Pub Date : 2023-03-22DOI: 10.1109/JSAIT.2023.3276054
Chen Xu;Yao Xie;Daniel A. Zuniga Vazquez;Rui Yao;Feng Qiu
Due to severe societal and environmental impacts, wildfire prediction using multi-modal sensing data has become a highly sought-after data-analytical tool by various stakeholders (such as state governments and power utility companies) to achieve a more informed understanding of wildfire activities and plan preventive measures. A desirable algorithm should precisely predict fire risk and magnitude for a location in real time. In this paper, we develop a flexible spatio-temporal wildfire prediction framework using multi-modal time series data. We first predict the wildfire risk (the chance of a wildfire event) in real-time, considering the historical events using discrete mutually exciting point process models. Then we further develop a wildfire magnitude prediction set method based on the flexible distribution-free time-series conformal prediction (CP) approach. Theoretically, we prove a risk model parameter recovery guarantee, as well as coverage and set size guarantees for the CP sets. Through extensive real-data experiments with wildfire data in California, we demonstrate the effectiveness of our methods, as well as their flexibility and scalability in large regions.
{"title":"Spatio-Temporal Wildfire Prediction Using Multi-Modal Data","authors":"Chen Xu;Yao Xie;Daniel A. Zuniga Vazquez;Rui Yao;Feng Qiu","doi":"10.1109/JSAIT.2023.3276054","DOIUrl":"10.1109/JSAIT.2023.3276054","url":null,"abstract":"Due to severe societal and environmental impacts, wildfire prediction using multi-modal sensing data has become a highly sought-after data-analytical tool by various stakeholders (such as state governments and power utility companies) to achieve a more informed understanding of wildfire activities and plan preventive measures. A desirable algorithm should precisely predict fire risk and magnitude for a location in real time. In this paper, we develop a flexible spatio-temporal wildfire prediction framework using multi-modal time series data. We first predict the wildfire risk (the chance of a wildfire event) in real-time, considering the historical events using discrete mutually exciting point process models. Then we further develop a wildfire magnitude prediction set method based on the flexible distribution-free time-series conformal prediction (CP) approach. Theoretically, we prove a risk model parameter recovery guarantee, as well as coverage and set size guarantees for the CP sets. Through extensive real-data experiments with wildfire data in California, we demonstrate the effectiveness of our methods, as well as their flexibility and scalability in large regions.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"302-313"},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42615184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-16DOI: 10.1109/JSAIT.2023.3276897
Daniel Pook-Kolb;Erik Agrell;Bruce Allen
We give a detailed description of the Voronoi region of the Barnes–Wall lattice $Lambda _{16}$ , including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.
{"title":"The Voronoi Region of the Barnes–Wall Lattice Λ16","authors":"Daniel Pook-Kolb;Erik Agrell;Bruce Allen","doi":"10.1109/JSAIT.2023.3276897","DOIUrl":"10.1109/JSAIT.2023.3276897","url":null,"abstract":"We give a detailed description of the Voronoi region of the Barnes–Wall lattice \u0000<inline-formula> <tex-math>$Lambda _{16}$ </tex-math></inline-formula>\u0000, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"16-23"},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8700143/10153947/10126076.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42379813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-15DOI: 10.1109/JSAIT.2023.3276296
Tao Jiang;Foad Sohrabi;Wei Yu
Beam alignment is an important task for millimeter-wave (mmWave) communication, because constructing aligned narrow beams both at the transmitter (Tx) and the receiver (Rx) is crucial in terms of compensating the significant path loss in very high-frequency bands. However, beam alignment is also a highly nontrivial task because large antenna arrays typically have a limited number of radio-frequency chains, allowing only low-dimensional measurements of the high-dimensional channel. This paper considers a two-sided beam alignment problem based on an alternating ping-pong pilot scheme between Tx and Rx over multiple rounds without explicit feedback. We propose a deep active sensing framework in which two long short-term memory (LSTM) based neural networks are employed to learn the adaptive sensing strategies (i.e., measurement vectors) and to produce the final aligned beamformers at both sides. In the proposed ping-pong protocol, the Tx and the Rx alternately send pilots so that both sides can leverage local observations to sequentially design their respective sensing and data transmission beamformers. The proposed strategy can be extended to scenarios with a reconfigurable intelligent surface (RIS) for designing, in addition, the reflection coefficients at the RIS for both sensing and communications. Numerical experiments demonstrate significant and interpretable performance improvement. The proposed strategy works well even for the challenging multipath channel environments.
{"title":"Active Sensing for Two-Sided Beam Alignment and Reflection Design Using Ping-Pong Pilots","authors":"Tao Jiang;Foad Sohrabi;Wei Yu","doi":"10.1109/JSAIT.2023.3276296","DOIUrl":"10.1109/JSAIT.2023.3276296","url":null,"abstract":"Beam alignment is an important task for millimeter-wave (mmWave) communication, because constructing aligned narrow beams both at the transmitter (Tx) and the receiver (Rx) is crucial in terms of compensating the significant path loss in very high-frequency bands. However, beam alignment is also a highly nontrivial task because large antenna arrays typically have a limited number of radio-frequency chains, allowing only low-dimensional measurements of the high-dimensional channel. This paper considers a two-sided beam alignment problem based on an alternating ping-pong pilot scheme between Tx and Rx over multiple rounds without explicit feedback. We propose a deep active sensing framework in which two long short-term memory (LSTM) based neural networks are employed to learn the adaptive sensing strategies (i.e., measurement vectors) and to produce the final aligned beamformers at both sides. In the proposed ping-pong protocol, the Tx and the Rx alternately send pilots so that both sides can leverage local observations to sequentially design their respective sensing and data transmission beamformers. The proposed strategy can be extended to scenarios with a reconfigurable intelligent surface (RIS) for designing, in addition, the reflection coefficients at the RIS for both sensing and communications. Numerical experiments demonstrate significant and interpretable performance improvement. The proposed strategy works well even for the challenging multipath channel environments.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"24-39"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44233552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-12DOI: 10.1109/JSAIT.2023.3275877
Meng-Che Chang;Shi-Yuan Wang;Tuna Erdoğan;Matthieu R. Bloch
We study the information-theoretic limits of joint communication and sensing when the sensing task is modeled as the estimation of a discrete channel state fixed during the transmission of an entire codeword. This setting captures scenarios in which the time scale over which sensing happens is significantly slower than the time scale over which symbol transmission occurs. The tradeoff between communication and sensing then takes the form of a tradeoff region between the rate of reliable communication and the state detection-error exponent. We investigate such tradeoffs for both mono-static and bi-static scenarios, in which the sensing task is performed at the transmitter or receiver, respectively. In the mono-static case, we develop an exact characterization of the tradeoff in open-loop, when the sensing is not used to assist the communication. We also show the strict improvement brought by a closed-loop operation, in which the sensing informs the communication. In the bi-static case, we develop an achievable tradeoff region that highlights the fundamentally different nature of the bi-static scenario. Specifically, the rate of communication plays a key role in the characterization of the tradeoff and we show how joint strategies, which simultaneously estimate message and state, outperform successive strategies, which only estimate the state after decoding the transmitted message.
{"title":"Rate and Detection-Error Exponent Tradeoff for Joint Communication and Sensing of Fixed Channel States","authors":"Meng-Che Chang;Shi-Yuan Wang;Tuna Erdoğan;Matthieu R. Bloch","doi":"10.1109/JSAIT.2023.3275877","DOIUrl":"10.1109/JSAIT.2023.3275877","url":null,"abstract":"We study the information-theoretic limits of joint communication and sensing when the sensing task is modeled as the estimation of a discrete channel state fixed during the transmission of an entire codeword. This setting captures scenarios in which the time scale over which sensing happens is significantly slower than the time scale over which symbol transmission occurs. The tradeoff between communication and sensing then takes the form of a tradeoff region between the rate of reliable communication and the state detection-error exponent. We investigate such tradeoffs for both mono-static and bi-static scenarios, in which the sensing task is performed at the transmitter or receiver, respectively. In the mono-static case, we develop an exact characterization of the tradeoff in open-loop, when the sensing is not used to assist the communication. We also show the strict improvement brought by a closed-loop operation, in which the sensing informs the communication. In the bi-static case, we develop an achievable tradeoff region that highlights the fundamentally different nature of the bi-static scenario. Specifically, the rate of communication plays a key role in the characterization of the tradeoff and we show how joint strategies, which simultaneously estimate message and state, outperform successive strategies, which only estimate the state after decoding the transmitted message.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"245-259"},"PeriodicalIF":0.0,"publicationDate":"2023-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48253199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-10DOI: 10.1109/JSAIT.2023.3275048
Onur Günlü;Matthieu R. Bloch;Rafael F. Schaefer;Aylin Yener
This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a key attribute, e.g., location. For independent and identically distributed states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The partial characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with binary joint communication and sensing models.
{"title":"Secure Integrated Sensing and Communication","authors":"Onur Günlü;Matthieu R. Bloch;Rafael F. Schaefer;Aylin Yener","doi":"10.1109/JSAIT.2023.3275048","DOIUrl":"10.1109/JSAIT.2023.3275048","url":null,"abstract":"This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a key attribute, e.g., location. For independent and identically distributed states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The partial characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with binary joint communication and sensing models.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"40-53"},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48623002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a data-driven framework to identify the interconnections between firms using an information-theoretic measure. This measure generalizes Granger causality and is capable of detecting nonlinear relationships within a network. Moreover, we develop an algorithm using recurrent neural networks and the aforementioned measure to identify the interconnections of high-dimensional nonlinear systems. The outcome of this algorithm is the causal graph encoding the interconnections among the firms. These causal graphs can be used as preliminary feature selection for another predictive model or for policy design. We evaluate the performance of our algorithm using both synthetic linear and nonlinear experiments and apply it to the daily stock returns of U.S. listed firms and infer their interconnections.
{"title":"Analysis of Large Market Data Using Neural Networks: A Causal Approach","authors":"Marc-Aurèle Divernois;Jalal Etesami;Damir Filipovic;Negar Kiyavash","doi":"10.1109/JSAIT.2024.3351549","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3351549","url":null,"abstract":"We develop a data-driven framework to identify the interconnections between firms using an information-theoretic measure. This measure generalizes Granger causality and is capable of detecting nonlinear relationships within a network. Moreover, we develop an algorithm using recurrent neural networks and the aforementioned measure to identify the interconnections of high-dimensional nonlinear systems. The outcome of this algorithm is the causal graph encoding the interconnections among the firms. These causal graphs can be used as preliminary feature selection for another predictive model or for policy design. We evaluate the performance of our algorithm using both synthetic linear and nonlinear experiments and apply it to the daily stock returns of U.S. listed firms and infer their interconnections.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"833-847"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139715152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1109/JSAIT.2023.3285665
Alexander Vardy;Eitan Yaakobi
Private information retrieval (PIR) protocols allow a user to retrieve a data item from a database without revealing any information about the identity of the item being retrieved. Specifically, in information-theoretic $k$ -server PIR, the database is replicated among $k$ non-communicating servers, and each server learns nothing about the item retrieved by the user. The effectiveness of PIR protocols is usually measured in terms of their communication complexity, which is the total number of bits exchanged between the user and the servers. However, another important cost parameter is storage overhead, which is the ratio between the total number of bits stored on all the servers and the number of bits in the database. Since single-server information-theoretic PIR is impossible, the storage overhead of all existing PIR protocols is at least 2 (or $k$ , in the case of $k$ -server PIR). In this work, we show that information-theoretic PIR can be achieved with storage overhead arbitrarily close to the optimal value of 1, without sacrificing the communication complexity asymptotically. Specifically, we prove that all known linear $k$ -server PIR protocols can be efficiently emulated, while preserving both privacy and communication complexity but significantly reducing the storage overhead. To this end, we distribute the $n$ bits of the database among $s+r$ servers, each storing $n/s$ coded bits (rather than replicas). Notably, our coding scheme remains the same, regardless of the specific $k$ -server PIR protocol being emulated. For every fixed $k$ , the resulting storage overhead $(s+r)/s$ approaches 1 as $s$ grows; explicitly we have $r le k sqrt {s}(1 + o(1))$ . Moreover, in the special case $k = 2$ , the storage overhead is only $1 + {}frac {1}{s}$ . In order to achieve these results, we introduce and study a new kind of binary linear codes, called here
{"title":"Private Information Retrieval Without Storage Overhead: Coding Instead of Replication","authors":"Alexander Vardy;Eitan Yaakobi","doi":"10.1109/JSAIT.2023.3285665","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3285665","url":null,"abstract":"Private information retrieval (PIR) protocols allow a user to retrieve a data item from a database without revealing any information about the identity of the item being retrieved. Specifically, in information-theoretic <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>-server PIR, the database is replicated among <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula> non-communicating servers, and each server learns nothing about the item retrieved by the user. The effectiveness of PIR protocols is usually measured in terms of their communication complexity, which is the total number of bits exchanged between the user and the servers. However, another important cost parameter is storage overhead, which is the ratio between the total number of bits stored on all the servers and the number of bits in the database. Since single-server information-theoretic PIR is impossible, the storage overhead of all existing PIR protocols is at least 2 (or <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>, in the case of <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>-server PIR). In this work, we show that information-theoretic PIR can be achieved with storage overhead arbitrarily close to the optimal value of 1, without sacrificing the communication complexity asymptotically. Specifically, we prove that all known linear <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>-server PIR protocols can be efficiently emulated, while preserving both privacy and communication complexity but significantly reducing the storage overhead. To this end, we distribute the <inline-formula> <tex-math notation=\"LaTeX\">$n$ </tex-math></inline-formula> bits of the database among <inline-formula> <tex-math notation=\"LaTeX\">$s+r$ </tex-math></inline-formula> servers, each storing <inline-formula> <tex-math notation=\"LaTeX\">$n/s$ </tex-math></inline-formula> coded bits (rather than replicas). Notably, our coding scheme remains the same, regardless of the specific <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>-server PIR protocol being emulated. For every fixed <inline-formula> <tex-math notation=\"LaTeX\">$k$ </tex-math></inline-formula>, the resulting storage overhead <inline-formula> <tex-math notation=\"LaTeX\">$(s+r)/s$ </tex-math></inline-formula> approaches 1 as <inline-formula> <tex-math notation=\"LaTeX\">$s$ </tex-math></inline-formula> grows; explicitly we have <inline-formula> <tex-math notation=\"LaTeX\">$r le k sqrt {s}(1 + o(1))$ </tex-math></inline-formula>. Moreover, in the special case <inline-formula> <tex-math notation=\"LaTeX\">$k = 2$ </tex-math></inline-formula>, the storage overhead is only <inline-formula> <tex-math notation=\"LaTeX\">$1 + {}frac {1}{s}$ </tex-math></inline-formula>. In order to achieve these results, we introduce and study a new kind of binary linear codes, called here <inline-formula> <tex-math no","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"286-301"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1109/JSAIT.2023.3300901
Arya Mazumdar
Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on channels with random erasures or errors has been mostly unexplored. In this paper, we analyze the performance of LRCs over such stochastic channels. In particular, for input-symmetric discrete memoryless channels, we give a tight characterization of the gap to Shannon capacity when LRCs are used over the channel. Our results hold for a general notion of LRCs that correct multiple local erasures.
{"title":"Capacity of Locally Recoverable Codes","authors":"Arya Mazumdar","doi":"10.1109/JSAIT.2023.3300901","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3300901","url":null,"abstract":"Motivated by applications in distributed storage, the notion of a locally recoverable code (LRC) was introduced a few years back. In an LRC, any coordinate of a codeword is recoverable by accessing only a small number of other coordinates. While different properties of LRCs have been well-studied, their performance on channels with random erasures or errors has been mostly unexplored. In this paper, we analyze the performance of LRCs over such stochastic channels. In particular, for input-symmetric discrete memoryless channels, we give a tight characterization of the gap to Shannon capacity when LRCs are used over the channel. Our results hold for a general notion of LRCs that correct multiple local erasures.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"276-285"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1109/JSAIT.2023.3294423
Johan Chrisnata;Han Mao Kiah;Alexander Vardy;Eitan Yaakobi
Motivated by DNA-based applications, we generalize the bee identification problem proposed by Tandon et al. (2019). In this setup, we transmit all $M$ codewords from a codebook over some channel and each codeword results in $N$ noisy outputs. Then our task is to identify each codeword from this unordered set of $MN$ noisy outputs. First, via a reduction to a minimum-cost flow problem on a related bipartite flow network called the input-output flow network, we show that the problem can be solved in $O(M^{3})$ time in the worst case. Next, we consider the deletion and the insertion channels individually, and in both cases, we study the expected number of edges in their respective input-output networks. Specifically, we obtain closed expressions for this quantity for certain codebooks and when the codebook comprises all binary words, we show that this quantity is sub-quadratic when the deletion or insertion probability is less than 1/2. This then implies that the expected running time to perform joint decoding for this codebook is $o(M^{3})$ . For other codebooks, we develop methods to compute the expected number of edges efficiently. Finally, we adapt classical peeling-decoding techniques to reduce the number of nodes and edges in the input-output flow network.
{"title":"Bee Identification Problem for DNA Strands","authors":"Johan Chrisnata;Han Mao Kiah;Alexander Vardy;Eitan Yaakobi","doi":"10.1109/JSAIT.2023.3294423","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3294423","url":null,"abstract":"Motivated by DNA-based applications, we generalize the bee identification problem proposed by Tandon et al. (2019). In this setup, we transmit all <inline-formula> <tex-math notation=\"LaTeX\">$M$ </tex-math></inline-formula> codewords from a codebook over some channel and each codeword results in <inline-formula> <tex-math notation=\"LaTeX\">$N$ </tex-math></inline-formula> noisy outputs. Then our task is to identify each codeword from this unordered set of <inline-formula> <tex-math notation=\"LaTeX\">$MN$ </tex-math></inline-formula> noisy outputs. First, via a reduction to a minimum-cost flow problem on a related bipartite flow network called the input-output flow network, we show that the problem can be solved in <inline-formula> <tex-math notation=\"LaTeX\">$O(M^{3})$ </tex-math></inline-formula> time in the worst case. Next, we consider the deletion and the insertion channels individually, and in both cases, we study the expected number of edges in their respective input-output networks. Specifically, we obtain closed expressions for this quantity for certain codebooks and when the codebook comprises all binary words, we show that this quantity is sub-quadratic when the deletion or insertion probability is less than 1/2. This then implies that the expected running time to perform joint decoding for this codebook is <inline-formula> <tex-math notation=\"LaTeX\">$o(M^{3})$ </tex-math></inline-formula>. For other codebooks, we develop methods to compute the expected number of edges efficiently. Finally, we adapt classical peeling-decoding techniques to reduce the number of nodes and edges in the input-output flow network.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"190-204"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50426686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1109/JSAIT.2023.3295836
James Chin-Jen Pang;Hessam Mahdavifar;S. Sandeep Pradhan
Let $A(n, d)$ denote the maximum size of a binary code of length $n$ and minimum Hamming distance $d$ . Studying $A(n, d)$ , including efforts to determine it as well to derive bounds on $A(n, d)$ for large $n$ ’s, is one of the most fundamental subjects in coding theory. In this paper, we explore new lower and upper bounds on $A(n, d)$ in the large-minimum distance regime, in particular, when $d = n/2 - Omega (sqrt {n})$ . We first provide a new construction of cyclic codes, by carefully selecting specific roots in the binary extension field for the check polynomial, with length $n= 2^{m} -1$ , distance $d geq n/2 - 2^{c-1}sqrt {n}$ , and size $n^{c+1/2}$ , for any $mgeq 4$ and any integer $c$ with $0 leq c leq m/2 - 1$ . These code parameters are slightly worse than those of the Delsarte–Goethals (DG) codes that provide the previously known best lower bound in the large-minimum distance regime. However, using a similar and extended code construction technique we show a sequence of cyclic codes that improve upon DG codes and provide the best lower bound in a narrower range of the minimum distance $d$ , in particular, when $d = n/2 - Omega (n^{2/3})$ . Furthermore, by leveraging a Fourier-analytic view of Delsarte’s linear program, upper bounds on $A(n, left lceil{ n/2 - rho sqrt {n}, }right rceil)$ with $rho in (0.5, 9.5)$ are obtained that scale polynomially in $n$ . To the best of authors’ knowledge, the upper bound due to Barg and Nogin (2006) is the only previously known upper bound that scale polynomially in $n$ in this
{"title":"New Bounds on the Size of Binary Codes With Large Minimum Distance","authors":"James Chin-Jen Pang;Hessam Mahdavifar;S. Sandeep Pradhan","doi":"10.1109/JSAIT.2023.3295836","DOIUrl":"https://doi.org/10.1109/JSAIT.2023.3295836","url":null,"abstract":"Let <inline-formula> <tex-math notation=\"LaTeX\">$A(n, d)$ </tex-math></inline-formula> denote the maximum size of a binary code of length <inline-formula> <tex-math notation=\"LaTeX\">$n$ </tex-math></inline-formula> and minimum Hamming distance <inline-formula> <tex-math notation=\"LaTeX\">$d$ </tex-math></inline-formula>. Studying <inline-formula> <tex-math notation=\"LaTeX\">$A(n, d)$ </tex-math></inline-formula>, including efforts to determine it as well to derive bounds on <inline-formula> <tex-math notation=\"LaTeX\">$A(n, d)$ </tex-math></inline-formula> for large <inline-formula> <tex-math notation=\"LaTeX\">$n$ </tex-math></inline-formula>’s, is one of the most fundamental subjects in coding theory. In this paper, we explore new lower and upper bounds on <inline-formula> <tex-math notation=\"LaTeX\">$A(n, d)$ </tex-math></inline-formula> in the large-minimum distance regime, in particular, when <inline-formula> <tex-math notation=\"LaTeX\">$d = n/2 - Omega (sqrt {n})$ </tex-math></inline-formula>. We first provide a new construction of cyclic codes, by carefully selecting specific roots in the binary extension field for the check polynomial, with length <inline-formula> <tex-math notation=\"LaTeX\">$n= 2^{m} -1$ </tex-math></inline-formula>, distance <inline-formula> <tex-math notation=\"LaTeX\">$d geq n/2 - 2^{c-1}sqrt {n}$ </tex-math></inline-formula>, and size <inline-formula> <tex-math notation=\"LaTeX\">$n^{c+1/2}$ </tex-math></inline-formula>, for any <inline-formula> <tex-math notation=\"LaTeX\">$mgeq 4$ </tex-math></inline-formula> and any integer <inline-formula> <tex-math notation=\"LaTeX\">$c$ </tex-math></inline-formula> with <inline-formula> <tex-math notation=\"LaTeX\">$0 leq c leq m/2 - 1$ </tex-math></inline-formula>. These code parameters are slightly worse than those of the Delsarte–Goethals (DG) codes that provide the previously known best lower bound in the large-minimum distance regime. However, using a similar and extended code construction technique we show a sequence of cyclic codes that improve upon DG codes and provide the best lower bound in a narrower range of the minimum distance <inline-formula> <tex-math notation=\"LaTeX\">$d$ </tex-math></inline-formula>, in particular, when <inline-formula> <tex-math notation=\"LaTeX\">$d = n/2 - Omega (n^{2/3})$ </tex-math></inline-formula>. Furthermore, by leveraging a Fourier-analytic view of Delsarte’s linear program, upper bounds on <inline-formula> <tex-math notation=\"LaTeX\">$A(n, left lceil{ n/2 - rho sqrt {n}, }right rceil)$ </tex-math></inline-formula> with <inline-formula> <tex-math notation=\"LaTeX\">$rho in (0.5, 9.5)$ </tex-math></inline-formula> are obtained that scale polynomially in <inline-formula> <tex-math notation=\"LaTeX\">$n$ </tex-math></inline-formula>. To the best of authors’ knowledge, the upper bound due to Barg and Nogin (2006) is the only previously known upper bound that scale polynomially in <inline-formula> <tex-math notation=\"LaTeX\">$n$ </tex-math></inline-formula> in this","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"4 ","pages":"219-231"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50354353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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