Auxiliary Symbols Research Articles

Evaluation of FBMC Channel Estimation using multiple Auxiliary symbols for high throughput and low BER 5G and beyond communications

Filter Bank Multi-Carrier (FBMC) modulation has been recognized as a consistent contender and a possible successor for Orthogonal Frequency Division Multiplexing (OFDM) in 5G and beyond because of its outstanding spectral properties. The channel is assessed in FBMC using pilot-symbol aided channel estimation that provides robust estimates even for severe channel conditions. In the present work, neutraliz ing the imaginary interference at the pilot positions is focused while estimating the channel. To neutralize the imaginary in terference, multiple auxiliary symbols have been proposed to enhance the throughput and channel capacity. The Iterative Minimum Mean Squared Error (IMMSE) cancellation scheme has been proposed to reduce the interference at the pilot and data positions. Transmission power, Bit Error Rate (BER) and throughput are computed for Filter Bank Multi Carrier (FBMC), OFDM and proven that better system performance is obtained for FBMC. The performance of channel estimation is evaluated through 5G standards and indicates that the usage of multiple auxiliary symbols per pilot leads to better throughput and low Bit Error Rate at low power transmission.

A hierarchy of jumping restarting automata

Restarting automata are a formal model for the linguistic technique of analysis by reduction. In earlier works, all the variants of restarting automata proceed always in a continuous manner. Here we introduce jumping restarting automata that only scan the key information from the input in a discontinuous fashion, which can greatly improve the efficiency in describing the process of a computation. Such an automaton can jump right and skip over a part of tape content. In this work, we investigate the language classes defined through various types of jumping restarting automata. First, we prove that jumping restarting automata can characterize various long-familiar classes of formal languages by taking different degrees, which indicate the number of jump-right operations allowed to be performed per cycle. Further, we show that the language classes defined through jumping restarting automata without auxiliary symbols yield infinite hierarchies based on degrees. Particularly, we prove that for the types of jumping restarting automata with auxiliary symbols, the variant that can continue reading after executing a rewrite operation is strictly more expressive than the variant that cannot do so. This is the first time that the variants above are shown to have different expressive powers in nonmonotone case.

Parenthesis Notation

The formal language of a logical system usually contains several types of symbols. In infix notation, two different kinds of symbols are used to construct compound formula and to indicate the order of combination. The logical constants such as Ø, Ú are used to construct compound formula, and auxiliary symbols such as ( ) are used to indicate the order of a combination. In Polish notation, there is no need for auxiliary symbols such as ( ), and only one class of symbols, N, C, K, etc., is used as a conjunction to make it function as a parenthesis. Contrary to Polish notation, a new parenthesis notation is put forward in this paper. Parenthesis notation uses only parentheses, and empowers them the function of connectives. More importantly, it is proved in this paper that we can define logical constants such as propositional connectives, quantifiers, modal operators and temporal operators in the same formula by using only parenthesis, which can greatly simplify the initial connectives needed to construct the formal system.

Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission

This paper proposes a code defined on a finite ring ℤpM, where pM = 2m−1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,…, ±2m−1. The elements of E correspond to the weights of binary error patterns that can be corrected, with the bidirectional single-bit error being the representative that occurs the most. The splitting set splits the code-word into sub-words, which inspired the name splitting code. Each sub-word, provided with auxiliary control symbols that are a byproduct of the coding procedure, corrects a single symbol error. The code can be defined, with some constraints, for general Mersenne numbers as well, while the multiplier set can be adjusted for adjacent binary errors correction. The application proposed for this code is a hybrid three-stage incremental ARQ procedure that transmits the code-word in the first stage, auxiliary control symbols in the second stage, and retransmits the sub-words detected as incorrect in the third stage. At each stage, error correction can be turned on or off, keeping both the retransmission rate and residual error rate at a low level.

A Complete Taxonomy of Restarting Automata without Auxiliary Symbols*

A complete taxonomy is presented for restarting automata without auxiliary symbols. In this taxonomy, the language classes that are accepted by deterministic and nondeterministic, monotone, weakly monotone, and non-monotone, shrinking and length-reducing restarting automata are compared to each other with respect to inclusion. As it turns out, the 45 types of restarting automata considered yield 29 different classes of languages. By presenting a collection of rather simple example languages, it is shown that, for any two of these language classes ℒ1 and ℒ2, the class ℒ1 is a subclass of ℒ2 if and only if ℒ1 is defined by a type of restarting automaton that is a restriction of a type of restarting automaton that defines the class ℒ2.

Languages Accepted by Weighted Restarting Automata*

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.

On restarting automata with auxiliary symbols and small window size

Here we show that for monotone RWW- (and RRWW-) automata, window size two is sufficient, both in the nondeterministic as well as in the deterministic case. For the former case, this is done by proving that each context-free language is already accepted by a monotone RWW-automaton of window size two. In the deterministic case, we first prove that each deterministic pushdown automaton can be simulated by a deterministic monotone RWW-automaton of window size three, and then we present a construction that transforms a deterministic monotone RWW-automaton of window size three into an equivalent automaton of the same type that has window size two. Furthermore, we study the expressive power of shrinking RWW- and RRWW-automata the window size of which is just one or two. We show that for shrinking RRWW-automata that are nondeterministic, window size one suffices, while for nondeterministic shrinking RWW-automata, we already need window size two to accept all growing context-sensitive languages. In the deterministic case, shrinking RWW- and RRWW-automata of window size one accept only regular languages, while those of window size two characterize the Church-Rosser languages.

Efficient teleportation-based quantum secure communication using quantum channel compression

The paper proposes an efficient protocol for direct secure quantum communication that establishes cryptographic keys between two parties. It relies on two-particle teleportation and quantum channel compression (QCC). The teleportation is accomplished via GHZ-like state quantum channel. The process of quantum channel compression is used to encode four-bit symbols into both two-qubit states (Bell states) and two-bit auxiliary symbols. This leads to reducing the overall classical and quantum resources employed to transfer four-bit symbols at any teleportation procedure in the protocol. The novel teleportation-based protocol achieves an efficiency of 0.4 (40%). It is shown that this is the highest value obtained so far by a protocol of this kind.

A Tunable Energy Signal for Intensity Modulation and Direct Detection Systems: Theory, Simulations, and Experiments

In this paper, we propose a novel method to generate real signal for Visible Light Communication (VLC) systems without using traditional hermitian symmetry on the data symbols obtained using M-ary Pulse Amplitude Modulation (PAM) which is named as Auxiliary PAM (Ax-PAM). We mathematically analyse this method to generate a real signal with tunable energy using auxiliary symbols at the transmitter and the corresponding receiver. Simulation results for Bit Error Rate (BER) show better performance over conventional PAM Discrete Multi-Tone (PAM-DMT) and Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (ACO-OFDM) even under clipping distortion and also demonstrate the tunable energy for the proposed scheme. Furthermore, the proposed scheme is implemented on a VLC test bed designed using Universal Software defined Radio Peripheral (USRP). The experimental results for estimated Signal to Noise Ratio (SNR) and achieved BER for Ax-PAM outperforms PAM-DMT and ACO-OFDM.

Joint Symbol Timing and Channel Estimation for FBMC-OQAM Systems

Filter bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) can achieve very low out-of-band radiation and is considered to be an important candidate waveform for future communication networks. However, the synchronization sequence design and channel estimation issues are complicated in FBMC-OQAM systems owing to the pulses overlap and the intrinsic interference. In this paper, we propose a new training sequence pattern with a high bandwidth efficiency. A pilot symbol and two auxiliary data symbols are used to generate a conjugate symmetric sequence in the time domain while protecting the pilots from the intrinsic interference. Thus, channel estimation can be performed directly by the pilots, and an auto-correlation symbol timing algorithm is introduced by exploiting the conjugate symmetry property. In addition, a pulse tail truncation method is proposed to improve the bandwidth efficiency for burst-mode transmission. Finally, some numerical simulation results are presented to validate the proposed symbol timing, channel estimation, and truncation methods in various scenarios.

Describing of elements IO field in a testing computer program

A standard of describing the process of displaying interactive windows on a computer monitor, through which an output of questions and input of answers are implemented during computer testing, is presented in the article [11]. According to the proposed standard, the description of the process mentioned above is performed with a format line, containing element names, their parameters as well as grouping and auxiliary symbols. Program objects are described using elements of standard. The majority of objects create input and output windows on a computer monitor. The aim of our research was to develop a minimum possible set of elements of standard to perform mathematical and computer science testing. The choice of elements of the standard was conducted in parallel with the development and testing of the program that uses them. This approach made it possible to choose a sufficiently complete set of elements for testing in fields of study mentioned above. For the proposed elements, names were selected in such a way: firstly, they indicate their function and secondly, they coincide with the names of elements in other programming languages that are similar by function. Parameters, their names, their assignments and accepted values are proposed for the elements. The principle of name selection for the parameters was the same as for elements of the standard: the names should correspond to their assignments or coincide with names of similar parameters in other programming languages. The parameters define properties of objects. Particularly, while the elements of standard create windows, the parameters define object properties (location, size, appearance) and the sequence in which windows are created. All elements of standard, proposed in this article are composed in a table, the columns of which have names and functions of these elements. Inside the table, the elements of standard are grouped row by row into four sets: input elements, output elements, input-output elements, grouping elements. All parameters are collected into another table, columns of which have names, assignments and values of parameters. Elements, for which the parameters are intended, are indicated in whole lines inside of this table. After each table, the necessary explanations are given to some of its items. An eхаmple of use of the standard for creating an input window of polynomial coefficients is demonstrated at the end of this article. The example shows significant compactness and ease of recording. Moreover, the testing program, based on the elements of standard, proposed in this article was written on HTML, JavaScript, PHP program languages and allows to perform mathematical and computer science testing. The program is available on the website [20]. Students of Moscow State (National Research) University of Civil Engineering were tested frequently using this program. The composition of elements and their parameters proposed above is convenient and does not require the creators of test problems to have a high level knowledge of programming languages.

Weighted restarting automata and pushdown relations

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. Here we study the special case that words over a given (output) alphabet are assigned as weights to the transitions of a restarting automaton. In this way the automaton is extended to define a mapping from the words over its input alphabet into the semiring of formal languages over a given (output) alphabet, generalizing the restarting transducers introduced by Hundeshagen (2013) [7]. We establish that the monotone restarting transducers that are allowed to use auxiliary symbols characterize the class of almost-realtime pushdown relations, and we characterize the deterministic pushdown functions by a particular type of deterministic monotone restarting transducer. Further, we show that already linearly bounded (word-)weighted monotone restarting automata that use auxiliary symbols are more expressive than the corresponding restarting transducers, both in the deterministic as well as in the nondeterministic case. Finally, we prove that for (word-)weighted monotone restarting automata with auxiliary symbols, the variant that may keep on reading after performing a rewrite step (the so-called RRWW-automaton) is strictly more expressive than the variant that must restart immediately after performing a rewrite step (the so-called RWW-automaton), which again holds in the deterministic as well as in the nondeterministic case. This is the first time that a version of the monotone RRWW-automaton is shown to differ in expressive power from the corresponding version of the monotone RWW-automaton.

Restarting automata with auxiliary symbols restricted by lookahead size

This paper presents a study on lookahead hierarchies for restarting automata with auxiliary symbols. We show that the class of languages for deterministic monotone or monotone restarting automaton, whose restart step and rewrite step are separated, coincides with that of the same type of restarting automaton whose restart and rewrite steps are not separated, for any fixed lookahead size. For the non-monotone deterministic case, the lookahead length must be approximately doubled. We then turn our attention to restarting automata with small lookahead. For the general restarting automaton model, we show that there are just two different classes of languages recognized, through the restriction of lookahead size: those with lookahead size 1 and those with lookahead size 2. We also show that the respective (left-) monotone restarting automaton models characterize the context-free languages and that the respective right–left-monotone restarting automata characterize the linear languages both with just lookahead length 2.

Systems of parallel communicating restarting automata

Several types of systems of parallel communicating restarting automata are introduced and studied. The main result shows that, for all types of restarting automata X, centralized systems of restarting automata of type X have the same computational power as non-centralized systems of restarting automata of the same type and the same number of components. This result is proved by a direct simulation. In addition, it is shown that for one-way restarting automata without auxiliary symbols, systems of degree at least two are more powerful than the component automata themselves. Finally, a lower and an upper bound are given for the expressive power of systems of parallel communicating restarting automata.

Polar Coding Without Alphabet Extension for Asymmetric Models

This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallager's scheme which maps multiple auxiliary symbols distributed uniformly to an actual symbol. However, the complexity of Gallager's scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asymmetric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases.

Foundations of instance level updates in expressive description logics

In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs, in particular addressing questions of expressibility and succinctness: can updated ABoxes always be expressed in the DL in which the original ABox was formulated and, if so, what is the size of the updated ABox? It turns out that DLs have to include nominals and the ‘@’ constructor of hybrid logic for updated ABoxes to be expressible, and that this still holds when updated ABoxes are approximated. Moreover, the size of updated ABoxes is exponential in the role depth of the original ABox and the size of the update. We also show that this situation improves when updated ABoxes are allowed to contain additional auxiliary symbols. Then, DLs only need to include nominals for updated ABoxes to exist, and the size of updated ABoxes is polynomial in the size of both the original ABox and the update.

On stateless deterministic restarting automata

The transitions of a stateless automaton do not depend on internal states but solely on the symbols currently scanned by its head accessing the input and memory. We investigate stateless deterministic restarting automata that, after executing a rewrite step, continue to read their tape before performing a restart. Even the weakest class thus obtained contains the regular languages properly. The relations between different classes of stateless automata as well as between stateless automata and the corresponding types of automata with states are investigated, and it is shown that the language classes defined by the various types of deterministic stateless restarting automata without auxiliary symbols are anti-AFLs that are not even closed under reversal.

Two-dimensional hierarchies of proper languages of lexicalized FRR-automata

Various syntactical phenomena play an important role when developing grammars for natural languages. Among them are the dependencies (subordination) or valences, which are closely related to the complexity of the word-order of the language considered, and the number and types of categories that are used during the process of syntactic disambiguation. Here we present the freely rewriting restarting automaton ( FRR-automaton), which is a variant of the restarting automaton that is tuned towards modeling such phenomena. We study proper languages of deterministic FRR-automata that are (strongly) lexicalized, where we focus on two types of constraints: the number of rewrites per cycle, which models the degree of valences within sentences, and the number of occurrences of auxiliary symbols (categories) in the sentences (words) of the corresponding characteristic language, which models the use of categories during the process of syntactic disambiguation. Based on these constraints we obtain four variants of two-dimensional hierarchies of language classes.

The degree of word-expansion of lexicalized RRWW-automata — A new measure for the degree of nondeterminism of (context-free) languages

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of occurrences of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet. This type of recognition is typical for analysis by reduction, a method used in linguistics for the creation and verification of formal descriptions of natural languages. Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.

ON DETERMINISTIC CD-SYSTEMS OF RESTARTING AUTOMATA

Three variants of determinism are introduced for CD-systems of restarting automata, called strict determinism, global determinism, and local determinism. In mode = 1 globally deterministic CD-systems of restarting automata are of the same expressive power as nonforgetting deterministic restarting automata of the same type, which corresponds to the situation for nondeterministic CD-systems. On the other hand, for the various types of restarting automata without auxiliary symbols, strictly deterministic CD-systems of restarting automata are strictly less expressive than the corresponding deterministic types of nonforgetting restarting automata. Further, globally deterministic CD-systems of restarting automata can be simulated by locally deterministic CD-systems of restarting automata of the same type. In fact, we conjecture that, for all types of restarting automata without auxiliary symbols, the latter are strictly more expressive than the former, but they are strictly less expressive than the corresponding nondeterministic CD-systems of restarting automata.