In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into T non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In [S. A. Obead, H. Y. Lin and E. Rosnes, “Single-Server Pliable Private Information Retrieval With Side Information,” arXiv:2305.06857 [cs.IT]], authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class. Identity of each message can be represented as a class-subclass index pair, where subclass index represents the membership of a message within a class. If the user does not know the subclass indices of its side information from a class, that class is termed as unidentifiable. Conversely, if the user knows the subclass indices of its side information from a class, that class is termed as identifiable. A scheme for the PPIR-SI is given by Obead et al. for the case when all classes are unidentifiable, i.e., the user is unaware of the subclass indices of all its side information, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). There are η number of identifiable classes, where 1 ≤η≤r. We give a scheme for PPIR-ISI, and we prove that having some identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases.
In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the quantum code is at least the old soundness divided by the classical code length (up to a constant factor). This allows us to use any classical code with independent checks when distance balancing, where previously only the repetition code had been considered for qLTCs. By using a good classical LDPC code, we are able to grow the dimension of the hypersphere product codes arXiv:1608.05089 [quant-ph] and the hemicubic codes arXiv:1911.03069 [quant-ph] while maintaining their distance and locality, but at the expense of soundness. From this, and also by distance balancing a chain complex of Cross et al. arXiv:2209.11405 [cs.IT], we obtain quantum locally testable codes of new parameters.
Rahat Ullah, Sibghat Ullah, Waqas A. Imtiaz
et al.
With the expansion of Information and Communication Technology, it is important to develop a communication network that can provide high-capacity ubiquitous connectivity. This work proposes an energy-efficient passive optical network (PON) using orthogonal frequency division multiple access (OFDMA) and wavelength division multiplexing (WDM) to facilitate the dense deployment of radio units (RUs) in a beyond 5G (B5G) communication network. High-speed connectivity is ensured by employing a hybrid PON architecture that includes a combination of free space optics (FSO) links and optical fiber (OF) media to carry OFDM and WDM multiplexed traffic. Furthermore, an optical frequency comb generator (OFCG) is utilized at the transmitter module to generate and leverage the spectrum for transmitting information from baseband units (BBUs) to the RUs situated near the end users. The proposed system is analyzed through (i) simulation analysis using Optisystem for transmission capacity computations and (ii) mathematical analysis to determine the total savings in energy. The simulation analysis shows that the given architecture can carry data across 3 km of FSO medium using 512 subcarriers per BBU transmitting at 10 Gbps of data with QPSK-modulated bit sequence. Additionally, energy efficiency shows that the use of an OFCG cuts the total energy usage by 22% at the transmitter module without negatively impacting the system’s high cardinality and transmission capacity.
Rahat Ullah, Sibghat Ullah, Gul Zameen Khan
et al.
A new mechanism for ultra-wide and tunable self-oscillating optical frequency comb (OFC) based on a novel frequency tunable optoelectronic oscillator (OEO) is proposed using cascaded configuration of optical phase-modulator (PM) and electro-absorption-modulator (EAM). The proposed scheme does not require a dedicated RF source to drive the optical-modulators. The OEO is configured by incorporating the self-oscillation loop with cascaded modulators. A high-speed PIN-photodetector (PD) with a dark current of 10nA, bandwidth of 20 GHz, and responsivity of 1A/W in correspondence with an electrical-amplifier (EA), and bandpass Bessel filter (BPBF) is utilized to convert the optical signal into a microwave signal. The PD detected signal is amplified by the EA. The BPBF is used to extract a 10 Mhz bandwidth from the amplified signal with tunable central frequencies. Part of the extracted OEO signal is directly connected to the PM, whereas, a 180-degree phase-shift is added to the signal before transmitting into the EAM. The PM produces ~19 carrier frequencies, whereas, the generated tunable carriers by the EAM ranges from 85 to 35carrriers with an overall bandwidth of ~1.28THz. The negligible power-fluctuations, good number of generated carriers, and high tone-to-noise-ratio of around 40 dB endorse the applicability of the proposed scheme.
A new variant of index coding problem termed as Pliable Index Coding Problem (PICOD) is formulated in [S. Brahma, C. Fragouli, "Pliable index coding", IEEE Transactions on Information Theory, vol. 61, no. 11, pp. 6192-6203, 2015]. In PICOD, we consider a server holding a set of messages and there is a set of clients having a subset of messages with them. Each client is satisfied if it receives any of the message which it doesn't have. We discuss about a class of PICOD where the side information is consecutive. We provide index codes for two extreme cases - for the class where each client gets exactly one desired message and for a class where total number of messages decoded by the effective clients is maximized. Another variant of index coding problem is - c-Constrained Pliable Index Coding Problem [Linqi Song, Christina Fragouli and Tianchu Zhao, "A Pliable Index Coding Approach to Data Shuffling," arXiv:1701.05540v3 [cs.IT] 3 May 2018]. It is basically PICOD with a c-constraint, i.e, each message is decoded by atmost c clients demanding that message. We provide index codes for some classes of this variant with consecutive side information.
Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data resulting from queries. The similarity identification task is to identify the items in a database that are similar to a given query item for a given metric. The problem of compression for similarity identification has been studied in arXiv:1307.6609 [cs.IT]. Unlike classical compression problems, the focus is not on reconstructing the original data. Instead, the compression rate is determined by the desired reliability of the answers. Specifically, the information measure identification rate characterizes the minimum rate that can be achieved among all schemes which guarantee reliable answers with respect to a given similarity threshold. In this paper, we propose a component-based model for computing correlated similarity queries. The correlated signals are first decorrelated by the KLT transform. Then, the decorrelated signal is processed by a distinct D-admissible system for each component. We show that the component-based model equipped with KLT can perfectly represent the multivariate Gaussian similarity queries when optimal rate-similarity allocation applies. Hence, we can derive the identification rate of the multivariate Gaussian signals based on the component-based model. We then extend the result to general Gaussian sources with memory. We also study the models equipped with practical compone\nt systems. We use TC-$\triangle$ schemes that use type covering signatures and triangle-inequality decision rules as our component systems. We propose an iterative method to numerically approximate the minimum achievable rate of the TC-$\triangle$ scheme. We show that our component-based model equipped with TC-$\triangle$ schemes can achieve better performance than the TC-$\triangle$ scheme unaided on handling the multivariate Gaussian sources.
Nujoom Sageer Karat, Spandan Dey, Anoop Thomas
et al.
Classical coded caching setting avails each user to have one dedicated cache. This is generalized to a more general shared cache scheme and the exact expression for the worst case rate was derived in [E. Parrinello, A. Unsal, P. Elia, " Fundamental Limits of Caching in Heterogeneous Networks with Uncoded Prefetching," available on arXiv:1811.06247 [cs.IT], Nov. 2018]. For this case, an optimal linear error correcting delivery scheme is proposed and an expression for the peak rate is established for the same. Furthermore, a new delivery scheme is proposed, which gives an improved rate for the case when the demands are not distinct.
A new variant of index coding problem termed as Pliable Index Coding Problem (PICOD) is formulated in [S. Brahma, C. Fragouli, "Pliable index coding", IEEE Transactions on Information Theory, vol. 61, no. 11, pp. 6192-6203, 2015]. In PICOD, we consider a server holding a set of messages and there is a set of clients having a subset of messages with them. Each client is satisfied if it receives any of the message which it doesn’t have. We discuss the class of PICOD where the side information is consecutive. We provide index codes for two cases - for the class where each client gets exactly one desired message and for a class where total number of messages decoded by the effective clients is maximized. Another variant of index coding problem is - c-Constrained Pliable Index Coding Problem [Linqi Song, Christina Fragouli and Tianchu Zhao, "A Pliable Index Coding Approach to Data Shuffling," arXiv:1701.05540v3 [cs.IT] 3 May 2018]. It is basically PICOD with a c-constraint, i.e, each message is decoded by at most c clients demanding that message. We provide index codes for some classes of this variant with consecutive side information.
Nujoom Sageer Karat, Spandan Dey, Anoop Thomas
et al.
Classical coded caching setting avails each user to have one dedicated cache. This is generalized to a more general shared cache scheme and the exact expression for the worst case rate was derived in [E. Parrinello, A. Unsal, P. Elia, "Fundamental Limits of Caching in Heterogeneous Networks with Uncoded Prefetching," available on arXiv:1811.06247 [cs.IT], Nov. 2018]. For this case, an optimal linear error correcting delivery scheme is proposed and an expression for the peak rate is established for the same. Furthermore, a new delivery scheme is proposed, which gives an improved rate for the case when the demands are not distinct.
This paper examines the linear complexity of new generalized cyclotomic binary sequences of period $2p^n$ recently proposed by Yi Ouang et al. (arXiv:1808.08019v1 [cs.IT] 24 Aug 2018). We generalize results obtained by them and discuss author's conjecture of this paper.
This paper examines the linear complexity of new generalized cyclotomic binary sequences of period $2p^n$ recently proposed by Yi Ouang et al. (arXiv:1808.08019v1 [cs.IT] 24 Aug 2018). We generalize results obtained by them and discuss author's conjecture of this paper.
We examine the task of privacy amplification from information-theoretic and coding-theoretic points of view. In the former, we give a one-shot characterization of the optimal rate of privacy amplification against classical adversaries in terms of the optimal type-II error in asymmetric hypothesis testing. This formulation can be easily computed to give finite- blocklength bounds and turns out to be equivalent to smooth min-entropy bounds by Renner and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a bound in terms of the Eγ divergence by Yang, Schaefer, and Poor [arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy amplification based on linear codes can be easily repurposed for lossy compression. Our construction leads to protocols of optimal rate in the asymptotic i.i.d. limit for a variety of compression scenarios. Finally, appealing to the notion of channel duality recently detailed by us in [IEEE Trans. Inf. Theory 64,577 (2018)], we show that linear error-correcting codes for symmetric channels with quantum output can be transformed into linear lossy source coding schemes for classical variables arising from the dual channel. This explains a “curious duality” in these problems for the (self-dual) erasure channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and partly anticipates recent results on optimal lossy compression by polar and low-density generator matrix codes.
For index coding problems with special structure on the side-information graphs called Interlinked Cycle (IC) structures index codes have been proposed in the literature (C. Thapa, L. Ong, and S. Johnson, "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017 with a correction in "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in arxiv (arxiv:1603.00092v2 [cs.IT] 25 Feb 2018)). In this paper we consider a generalization of IC structures called IC structures with interlocked outer cycles. For IC structures with interlocked outer cycles we show that the optimal length (also known as the minrank of the index coding problem) depends on the maximum number of disjoint outer cycles. We give two sufficient conditions such that if any of these is satisfied then we provide explicit optimal index code construction. The conditions mentioned above are shown to be not necessary by an explicit example.
For index coding problems with special structure on the side-information graphs called Interlinked Cycle (IC) structures index codes have been proposed in the literature (C. Thapa, L. Ong, and S. Johnson, "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in \textit{IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017} with a correction in "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in arxiv (arxiv:1603.00092v2 [cs.IT] 25 Feb 2018)). In this paper we consider a generalization of IC structures called {\it IC structures with interlocked outer cycles}. For IC structures with interlocked outer cycles we show that the optimal length (also known as the minrank of the index coding problem) depends on the maximum number of disjoint outer cycles. We give two sufficient conditions such that if any of these is satisfied then we provide explicit optimal index code construction. The conditions mentioned above are shown to be not necessary by an explicit example.
For side-information graphs called Interlinked Cycle (IC) structures, which generalize cycles and cliques, Thapa, Ong and Johnson ("Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017 and "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in arxiv (arxiv:1603.00092v2 [cs.IT] 25 Feb 2018)) have given an index code construction and a decoding algorithm, for the case where the IC structure does not have any cycles consisting only of non-inner vertices (called outer cycles). In this paper, for IC structures with outer cycles, we give a set of necessary and sufficient conditions for the code construction and the decoding algorithm of Thapa, Ong and Johnson to be valid.
For index coding problems with special structure on the side-information graphs called Interlinked Cycle (IC) structures index codes have been proposed in the literature (C. Thapa, L. Ong, and S. Johnson, "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017, with a correction in "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in arxiv (arxiv:1603.00092v2 [cs.IT] 25 Feb 2018)). Recently (S. Sasi and B.S. Rajan, "On Optimal Index Codes for Interlinked Cycle Structures with Outer Cycles," in arxiv (arXiv:1804.09120v1 [cs.IT]), 24 Apr 2018) for a generalization of IC structures called IC structures with interlocked outer cycles optimal length index codes have been reported and it is shown that the optimal length depends on the maximum number of disjoint outer cycles. In this paper we discuss certain structural properties of IC structures with interlocked outer cycles and provide a simple algorithm to find the maximum number of disjoint outer cycles.
Проведен геометрический и топологический анализ металлооксида с минимальным известным содержанием кислорода CsO, образующегося из кислородсодержащего расплава металлического Cs. Для определения кластеров-прекурсоров кристаллических структур использованы специальные алгоритмы разложения структурных графов на кластерные субструктуры (пакет программ ToposPro). Определены участвующие в самосборке кристаллических структур кластеры-прекурсоры: трехоктаэдрические кластеры CsO, октаэдрические кластеры Cs, тетраэдрические кластеры Cs. Реконструированы симметрийный и топологический коды процессов самосборки кристаллических структур из кластеров-прекурсоров в виде: первичная цепь микрослой микрокаркас.