiver has prior side information comprising a subset of the bits of $x$ , and the goal is to minimize the length of the information sent via the broadcast channel. Porter and Wootters have recently introduced the model of embedded index coding , where the receivers also play the role of the sender and the goal is to minimize the total length of their broadcast information. An embedded index code is said to be task-based if every receiver retrieves its bit based only on the information provided by one of the receivers. This paper studies the effect of the task-based restriction on linear embedded index coding. It is shown that for certain side information maps there exists a linear embedded index code of length quadratically smaller than that of any task-based embedded index code. The result attains, up to a multiplicative constant, the largest possible gap between the two quantities. The proof is by an explicit construction and the analysis involves spectral techniques.

Fiber Bragg Grating Sensor Based on Refractive Index Segment Code of Mobile Modulation

Fiber Bragg Grating (FBG) is achieved by refractive index modulation. Temperature and strain can be measured by FBG. The echo spectral distribution is determined by the refractive index of the fiber and the grating pitch. Therefore, there are few types of conventional refractive index modulation methods, and there are few types of echo spectrum. In this paper, an index code modulation based on IoT method was proposed. The FBG is divided into a plurality of interval segments in the method. The spectral shape of the echo is controlled by encoding and modulating each interval. When the segment size satisfies some requirements, the positive and negative modes of the sub-FBG are calculated by the coupled-mode theory, and then the mode functions of each segment are solved by the matrix transmission algorithm. The equivalent function of the reflectance distribution field is obtained. According to the relevant parameters of FBG, the mathematical model of the FBG modulation spectral distribution is established by the refractive index modulation method. Through the simulation analysis of the fractional refractive index modulation, the results show that the echo spectral peak, half-width, etc. have a larger tunable range. In the experiment, a femtosecond laser was used to accurately encode and modulate the refractive index, and two different types of segmented FBGs were fabricated according to design requirements. The experimental results show that the design of different segmented structures has a significant impact on the spectral distribution of the echo. Spectral shape control can be achieved by refractive index modulation method.

A-245 So What's the Damage? The Effect of the WISC-V Digitization Debacle

Abstract Objective The WISC-V can now be administered in paper format or digitally. Though most subtests are comparable, Processing Speed Index (PSI) subtests, Coding and Symbol Search required complete redesign for digital presentation. We initially collected data to assess comparability of paper versus digital PSI tasks for future use. However, in March of 2020, Pearson issued an alert stating that, due to a programming error, Coding scores may be inflated secondary to timing inaccuracy; they advised against further use of digital Coding. We refocused our analyses to assess the degree to which inaccurate digital Coding impacted overall test results. Method Children with neurological disorders (N=104) received both versions of the PSI subtests (order randomized). Correlational analyses assessed relations between versions, t-tests assessed for administration order effects, and Kappa coefficients assessed agreement across platforms. Results Correlations between paper and digital subtests (r=.570 to .853) and composites (r=.848 to .987) were robust. As expected, Coding was higher digitally (difference=1.91, p < .01, d=.52), but Symbol Search, PSI, and FSIQ were comparable (p>.05). Given evident practice effects, subsequent analyses considered “first administered” versions and score range agreement was best when PSI tasks were administered digitally first (Kappa=.452, p < .001) versus paper first (Kappa=.153, p=.023). Agreement was strong for FSIQ regardless of order (Kappa≥.760, p < .001). Importantly, in highest stakes evaluations (i.e., presence versus absence of intellectual disability), agreement was extraordinarily strong (Kappa≥.93, p < .001). Conclusions Digital Coding scores are inflated in comparison to traditional paper version, but the impact of this programming error was minimal at the level of PSI and FSIQ.

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.

Index Coded Automatic Repeat Request (ARQ)

In this paper, an index-coded Automatic Repeat Request (ARQ) is studied in the perspectives of transmission efficiency and memory overhead. Motivated by reducing significant computational complexity from huge matrix inverse computation of random linear network coding, a near-to-optimal broadcasting scheme, called index-coded Automatic Repeat Request (ARQ) is proposed. The main idea is to consider the principal packet error pattern across all receivers. With the help of coded side information formed by successfully decoded packets associated with the dominant packet error pattern, it is shown that two contradictory performance metrics such as transmission efficiency and transmit (receive) cache memory size for index coding (decoding) can be enhanced with a reasonable trade-off. Specifically, the transmission efficiency of the proposed scheme is proved to be asymptotically optimal, and memory overhead is shown to be asymptotically close to the conventional ARQ scheme. Numerical results also validate the proposed scheme in the sense of memory overhead and transmission efficiency in comparison with the conventional ARQ scheme and the optimal scheme using random linear network coding.

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.

Optimal Linear Error Correcting Delivery Schemes for Two Optimal Coded Caching Schemes.

For coded caching problems with small buffer sizes and the number of users no less than the amount of files in the server, an optimal delivery scheme was proposed by Chen, Fan, and Letaief in 2016. This scheme is referred to as the CFL scheme. In this paper, an extension to the coded caching problem where the link between the server and the users is error prone, is considered. The closed form expressions for average rate and peak rate of error correcting delivery scheme are found for the CFL prefetching scheme using techniques from index coding. Using results from error correcting index coding, an optimal linear error correcting delivery scheme for caching problems employing the CFL prefetching is proposed. Another scheme that has lower sub-packetization requirement as compared to CFL scheme for the same cache memory size was considered by J. Gomez-Vilardebo in 2018. An optimal linear error correcting delivery scheme is also proposed for this scheme.

Generalized Index Coding Problem and Discrete Polymatroids.

The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can be viewed as a generalization of the matroids, were used. The index coding problem has been generalized recently to accommodate receivers that demand functions of messages and possess functions of messages. In this work we explore the connections between generalized index coding and discrete polymatroids. The conditions that need to be satisfied by a representable discrete polymatroid for a generalized index coding problem to have a vector linear solution is established. From a discrete polymatroid, an index coding problem with coded side information is constructed and it is shown that if the index coding problem has a certain optimal length solution then the discrete polymatroid is representable. If the generalized index coding problem is constructed from a matroid, it is shown that the index coding problem has a binary scalar linear solution of optimal length if and only if the matroid is binary representable.

AutoPruner: An end-to-end trainable filter pruning method for efficient deep model inference

Channel pruning is an important method to speed up CNN model’s inference. Previous filter pruning algorithms regard importance evaluation and model fine-tuning as two independent steps. This paper argues that combining them into a single end-to-end trainable system will lead to better results. We propose an efficient channel selection layer, namely AutoPruner, to find less important filters automatically in a joint training manner. Our AutoPruner takes previous activation responses as an input and generates a true binary index code for pruning. Hence, all the filters corresponding to zero index values can be removed safely after training. By gradually erasing several unimportant filters, we can prevent an excessive drop in model accuracy. Compared with previous state-of-the-art pruning algorithms (including training from scratch), AutoPruner achieves significantly better performance. Furthermore, ablation experiments show that the proposed novel mini-batch pooling and binarization operations are vital for the success of model pruning.

Coordinated activities of retrosplenial ensembles during resting-state encode spatial landmarks.

The brain likely uses offline periods to consolidate recent memories. One hypothesis holds that the hippocampal output provides a unique, global linking or 'index' code for each memory, and that this code is stored in the cortex in association with locally encoded attributes of each memory. Activation of the index code is hypothesized to evoke coordinated memory trace reactivation thus facilitating consolidation. Retrosplenial cortex (RSC) is a major recipient of hippocampal outflow and we have described populations of neurons there with sparse and orthogonal coding characteristics that resemble hippocampal 'place' cells, and whose expression depends on an intact hippocampus. Using two-photon Ca2+ imaging, we recorded ensembles of neurons in the RSC during periods of immobility before and after active running on a familiar linear treadmill track. Synchronous bursting of distinct groups of neurons occurred during rest both prior to and after running. In the second rest epoch, these patterns were associated with the locations of tactile landmarks and reward. Complementing established views on the functions of the RSC, our findings indicate that the structure is involved with processing landmark information during rest. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

Database of open-framework aluminophosphate structures

Open-framework aluminophosphates are an important class of inorganic crystalline compounds because of their rich structural chemistry and diverse properties. We have collected 312 open-framework aluminophosphate crystal structures from published literature and established a database for these structures. For each aluminophosphate structure, we have assigned a unique index code and extracted its key chemical and crystallographic information from the original literature and the associated CIF file, such as the name, chemical formula, extra-framework species, Al/P ratio, space group, and unit cell parameters of the compound. More importantly, we have calculated the topological features for each aluminophosphate framework, including local connectivity, framework dimension, coordination sequences, vertex symbols, topology density, and the largest ring. To help experimental chemists identify their products, we have also calculated theoretical XRD peaks for all aluminophosphate structures. This database will provide important insight into understanding the structural chemistry of open-framework aluminophosphate compounds.

An Index Coding Approach to Caching With Uncoded Cache Placement

Caching is an efficient way to reduce network traffic congestion during peak hours, by storing some content at the user's local cache memory, even without knowledge of user's later demands. Maddah-Ali and Niesen proposed a two-phase (placement phase and delivery phase) coded caching strategy for broadcast channels with cache-aided users. This paper investigates the same model under the constraint that content is placed uncoded within the caches, that is, when bits of the files are simply copied within the caches. When the cache contents are uncoded and the users' demands are revealed, the caching problem can be connected to an index coding problem. This paper focuses on deriving fundamental performance limits for the caching problem by using tools for the index coding problem that were either known or are newly developed in this work. First, a converse bound for the caching problem under the constraint of uncoded cache placement is proposed based on the “acyclic index coding converse bound.” This converse bound is proved to be achievable by the Maddah-Ali and Niesen's scheme when the number of files is not less than the number of users, and by a newly derived index coding achievable scheme otherwise. The proposed index coding achievable scheme is based on distributed source coding and strictly improves on the widely used “composite (index) coding” achievable bound and its improvements, and is of independent interest. An important consequence of the findings of this paper is that advancements on the coded caching problem posed by Maddah-Ali and Niesen are thus only possible by considering strategies with coded placement phase. A recent work by Yu et al has however shown that coded cache placement can at most half the network load compared to the results presented in this paper.

MUL-TIBIOMETRIC PATTERN RETRIEVAL USING INDEX CODE TO IMPROVE RESPONSE TIME

In a biometric identification system, the identity corresponding to the input data (probe) is typically determined by comparing it against the templates of all identities in a database (gallery). Exhaustive matching against a large number of identities increases the response time of the system and may also reduce the accuracy of identification. Onaway to reduce the response time is by designing biometric templates that allow for rapid matching, as in the case of Iris Codes. An alternative approach is to limit the number of identities against which matching is performed based on criteria that are fast to evaluate. We propose a method for generating fixed-length codes for indexing biometric databases. An index code is constructed by computing match scores between a biometric image and a fixed set of reference images. Candidate identities are retrieved based on the similarity between the index code of the probe image and those of the identities in the database. The proposed technique can be easily extended to retrieve pertinent identities from multimodal databases. Experiments on a chimeric face and fingerprint bimodal database resulted in an 84% average reduction in the search space at a hit rate of 100%. These results suggest that the proposed indexing scheme has the potential to substantially reduce the response time without compromising the accuracy of identification.

Pollution, sources and environmental risk assessment of heavy metals in the surface AMD water, sediments and surface soils around unexploited Rona Cu deposit, Tibet, China

The pollution by heavy metals (HMs) of mining is a widespread problem in the world. However, the pollution by HMs around unexploited deposits (virgin fields) has been studied rarely, especially in Tibet, China. Water, sediments and surface soils were collected to investigate the concentrations of HMs around unexploited Rona Cu deposit in Tibet, China. Furthermore, geochemical fractions of these elements were also analyzed. Pollution and environmental risk introduced by HMs accumulation were assessed using pollution indices, geo-accumulation (Igeo), potential ecological risk index and risk assessment code (RAC). Results indicated that the pH values of Rona tributary river ranged from 2.70 to 3.08, and the average concentrations of Cu and Zn were 2114.00 ± 65.89 and 1402.14 ± 27.36 μg L−1, respectively, exceeding their standard limits. The concentrations (mg kg−1) of Cu, Zn and As ranged in 19.01–1763.10, 62.00–543.06 and 11.12–61.78 for sediments, respectively, and 154.60–1489.35, 55.38–344.74 and 10.05–404.03 for surface soils, respectively, exceeding their standard limits. According to RAC, almost all Cu, Zn and As near low risk status. However, Cd ranged from medium to very high risk in sediments, and low to high risk in surface soils. Statistical analysis suggested that Cu, Pb, Zn, As and Cd in sediments and surface soils may mainly derive from Rona deposit, whereas Cr and Hg may primarily originate from lithogenic sources. The results indicated that very high concentrations of HMs could be occurred in surface water, sediments and surface soils around unexploited deposits. Especially at high-altitude Tibet, the high environmental risk of HMs deserves more attention.

A modified Gilbert-Varshamov bound for self-dual quasi-twisted codes of index four

In this work, we study a family of self-dual four circulant codes and a family of self-dual four negacirculant codes, and the exact counting formula is derived for these families of codes. In addition, we prove that asymptotically good self-dual four circulant codes and negacirculant codes over finite fields exist, and both of them satisfy a modified Gilbert-Varshamov bound on the relative minimum distance with asymptotic rate 12.

Generalized Lexicographic Products and the Index Coding Capacity

The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product structure in the side information graph is introduced as a natural condition under which the corresponding index coding problem can be decomposed into multiple interacting subproblems, each consisting of vertices with the same adjacency pattern with respect to other subproblems. For side information graphs with this structure, the capacity region is characterized in terms of the subproblem capacity regions combined in the same product structure. The proof is based on dual uses of random coding-one for a new multiletter characterization of the capacity region of a general index coding problem via joint typicality decoding and the other for a construction of a new multiletter code of matching rates from a single-letter code via joint typicality encoding. Several special cases are discussed that recover and strengthen known structural properties of the index coding capacity region.

Codon Directional Asymmetry Suggests Swapped Prebiotic 1st and 2nd Codon Positions.

Background: Codon directional asymmetry (CDA) classifies the 64 codons into palindromes (XYX, CDA = 0), and 5′- and 3′-dominant (YXX and XXY, CDA < 0 and CDA > 0, respectively). Previously, CDA was defined by the purine/pyrimidine divide (A,G/C,T), where X is either a purine or a pyrimidine. For the remaining codons with undefined CDA, CDA was defined by the 5′ or 3′ nucleotide complementary to Y. This CDA correlates with cognate amino acid tRNA synthetase classes, antiparallel beta sheet conformation index and the evolutionary order defined by the self-referential genetic code evolution model (CDA < 0: class I, high beta sheet index, late genetic code inclusion). Methods: We explore associations of CDAs defined by nucleotide classifications according to complementarity strengths (A:T, weak; C:G, strong) and keto-enol/amino-imino groupings (G,T/A,C), also after swapping 1st and 2nd codon positions with amino acid physicochemical and structural properties. Results: Here, analyses show that for the eight codons whose purine/pyrimidine-based CDA requires using the rule of complementarity with the midposition, using weak interactions to define CDA instead of complementarity increases associations with tRNA synthetase classes, antiparallel beta sheet index and genetic code evolutionary order. CDA defined by keto-enol/amino-imino groups, 1st and 2nd codon positions swapped, correlates with amino acid parallel beta sheet formation indices and Doolittle’s hydropathicities. Conclusions: Results suggest (a) prebiotic swaps from N2N1N3 to N1N2N3 codon structures, (b) that tRNA-mediated translation replaced direct codon-amino acid interactions, and (c) links between codon structures and cognate amino acid properties.

Research on the Relationship Between FinTech Attention and Its Sector Returns

With the development and application of Internet technology, investors usually use Internet search engine to investigate the corporation and related information before making investment decision. As a result, Internet search engine has become an indicator of investors’ attention. This paper uses FinTech Baidu index derived from Baidu public platform to measure investors' attention, as well as FinTech index from Shenzhen stock exchange, whose index code is 399699. SZ. The index data covers a date range from June 9, 2017 to June 30, 2019. Empirically, this paper discusses the impact of online attention on the stock returns of financial science and technology sector. A vector auto-regressive (VAR) model is built to reveal the correlation between Fintech investor attention and its sector returns. Furthermore, the granger causality, impulse response and variance decomposition are analyzed. Granger causality test result indicates that FinTech investor attention is the granger cause of the stock returns of Fintech sector, and conversely the stock returns of Fintech sector are not the cause of FinTech investor attention. That is, FinTech online attention has a certain impact on the stock returns of Fintech sector. Impulse response indicates that the impact of FinTech online attention is positive, but the effect lasts in a short term. The conclusions play an important role for investors to understand the hotspot attention on FinTech which is a new emerging market investment opportunity, and provide a general knowledge about the relation between Fintech attention and market returns.

Changes in lead and chromium contents in sewage sludge evaluated using both single extractants and sequential method

ABSTRACT The aim of this study was to evaluate changes in lead and chromium amounts in sequentially separated fractions and available forms of four sewage sludge (SS). Lead and chromium sequential extraction in SS was performed using BCR method. Single extractants were used to assay available and bioavailable forms of metals. It was found that Pb and Cr were detected in the largest amounts in organic forms, while the lowest levels were recorded for exchangeable ones. Sewage sludges from the small installations contained significantly lower amounts of metals (both available, bioavailable and sequentially separated fractions of sewage sludge) in comparison with those originating from the large treatment installations. Generally amounts of metals detected in sewage sludge were small in the years of this study, which should be considered a positive trend. Additionally, the bioavailability index (φ) and risk assessment code (RAC) indicated no negative impact of metals contained in the analysed SS on the soil environment.