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We consider the problem of communicating over a channel that randomly “tears” the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length $n$ and pieces of length ${\mathrm{ Geometric}}(p_{n})$ , we characterize the capacity as $C = e^{-\alpha }$ , where $\alpha = \lim _{n\to \infty } p_{n} \log n$. Our results show that the case of ${\mathrm{ Geometric}}(p_{n})$ -length fragments and the case of deterministic length- $(1/p_{n})$ fragments are qualitatively different and, surprisingly, the capacity of the former is larger. Intuitively, this is due to the fact that, in the random fragments case, large fragments are sometimes observed, which boosts the capacity. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Language & Law / Revista de Llengua i Dret is the property of Revista de Llengua i Dret and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we show that the communication channel known as writing in memory with defective cells is a relevant information-theoretical model for a specific case of passive warden steganography when the sender embeds a secret message into a subset C of the cover object X without sharing C with the recipient. The set C, which is also called the selection channel, could be arbitrary, determined by the sender from the cover object using a deterministic, pseudo-random, or a truly random process. We call this steganography "writing on wet paper" and realize it using a simple variable-rate random linear code that gives the sender a convenient flexibility and control over the embedding process and is thus suitable for practical implementation. The importance of the wet paper scenario for covert communication is discussed within the context of adaptive steganography and perturbed quantization steganography. Heuristic arguments supported by tests using blind steganalysis indicate that the wet paper steganography provides improved steganographic security and is less vulnerable to steganalytic attacks compared with existing methods with shared selection channels. [ABSTRACT FROM PUBLISHER]

This report describes The University of Texas Student Cluster Competition team’s effort to reproduce the results of “MemXCT: memory-centric X-ray CT reconstruction with massive parallelization” (Hidayetoğlu et al., 2019). The article details a new memory-centric approach that reconstructs X-ray computed tomography (XCT) from noisy raw data. In our reproduction experiments, we utilized Microsoft Azure’s CycleCloud tool to provision, orchestrate, and manage our computing cluster in the cloud. In particular, we scheduled and benchmarked reconstruction workloads using Azure’s CPU-based HC44rs and GPU-based NC12s v2 virtual machine (VM) types to evaluate the scalability properties of the reconstruction approach and the performance differences between architectures. The HC44rs VMs contained 44 Intel Xeon Platinum cores, while the NC12s v2 VM was equipped with two NVIDIA P100 GPUs. We used a recent version of Intel’s compiler stack with the MKL library for our CPU code along with CUDA 11.1 on GPUs. Overall, our results confirm the findings of the original article, demonstrating similar acceleration on GPUs and scalability properties on CPUs. Digital artifacts from these experiments are available at: 10.5281/zenodo.5598108 [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study a number of American key films from the 1960s and to relate them to the cultural and historical spirit of the age. In its critical approach, this paper depends mainly on Roland Barthes' theories and concepts regarding the visual image and semiotics. The main films that will be studied include "Midnight Cowboy" (1969), directed by John Schlesinger; "Bonnie and Clyde" (1967), directed by Arthur Penn; and "The Wild Bunch" (1969), directed by Sam Peckinpah. The researchers argue that studying the content and various forms of these films in particular is significant because it reveals cultural and ideological messages about the 1960s. The present paper is also an attempt to shed light on Roland Barthes' arguments about film theory. Despite the fact that the sum of his writings on film is relatively small, a closer scrutiny of these writings reveals that he has a vast influence on the field of film studies. His ideas on semiotics and structuralism are influential and can be extensively applied during film analysis. [ABSTRACT FROM AUTHOR]

Personality determines various human daily and working behaviours. Recently, a large number of automatic personality computing approaches have been developed to predict either the apparent or self-reported personality of the subject based on non-verbal audio-visual behaviours. However, most of them suffer from complex and dataset-specific pre-processing steps and model training tricks. In the absence of a standardized benchmark with consistent experimental settings, it is not only impossible to fairly compare the real performances of these personality computing models but also makes them difficult to be reproduced. This paper presents the first reproducible audio-visual benchmark to provide a fair and consistent evaluation of eight existing personality computing models (e.g., audio, visual and audio-visual) and seven standard deep learning models on both self-reported and apparent personality recognition tasks. Building upon a set of benchmarked models, we also investigate the impact of two previously-used long-term modelling strategies for summarising short-term/frame-level predictions on personality computing results. We comprehensively investigate all benchmarked models on two publicly available datasets, ChaLearn First Impression and UDIVA self-reported personality datasets, and conclude: (i) apparent personality traits, inferred from facial behaviours by most benchmarked deep learning models, show more reliability than self-reported ones; (ii) visual models frequently achieved superior performances than audio models on personality recognition; (iii) non-verbal behaviours contribute differently in predicting different personality traits; and (iv) our reproduced personality computing models generally achieved worse performances than their original reported results. [ABSTRACT FROM AUTHOR]

Thematic analysis is a highly popular technique among qualitative researchers for analyzing qualitative data, which usually comprises thick descriptive data. However, the application and use of thematic analysis has also involved complications due to confusion regarding the final outcome's presentation as a conceptual model. This paper develops a systematic thematic analysis process for creating a conceptual model from qualitative research findings. It explores the adaptability of the proposed process across various research methodologies, including constructivist methodologies, positivist methodologies, grounded theory, and interpretive phenomenology, and justifies their application. The paper distinguishes between inductive and deductive coding approaches and emphasizes the merits of each. It suggests that the derived systematic thematic analysis model is valuable across multiple disciplines, particularly in grounded theory, ethnographic approaches, and narrative approaches, while also being adaptable to more descriptive, positivist-based methodologies. By providing a methodological roadmap, this study enhances the rigor and replicability of thematic analysis and offers a comprehensive strategy for theoretical conceptualization in qualitative research. The contribution of this paper is a systematic six-step thematic analysis process that leads to the development of a conceptual model; each step is described in detail and examples are given. [ABSTRACT FROM AUTHOR]

This report analyzes the reproducibility of the paper “MemXCT: Memory-Centric X-ray CT Reconstruction with Massive Parallelization” by Hidayetoğlu et al. in the cloud as part of the SC20 Virtual Student Cluster Competition (VSCC). To reproduce the results from the original work, the ETH Zürich SC20 VSCC team performed a series of CT reconstructions and performed a scaling study using three provided sinograms. All experimental runs were performed during the SC20 VSCC on an HPC cluster hosted in the Microsoft Azure CycleCloud. In this paper, we describe discrepancies in results as a factor of the differences in experiment environments and insufficient parameter tuning. We successfully reproduce the single device performance and partially reproduce the strong scaling behavior. Digital artifacts from these experiments are available at: 10.5281/zenodo.5598108. [ABSTRACT FROM AUTHOR]

The number-theoretic code is a class of codes defined by single or multiple congruences. These codes are mainly used for correcting insertion and deletion errors, and for correcting asymmetric errors. This paper presents a formula for a generalization of the complete weight enumerator for the number-theoretic codes. This formula allows us to derive the weight enumerators and cardinalities for the number-theoretic codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary Tenengolts’ codes, correcting single insertion or deletion. Moreover, we show that the formula deduces the MacWilliams identity for the linear codes over the ring of integers modulo $r$. [ABSTRACT FROM AUTHOR]

The article presents a study that examines the credibility of journalistic papers related to health. Researchers analyze the quality of the publications from PubMed and other websites based on journalistic guidelines. The study identifies that some documents require a knowledgeable audience and others are well explained and defined. Researchers recommend vital steps to expand the quality of health reporting such as having a journalist with enough biomedical background.

This paper briefly reviews the evolution of composite codes in the USA in the context of important changes for the 2022 edition of the American steel design specification for buildings Major changes include the incorporation of composite walls as a new type of composite member, the addition of new provisions for shear capacity of filled members, and the introduction of a performance‐based procedure for qualifying new types of anchors. An appendix also allows for the use of high strength materials for concrete filled rectangular members. The paper then describes the write's opinion on (1) important issues that need to be addressed on the direction of future codes, (2) areas where more research work is needed to provide more consistent and simpler design rules and (3) the desirability of including additional topics into the main specification. [ABSTRACT FROM AUTHOR]

Let I be the commutative non-unital ring of order 4 defined by generators and relations. I = a , b ∣ 2 a = 2 b = 0 , a 2 = b , a b = 0. Alahmadi et al. have classified QSD codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths n = 6 , and suggested two building-up methods for constructing QSD codes. In this paper, we construct more QSD codes, Type IV codes and quasi-Type IV codes for lengths n = 7 and 8, and describe five new variants of the two building-up construction methods. We find that when n = 8 there is at least one QSD code with minimun distance 4, which attains the highest minimum distance so far, and we give a generator matrix for the code. We also describe some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions. [ABSTRACT FROM AUTHOR]

Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of ${\mathbb {F}}_{q^{2}}^{*}$. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive performance comparison between a current robust military waveform; namely, MIL-STD-188-110D, Waveform 0, and a filter bank multicarrier spread-spectrum (FBMC-SS) waveform proposed for communications through ionospheric/skywave HF channels. Waveform 0 is effectively a direct sequence spread spectrum waveform that uses Walsh multi-codes to enhance the information transmission rate. It may thus be referred to as Walsh-DSSS. FBMC-SS, on the other hand, makes use of filter banks to provide excellent performance when the received signal is subject to partial band interference. Successful application of FBMC-SS for communications across skywave HF channels has been previously demonstrated, both theoretically and through experimental work. However, very little has been done to contrast FBMC-SS against Walsh-DSSS. The goal of this paper is to first add new features to FBMC-SS to bring it on par with Walsh-DSSS. These features include: (i), introduction of multi-codes that achieve a comparable (or better) data rate to Walsh-DSSS; and (ii), addition of a scrambling step applied to the multi-codes to make the receiver detection robust against widely spread multipaths. With this established, in the second part of the paper, we examine the performance of the developed FBMC-SS against Walsh-DSSS when both are applied for communications across skywave HF channels. The two waveforms are compared both through a theoretical study and through experimental works across several skywave channels ranging from hundreds to thousands of kilometers. [ABSTRACT FROM AUTHOR]

In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider the case where the process of encoding is distributed and prone to error. We introduce the problem of distributed encoding, comprised of a set of $K \in \mathbb {N}$ isolated source nodes and $N \in \mathbb {N}$ encoding nodes. Each source node has one symbol from a finite field, which is sent to each of the encoding nodes. Each encoding node stores an encoded symbol from the same field, as a function of the received symbols. However, some of the source nodes are controlled by the adversary and may send different symbols to different encoding nodes. Depending on the number of the adversarial nodes, denoted by $\beta \in \mathbb {N}$ , and the cardinality of the set of symbols that each one generates, denoted by $v \in \mathbb {N}$ , the process of decoding from the encoded symbols could be impossible. Assume that a decoder connects to an arbitrary subset of $t \in \mathbb {N}$ encoding nodes and wants to decode the symbols of the honest nodes correctly, without necessarily identifying the sets of honest and adversarial nodes. An important characteristic of a distributed encoding system is $t^{*} \in \mathbb {N}$ , the minimum of such $t$ , which is a function of $K$ , $N$ , $\beta $ , and $v$. In this paper, we study the distributed linear encoding system, i.e. one in which the encoding nodes use linear coding. We show that $t^{*}_{\textrm {Linear}}=K+2\beta (v-1)$ , if $N\ge K+2\beta (v-1)$ , and $t^{*}_{\textrm {Linear}}=N$ , if $N\le K+2\beta (v-1)$. In order to achieve $t^{*}_{\textrm {Linear}}$ , we use random linear coding and show that in any feasible solution that the decoder finds, the messages of the honest nodes are decoded correctly. In order to prove the converse of the fundamental limit, we show that when the adversary behaves in a particular way, it can always confuse the decoder between two feasible solutions that differ in the message of at least one honest node. [ABSTRACT FROM AUTHOR]

The management of existing structures is raising a number of pertinent questions to the owners and engineers. Many structures built more than 50 years ago (even those built hundreds of years ago) usually no longer comply with safety requirements of current codes, which are typically addressed in new structures. This is not necessarily only caused by a poor original design or degradation with time, but it may be, for example, the consequence of increase in actions, reducing the level of reliability of a structure. This paper focuses on strategies to be adopted for existing structures which do not comply with code requirements for new constructions (e.g., to repair, to demolish, to rebuild, etc.) on the basis of a more holistic approach that includes economic, social, and environmental considerations. To that aim, first, a brief review of the background concepts on the reliability of structures is presented, highlighting the differences for new and existing structures. Following this analysis, suitable values for the reliability index (including sustainability considerations) are proposed, as well as tailored maintenance strategies. Finally, the paper presents a case study based on a real project to emphasize the benefits of adopting such a holistic perspective. [ABSTRACT FROM AUTHOR]

A functional $k$ -batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. Any multiset request of size $k$ of linear combinations (or requests) of the information bits can be recovered by $k$ disjoint subsets of the servers. The goal under this paradigm is to find the minimum number of servers for given values of $s$ and $k$. A recent conjecture states that for any $k=2^{s-1}$ requests the optimal solution requires $2^{s}-1$ servers. This conjecture is verified for $s \leqslant 5$ but previous work could only show that codes with $n=2^{s}-1$ servers can support a solution for $k=2^{s-2} + 2^{s-4} + \left \lfloor{ \frac { 2^{s/2}}{\sqrt {24}} }\right \rfloor $ requests. This paper reduces this gap and shows the existence of codes for $k=\lfloor \frac {5}{6}2^{s-1} \rfloor - s$ requests with the same number of servers. Another construction in the paper provides a code with $n=2^{s+1}-2$ servers and $k=2^{s}$ requests, which is an optimal result. These constructions are mainly based on extended Simplex codes and equivalently provide constructions for parallel Random I/O (RIO) codes. [ABSTRACT FROM AUTHOR]

Quantum readout provides a general framework for formulating statistical discrimination of quantum channels. Several paths have been taken for such this problem. However, there is much to be done in the avenue of optimizing channel discrimination using classical codes. At least two open questions can be pointed out: how to construct low complexity encoding schemes that are interesting for channel discrimination and, more importantly, how to develop capacity-achieving protocols. This paper aims at presenting a solution to these questions using polar codes. Firstly, we characterize the information rate and reliability parameter of the channels under polar encoding. We also show that the error probability of the scheme proposed decays exponentially with the square root of the code length. Secondly, an analysis of the optimal quantum states to be used as probes is given. [ABSTRACT FROM AUTHOR]

For high-speed quantum key distribution (QKD) post processing, information reconciliation is the most computational step, which usually acts as the system speed bottleneck. Reconciliation efficiency and operation throughput are the two most important performance parameters, but they are often compromised to each other in actual realization due to the available hardware resources. Another characteristic of the information reconciliation is that its channel is time-varying, and in order to guarantee high efficiency, some rate-compatible error correction scheme should be adopted. To cope with the above problems, this paper proposes a rate-compatible high-efficiency reconciliation algorithm based on quasi-cyclic (QC) low-density parity-check (LDPC) codes and puncturing algorithms. On the other hand, in order to obtain high throughput while maintaining low implementation complexity, the normalized min-sum algorithm (NMSA) is realized and optimized by using the fast prototyping tool of high-level synthesis (HLS). The proposed information reconciliation module was implemented on the Xilinx Zynq Ultrascale+ ZCU102 development board. Experimental results show that the maximum throughput rate of the implemented reconciliation module in this paper can reach 136 Mbps, while the efficiency factor is kept lower than 1.32 across the error rate range of 1.7%∼10.6% under the remaining frame error rate level of 10−3. The comprehensive good performance obtained by our design can strongly support the development of modern high-speed QKD systems. [ABSTRACT FROM AUTHOR]

A common method for reading information stored in DNA molecules is shotgun sequencing. This method outputs a histogram of the frequencies of all the molecules’ substrings of a given length $\ell $. To protect against noisy readings, the rank-modulation scheme encodes the information in the relative ranking of the substring frequencies, instead of their absolute values. However, the best rank-modulation codes for shotgun sequencing have low rates which are asymptotically vanishing. In this paper we propose new constructions of rank-modulation codes for shotgun sequencing. The first code construction is systematic, allowing the user to arbitrarily set the frequencies of a large subset of the substrings, which the encoder then completes to a permutation that may be realized by a DNA molecule. The construction is then improved by allowing the user to set the frequencies of additional substrings, at the cost of imposing constraints on the frequencies. The resulting codes have higher, non-vanishing rates, compared with previously known codes. As an example, for histograms of substrings of length $\ell =2$ , and an alphabet of size 4 (as in DNA molecules), we are able to construct a code with rate $\approx 0.909$ , whereas previously, the best construction resulted in a code with rate $\approx 0.654$. Additionally, the encoded information in our construction may be written to shorter DNA molecules than possible before. We also prove that the systematic codes constructed in this paper are the largest possible among all systematic codes. [ABSTRACT FROM AUTHOR]

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. They are widely used in data storage and communication systems. A subclass of attractive BCH codes is the narrow-sense BCH codes over the Galois field ${\mathrm {GF}}(q)$ with length $q+1$ , which are closely related to the action of the projective general linear group of degree two on the projective line. Despite its interest, not much is known about this class of BCH codes. This paper aims to study some of the codes within this class and specifically narrow-sense antiprimitive BCH codes (these codes are also linear complementary duals (LCD) codes that have interesting practical recent applications in cryptography, among other benefits). We shall use tools and combine arguments from algebraic coding theory, combinatorial designs, and group theory (group actions, representation theory of finite groups, etc.) to investigate narrow-sense antiprimitive BCH Codes and extend results from the recent literature. Notably, the dimension, the minimum distance of some $q$ -ary BCH codes with length $q+1$ , and their duals are determined in this paper. The dual codes of the narrow-sense antiprimitive BCH codes derived in this paper include almost MDS codes. Furthermore, the classification of ${\mathrm {PGL}}(2, p^{m})$ -invariant codes over ${\mathrm {GF}}(p^{h})$ is completed. As an application of this result, the $p$ -ranks of all incidence structures invariant under the projective general linear group ${\mathrm {PGL}}(2, p^{m})$ are determined. Furthermore, infinite families of narrow-sense BCH codes admitting a 3-transitive automorphism group are obtained. Via these BCH codes, a coding-theory approach to constructing the Witt spherical geometry designs is presented. The BCH codes proposed in this paper are good candidates for permutation decoding, as they have a relatively large group of automorphisms. [ABSTRACT FROM AUTHOR]

Palmprint has gained popularity as a biometric modality and has recently attracted significant research interest. The competition-based method is the prevailing approach for hand-crafted palmprint recognition, thanks to its powerful discriminative ability to identify distinctive features. However, the competition mechanism possesses vast untapped advantages that have yet to be fully explored. In this paper, we reformulate the traditional competition mechanism and propose a $\boldsymbol {C}$ omprehensive $\boldsymbol {C}$ ompetition Network (CCNet). The traditional competition mechanism focuses solely on selecting the winner of different channels without considering the spatial information of the features. Our approach considers the spatial competition relationships between features while utilizing channel competition features to extract a more comprehensive set of competitive features. Moreover, existing methods for palmprint recognition typically focus on first-order texture features without utilizing the higher-order texture feature information. Our approach integrates the competition process with multi-order texture features to overcome this limitation. CCNet incorporates spatial and channel competition mechanisms into multi-order texture features to enhance recognition accuracy, enabling it to capture and utilize palmprint information in an end-to-end manner efficiently. Extensive experimental results have shown that CCNet can achieve remarkable performance on four public datasets, showing that CCNet is a promising approach for palmprint recognition that can achieve state-of-the-art performance. Related codes will be released at https://github.com/Zi-YuanYang/CCNet. [ABSTRACT FROM AUTHOR]

As the focus on embodied carbon within the built environment has grown in the U.S., local jurisdictional codes have increasingly proposed and implemented code language that requires the use of concrete mixtures that have reduced environmental impacts. This paper provides details about the various ways that localized sustainable concrete provisions have been proposed and implemented in the U.S., including limits on cement content and Global Warming Potential (GWP). These laws and code revisions vary in their measurement of low-carbon concrete and their exemptions and incentives. While the current version of the ACI Building Code, ACI 318-19, does allow for the consideration of sustainability in concrete design, specifics about how the relative sustainability of concrete mixtures and systems are to be measured and compared are not included. This paper addresses how the changing landscape of local jurisdictional codes is driving the development of future ACI 318 provisions to play a part in providing more consistency in the application of sustainable design practices in the United States. [ABSTRACT FROM AUTHOR]

Several sources of total cross sections for e+e− pair production by photon interaction with matter, used by major Monte Carlo codes for particle transport, are quantitatively evaluated with respect to experimental measurements collected from the literature. They include data libraries deriving from theoretical calculations and analytical formulae representing empirical fits to tabulations. Although most of these sources of cross sections are based on one theoretical reference, the statistical data analysis documented in this paper highlights differences in their compatibility with experiment. The cross sections collected in the 1997 version of the Evaluated Photon Data Library (EPDL) exhibit the lowest incompatibility with experiment; the paper details the validation results for all the examined cross section sources. The scarcity of experimental data does not allow the validation process to discern pair production in the field of the nucleus and in the field of atomic electrons; nevertheless, this paper documents relevant clues regarding the contribution of the latter to reproduce experimental measurements. [ABSTRACT FROM AUTHOR]

Smart contracts in Ethereum blockchain network are self-executable scripts used for managing tokenized assets and access rights between different entities on the blockchain network. They are significant addition to blockchain technology for achieving data transparency and reliability in maintaining the digital relationship between two or more entities. However, the smart contract is in its nascent stage and suffers from various limitations, including immutability and code secrecy. In this paper, we address the inability of smart contracts to access the on-chain data. The smart contract currently fetches the on-chain data by taking external oracle assistance, which can be compromised to influence the customers. To address the issue, we propose a decentralized mechanism for accessing the blockchain data directly from the smart contracts by indexing single or multiple parameters of a transaction in each block using the Merkle-Patricia Trie (MPT). The idea is to increase the data transparency of blockchain applications. The paper provides a sequential search methodology that can retrieve transactions from ${N}$ blocks, satisfying specific conditions, in ${O}$ (${N}$). The complexity is further reduced to ${O}$ (N/k) by partitioning the blockchain data into ${k}$ disjoint subsets to achieve parallelism in the search procedure. We experimentally verify the effectiveness of the proposed methodology with a case study on the Ethereum blockchain data. [ABSTRACT FROM AUTHOR]

Consider a massive random access scenario in which a small set of $k$ active users out of a large number of $n$ potential users need to be scheduled in $b\ge k$ slots. What is the minimum common feedback to the users needed to ensure that scheduling is collision-free? Instead of a naive scheme of listing the indices of the $k$ active users in the order in which they should transmit, at a cost of $k\log (n)$ bits, this paper shows that for the case of $b=k$ , the rate of the minimum fixed-length common feedback code scales only as $k \log (e)$ bits, plus an additive term that scales in $n$ as $\Theta (\log \log (n))$ for fixed $k$. If a variable-length code can be used, assuming uniform activity among the users, the minimum average common feedback rate still requires $k \log (e)$ bits, but the dependence on $n$ can be reduced to $O(1)$. When $b>k$ , the number of feedback bits needed for collision-free scheduling can be significantly further reduced. Moreover, a similar scaling on the minimum feedback rate is derived for the case of scheduling $m$ users per slot, when $k \le mb$. The problem of constructing a minimum collision-free feedback scheduling code is connected to that of constructing a perfect hashing family, which allows practical feedback scheduling codes to be constructed from perfect hashing algorithms. [ABSTRACT FROM AUTHOR]

Copyright of Letonica is the property of University of Latvia, Institute of Literature, Folklore & Art and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)