The recent increase in number of wireless devices has been driven by the growing markets of smart... more The recent increase in number of wireless devices has been driven by the growing markets of smart homes and the Internet of Things (IoT). As a result, expanding and/or efficient utilization of the radio frequency (RF) spectrum is critical to accommodate such an increase in wireless bandwidth. Alternatively, recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. Since FSO transmission does not interfere with the RF signals, such a system can be integrated with the current WiFi systems to provide orders of magnitude improvement in bandwidth. A novel component of WiFO is its ability to jointly encode bits from different flows for optimal transmissions. In this paper, we introduce the WiFO architecture and a novel cooperative transmission framework using location assisted coding (LAC) technique to increase the overall wireless capacity. Specifically, achievable rate regions for WiFO using LAC will be characterized. Both numerical and theoretical analyses are given to validate the proposed coding schemes.
Given a channel having binary input X = (x1, x2) having the probability distribution pX = (px 1 ,... more Given a channel having binary input X = (x1, x2) having the probability distribution pX = (px 1 , px 2) that is corrupted by a continuous noise to produce a continuous output y ∈ Y = R. For a given conditional distribution p y|x 1 = φ1(y) and p y|x 2 = φ2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z1, z2,. .. , zN) such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantizedoutput pZ = (pz 1 , pz 2 ,. .. , pz N) has to satisfy a certain constraint. Consider a new variable ry = px 1 φ1(y) px 1 φ1(y) + px 2 φ2(y) , we show that the optimal quantizer has a structure of convex cells in the new variable ry. Based on the convex cells property, a fast algorithm is proposed to find the global optimal quantizer in a polynomial time complexity. In additional, if the quantizedoutput is binary (N = 2), we show a sufficient condition such that the single threshold quantizer is optimal.
Consider a channel having the discrete input X that is corrupted by a continuous noise to produce... more Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuousvalued output U. A thresholding quantizer is then used to quantize the continuous-valued output U to the final discrete output V. One wants to design a thresholding quantizer that maximizes the mutual information between the input and the final quantized output I(X; V). In this paper, the structure of optimal thresholding quantizer is established that finally results in two efficient algorithms having the time complexities O(NM + K log 2 (NM)) for finding the local optimal quantizer and O(KM log(NM)) for finding the global optimal quantizer where N, M, K are the size of input X, received output U and quantized output V , respectively. Both theoretical and numerical results are provided to verify our contributions.
Recent free-space optical (FSO) communication technologies have demonstrated the feasibility of b... more Recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. In this paper, we introduce a cooperative transmission framework using location assisted coding (LAC) technique to increase the overall wireless capacity. For a given network topology, LAC provides three different schemes with different coding/decoding procedures. Based on these schemes, achievable zero-error rate regions for WiFO using LAC will be characterized. Both numerical and theoretical analyses are given to validate the proposed coding schemes.
The sustainable extraction of secondary metabolites from Brassica agro-industrial by-products oft... more The sustainable extraction of secondary metabolites from Brassica agro-industrial by-products often involves the use of high concentrations of ethanol, and/or high temperatures, which tends to decrease the efficiency of protein extraction (yield, profile, etc.). To understand the limits of the combination of these two extraction processes, aqueous ethanol extraction of secondary metabolites (e.g., phenolic compounds and glucosinolates) from Brassica carinata defatted meal was optimized using Response Surface Methodology. The validated models predicted that aqueous ethanol extraction of defatted Carinata meal, with a low aqueous EtOH concentration (22% EtOH) at moderate Te (50 °C), enables the efficient recovery of secondary metabolites (sinapine = 9.12 ± 0.05 mg/gDM, sinigrin = 86.54 ± 3.18 µmol/gDM) while maintaining good protein extractability (59.8 ± 2.1%) from successive alkaline extractions. The evaluation of functional properties of the resulting protein isolates revealed that...
While capacities of discrete memoryless channels are well studied, it is still not possible to ob... more While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush-Kuhn-Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin's disk.
IEEE International Conference on Image Processing 2005, 2005
Mining repeated patterns in television broadcast is important to advertisers in tracking a large ... more Mining repeated patterns in television broadcast is important to advertisers in tracking a large number of television commercials. It can also benefit long-term archival of television because historically significant events are usually marked by repeated airing of the same video clips or sound-bytes. In this paper, we describe a system that can efficiently mine repeated patterns of arbitrary lengths from television broadcast. Compared with existing work, our system has two main innovations: first, our system is robust against minor temporal variations among repeated patterns. This is important as broadcasters often perform temporal editing on commercials so as to fit them into different time slots. Second, our system does not rely on any temporal segmentation algorithm, which may lead to over-or under-segmentation of important patterns. Instead, our system scans the television broadcast with a fixed-size sliding window, summarizes each window into a hash value, and maintains a running frequency count and a reference time-stamp on each hash value. The boundaries of a repeated pattern are identified by the changes in frequency counts and reference time-stamps. Initial experiments show that our system is very efficient in identifying all the repeated commercials from 12 hours of television broadcast.
We consider a channel with a binary input X being corrupted by a continuous-valued noise that res... more We consider a channel with a binary input X being corrupted by a continuous-valued noise that results in a continuous-valued output Y. An optimal binary quantizer is used to quantize the continuous-valued output Y to the final binary output Z to maximize the mutual information I(X; Z). We show that when the ratio of the channel conditional density r(y) = P(Y=y|X=0)/ P(Y =y|X=1) is a strictly increasing/decreasing function of y, then a quantizer having a single threshold can maximize mutual information. Furthermore, we show that an optimal quantizer (possibly with multiple thresholds) is the one with the thresholding vector whose elements are all the solutions of r(y) = r* for some constant r* > 0. Interestingly, the optimal constant r* is unique. This uniqueness property allows for fast algorithmic implementation such as a bisection algorithm to find the optimal quantizer. Our results also confirm some previous results using alternative elementary proofs. We show some numerical e...
In this paper, we investigate the quantization of the output of a binary input discrete memoryles... more In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized output. A polynomial time algorithm is introduced that can find the truly global optimal quantizer. These results hold for binary input channels with an arbitrary number of quantized output. Finally, we extend these results to binary input continuous output channels and show a sufficient condition such that a single threshold quantizer is an optimal quantizer. Both theoretical results and numerical results are provided to justify our techniques.
We consider a channel with discrete binary input X that is corrupted by a given continuous noise ... more We consider a channel with discrete binary input X that is corrupted by a given continuous noise to produce a continuous-valued output Y. A quantizer is then used to quantize the continuous-valued output Y to the final binary output Z. The goal is to design an optimal quantizer Q* and also find the optimal input distribution p*(X) that maximizes the mutual information I(X; Z) between the binary input and the binary quantized output. A linear time complexity searching procedure is proposed. Based on the properties of the optimal quantizer and the optimal input distribution, we reduced the searching range that results in a faster implementation algorithm. Both theoretical and numerical results are provided to illustrate our method.
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inv... more The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have shown an inverse closed form for an interesting matrix which has much applications in communication system. The matrix is called Relay-MISO channel matrix which is channel matrix of the Relay-MISON channel. Base on this inverse closed form, the channel capacity closed form of a this Relay-MISO channel can be determined as a function of the error rate parameter α.
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inv... more The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have shown an inverse closed form for an interesting matrix which has much applications in communication system. Base on this inverse closed form, the channel capacity closed form of a communication system can be determined via the error rate parameter alpha
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
Packet loss and end-to-end delay limit delay sensitive applications over the best effort packet s... more Packet loss and end-to-end delay limit delay sensitive applications over the best effort packet switched networks such as the Internet. In our previous work, we have shown that substantial reduction in packet loss can be achieved by sending packets at appropriate sending rates to a receiver from multiple senders, using disjoint paths, and by protecting packets with forward error correction. In this paper, we propose a Path Diversity with Forward error correction (PDF) system for delay sensitive applications over the Internet in which, disjoint paths from a sender to a receiver are created using a collection of relay nodes. We propose a scalable, heuristic scheme for selecting a redundant path between a sender and a receiver, and show that substantial reduction in packet loss can be achieved by dividing packets between the default path and the redundant path. NS simulations are used to verify the effectiveness of PDF system.
Set partitioning is a key component of many algorithms in machine learning, signal processing, an... more Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there exists a wealth of literature on approximate algorithms and theoretical analyses of the partitioning problem under different settings. In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC). MIPUC finds an optimal partition that minimizes a given loss function under a given concave constraint. MIPUC generalizes the recently proposed deterministic information bottleneck problem which finds an optimal partition that maximizes the mutual information between the input and partition output while minimizing the partition output entropy. Our proposed algorithm is developed based on a novel optimality condition, which allows us to find a locally optimal solution efficiently. Mor...
Given an original discrete source X with the distribution p_X that is corrupted by noise to produ... more Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the pos...
Consider a channel whose the input alphabet set X = { 1 , 2 ,. .. , } contains discrete symbols m... more Consider a channel whose the input alphabet set X = { 1 , 2 ,. .. , } contains discrete symbols modeled as a discrete random variable having a probability mass function p(x) = [ (1), (2),. .. , ()] and the received signal being a continuous random variable. is a distorted version of caused by a channel distortion, characterized by the conditional densities (|) = (), = 1, 2,. .. ,. To recover , a quantizer is used to quantize back to a discrete output Z = { 1 , 2 ,. .. , } corresponding to a random variable with a probability mass function p(z) = [ (1), (2),. .. , ()] such that the mutual information (;) is maximized subject to an arbitrary constraint on p(z). Formally, we are interested in designing an optimal quantizer * that maximizes (;) − () where is a positive number that controls the trade-off between maximizing (;) and minimizing an arbitrary cost function (). Let p(x|) = [ (1 |), (2 |),. .. , (|)] be the posterior distribution of for a given value of , we show that for any arbitrary cost function (.), the optimal quantizer * separates the vectors p(x|) into convex regions. Using this result, a method is proposed to determine an upper bound on the number of thresholds (decision variables on) which is used to speed up the algorithm for finding an optimal quantizer. Numerical results are presented to validate the findings.
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020
Partitioning algorithms play a key role in machine learning, signal processing, and communication... more Partitioning algorithms play a key role in machine learning, signal processing, and communications. They are used in many well-known NP-hard problems such as k-means clustering and vector quantization. The goodness of a partition scheme is measured by a given impurity function over the resulted partitions. The optimal partition is one(s) with the minimum impurity. Practical algorithms for finding an optimal partitioning are approximate, heuristic, and often assume certain properties of the given impurity function such as concavity/convexity. In this paper, we propose a heuristic, efficient (linear time) algorithm for finding the minimum impurity for a broader class of impurity functions which includes popular impurities such as Gini index and entropy. We also make a connection to a well-known result which states that the optimal partitions correspond to the regions separated by hyperplane cuts in the probability space of the posterior distribution.
Proceedings of the 17th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems - MSWiM '14, 2014
Recent advances in free-space optical technology promise a complementary approach to increasing w... more Recent advances in free-space optical technology promise a complementary approach to increasing wireless capacity with minimal changes to the existing wireless technologies. This paper puts forth the hypothesis that it is possible to simultaneously achieve high capacity and high mobility by developing a communication system called WiFiFO (WiFi Free space Optic) that seamlessly integrates the recent freespace optics technologies and the current WiFi technologies. We briefly describe the WiFIFO architecture then discuss the main contribution of this paper that is optimizing the capacity of the proposed WiFiFO system. Specifically, we consider the problem of power allocation for multiple FSO and WiFi transmitters in order to achieve maximum system capacity for given budget power. A mathematical model of the combined capacity of FSO and WiFi channel is derived. We show that the power allocation problem for WiFiFO can be approximated well as a convex optimization problem. To that end, an algorithm based on gradient decent method is developed. Simulation results indicate that the proposed algorithm, together with system architecture can provide an order-of-magnitude increase in capacity over the existing WiFi systems.
Glucosinolates (GSLs) are secondary plant metabolites abundantly found in plant order Brassicales... more Glucosinolates (GSLs) are secondary plant metabolites abundantly found in plant order Brassicales. GSLs are constituted by an S-β-d-glucopyrano unit anomerically connected to O-sulfated (Z)-thiohydroximate moiety. The side-chain of the O-sulfate thiohydroximate moiety, which is derived from a different amino acid, contributes to the diversity of natural GSL, with more than 130 structures identified and validated to this day. Both the structural diversity of GSL and their biological implication in plants have been biochemically studied. Although chemical syntheses of GSL have been devised to give access to these secondary metabolites, direct extraction from biomass remains the conventional method to isolate natural GSL. While intact GSLs are biologically inactive, various products, including isothiocyanates, nitriles, epithionitriles, and cyanides obtained through their hydrolysis of GSLs, exhibit many different biological activities, among which several therapeutic benefits have bee...
The recent increase in number of wireless devices has been driven by the growing markets of smart... more The recent increase in number of wireless devices has been driven by the growing markets of smart homes and the Internet of Things (IoT). As a result, expanding and/or efficient utilization of the radio frequency (RF) spectrum is critical to accommodate such an increase in wireless bandwidth. Alternatively, recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. Since FSO transmission does not interfere with the RF signals, such a system can be integrated with the current WiFi systems to provide orders of magnitude improvement in bandwidth. A novel component of WiFO is its ability to jointly encode bits from different flows for optimal transmissions. In this paper, we introduce the WiFO architecture and a novel cooperative transmission framework using location assisted coding (LAC) technique to increase the overall wireless capacity. Specifically, achievable rate regions for WiFO using LAC will be characterized. Both numerical and theoretical analyses are given to validate the proposed coding schemes.
Given a channel having binary input X = (x1, x2) having the probability distribution pX = (px 1 ,... more Given a channel having binary input X = (x1, x2) having the probability distribution pX = (px 1 , px 2) that is corrupted by a continuous noise to produce a continuous output y ∈ Y = R. For a given conditional distribution p y|x 1 = φ1(y) and p y|x 2 = φ2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z1, z2,. .. , zN) such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantizedoutput pZ = (pz 1 , pz 2 ,. .. , pz N) has to satisfy a certain constraint. Consider a new variable ry = px 1 φ1(y) px 1 φ1(y) + px 2 φ2(y) , we show that the optimal quantizer has a structure of convex cells in the new variable ry. Based on the convex cells property, a fast algorithm is proposed to find the global optimal quantizer in a polynomial time complexity. In additional, if the quantizedoutput is binary (N = 2), we show a sufficient condition such that the single threshold quantizer is optimal.
Consider a channel having the discrete input X that is corrupted by a continuous noise to produce... more Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuousvalued output U. A thresholding quantizer is then used to quantize the continuous-valued output U to the final discrete output V. One wants to design a thresholding quantizer that maximizes the mutual information between the input and the final quantized output I(X; V). In this paper, the structure of optimal thresholding quantizer is established that finally results in two efficient algorithms having the time complexities O(NM + K log 2 (NM)) for finding the local optimal quantizer and O(KM log(NM)) for finding the global optimal quantizer where N, M, K are the size of input X, received output U and quantized output V , respectively. Both theoretical and numerical results are provided to verify our contributions.
Recent free-space optical (FSO) communication technologies have demonstrated the feasibility of b... more Recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. In this paper, we introduce a cooperative transmission framework using location assisted coding (LAC) technique to increase the overall wireless capacity. For a given network topology, LAC provides three different schemes with different coding/decoding procedures. Based on these schemes, achievable zero-error rate regions for WiFO using LAC will be characterized. Both numerical and theoretical analyses are given to validate the proposed coding schemes.
The sustainable extraction of secondary metabolites from Brassica agro-industrial by-products oft... more The sustainable extraction of secondary metabolites from Brassica agro-industrial by-products often involves the use of high concentrations of ethanol, and/or high temperatures, which tends to decrease the efficiency of protein extraction (yield, profile, etc.). To understand the limits of the combination of these two extraction processes, aqueous ethanol extraction of secondary metabolites (e.g., phenolic compounds and glucosinolates) from Brassica carinata defatted meal was optimized using Response Surface Methodology. The validated models predicted that aqueous ethanol extraction of defatted Carinata meal, with a low aqueous EtOH concentration (22% EtOH) at moderate Te (50 °C), enables the efficient recovery of secondary metabolites (sinapine = 9.12 ± 0.05 mg/gDM, sinigrin = 86.54 ± 3.18 µmol/gDM) while maintaining good protein extractability (59.8 ± 2.1%) from successive alkaline extractions. The evaluation of functional properties of the resulting protein isolates revealed that...
While capacities of discrete memoryless channels are well studied, it is still not possible to ob... more While capacities of discrete memoryless channels are well studied, it is still not possible to obtain a closed form expression for the capacity of an arbitrary discrete memoryless channel. This paper describes an elementary technique based on Karush-Kuhn-Tucker (KKT) conditions to obtain (1) a good upper bound of a discrete memoryless channel having an invertible positive channel matrix and (2) a closed form expression for the capacity if the channel matrix satisfies certain conditions related to its singular value and its Gershgorin's disk.
IEEE International Conference on Image Processing 2005, 2005
Mining repeated patterns in television broadcast is important to advertisers in tracking a large ... more Mining repeated patterns in television broadcast is important to advertisers in tracking a large number of television commercials. It can also benefit long-term archival of television because historically significant events are usually marked by repeated airing of the same video clips or sound-bytes. In this paper, we describe a system that can efficiently mine repeated patterns of arbitrary lengths from television broadcast. Compared with existing work, our system has two main innovations: first, our system is robust against minor temporal variations among repeated patterns. This is important as broadcasters often perform temporal editing on commercials so as to fit them into different time slots. Second, our system does not rely on any temporal segmentation algorithm, which may lead to over-or under-segmentation of important patterns. Instead, our system scans the television broadcast with a fixed-size sliding window, summarizes each window into a hash value, and maintains a running frequency count and a reference time-stamp on each hash value. The boundaries of a repeated pattern are identified by the changes in frequency counts and reference time-stamps. Initial experiments show that our system is very efficient in identifying all the repeated commercials from 12 hours of television broadcast.
We consider a channel with a binary input X being corrupted by a continuous-valued noise that res... more We consider a channel with a binary input X being corrupted by a continuous-valued noise that results in a continuous-valued output Y. An optimal binary quantizer is used to quantize the continuous-valued output Y to the final binary output Z to maximize the mutual information I(X; Z). We show that when the ratio of the channel conditional density r(y) = P(Y=y|X=0)/ P(Y =y|X=1) is a strictly increasing/decreasing function of y, then a quantizer having a single threshold can maximize mutual information. Furthermore, we show that an optimal quantizer (possibly with multiple thresholds) is the one with the thresholding vector whose elements are all the solutions of r(y) = r* for some constant r* > 0. Interestingly, the optimal constant r* is unique. This uniqueness property allows for fast algorithmic implementation such as a bisection algorithm to find the optimal quantizer. Our results also confirm some previous results using alternative elementary proofs. We show some numerical e...
In this paper, we investigate the quantization of the output of a binary input discrete memoryles... more In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized output. A polynomial time algorithm is introduced that can find the truly global optimal quantizer. These results hold for binary input channels with an arbitrary number of quantized output. Finally, we extend these results to binary input continuous output channels and show a sufficient condition such that a single threshold quantizer is an optimal quantizer. Both theoretical results and numerical results are provided to justify our techniques.
We consider a channel with discrete binary input X that is corrupted by a given continuous noise ... more We consider a channel with discrete binary input X that is corrupted by a given continuous noise to produce a continuous-valued output Y. A quantizer is then used to quantize the continuous-valued output Y to the final binary output Z. The goal is to design an optimal quantizer Q* and also find the optimal input distribution p*(X) that maximizes the mutual information I(X; Z) between the binary input and the binary quantized output. A linear time complexity searching procedure is proposed. Based on the properties of the optimal quantizer and the optimal input distribution, we reduced the searching range that results in a faster implementation algorithm. Both theoretical and numerical results are provided to illustrate our method.
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inv... more The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have shown an inverse closed form for an interesting matrix which has much applications in communication system. The matrix is called Relay-MISO channel matrix which is channel matrix of the Relay-MISON channel. Base on this inverse closed form, the channel capacity closed form of a this Relay-MISO channel can be determined as a function of the error rate parameter α.
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inv... more The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have shown an inverse closed form for an interesting matrix which has much applications in communication system. Base on this inverse closed form, the channel capacity closed form of a communication system can be determined via the error rate parameter alpha
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
Packet loss and end-to-end delay limit delay sensitive applications over the best effort packet s... more Packet loss and end-to-end delay limit delay sensitive applications over the best effort packet switched networks such as the Internet. In our previous work, we have shown that substantial reduction in packet loss can be achieved by sending packets at appropriate sending rates to a receiver from multiple senders, using disjoint paths, and by protecting packets with forward error correction. In this paper, we propose a Path Diversity with Forward error correction (PDF) system for delay sensitive applications over the Internet in which, disjoint paths from a sender to a receiver are created using a collection of relay nodes. We propose a scalable, heuristic scheme for selecting a redundant path between a sender and a receiver, and show that substantial reduction in packet loss can be achieved by dividing packets between the default path and the redundant path. NS simulations are used to verify the effectiveness of PDF system.
Set partitioning is a key component of many algorithms in machine learning, signal processing, an... more Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there exists a wealth of literature on approximate algorithms and theoretical analyses of the partitioning problem under different settings. In this paper, we formulate and solve a variant of the partition problem called the minimum impurity partition under constraint (MIPUC). MIPUC finds an optimal partition that minimizes a given loss function under a given concave constraint. MIPUC generalizes the recently proposed deterministic information bottleneck problem which finds an optimal partition that maximizes the mutual information between the input and partition output while minimizing the partition output entropy. Our proposed algorithm is developed based on a novel optimality condition, which allows us to find a locally optimal solution efficiently. Mor...
Given an original discrete source X with the distribution p_X that is corrupted by noise to produ... more Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the pos...
Consider a channel whose the input alphabet set X = { 1 , 2 ,. .. , } contains discrete symbols m... more Consider a channel whose the input alphabet set X = { 1 , 2 ,. .. , } contains discrete symbols modeled as a discrete random variable having a probability mass function p(x) = [ (1), (2),. .. , ()] and the received signal being a continuous random variable. is a distorted version of caused by a channel distortion, characterized by the conditional densities (|) = (), = 1, 2,. .. ,. To recover , a quantizer is used to quantize back to a discrete output Z = { 1 , 2 ,. .. , } corresponding to a random variable with a probability mass function p(z) = [ (1), (2),. .. , ()] such that the mutual information (;) is maximized subject to an arbitrary constraint on p(z). Formally, we are interested in designing an optimal quantizer * that maximizes (;) − () where is a positive number that controls the trade-off between maximizing (;) and minimizing an arbitrary cost function (). Let p(x|) = [ (1 |), (2 |),. .. , (|)] be the posterior distribution of for a given value of , we show that for any arbitrary cost function (.), the optimal quantizer * separates the vectors p(x|) into convex regions. Using this result, a method is proposed to determine an upper bound on the number of thresholds (decision variables on) which is used to speed up the algorithm for finding an optimal quantizer. Numerical results are presented to validate the findings.
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020
Partitioning algorithms play a key role in machine learning, signal processing, and communication... more Partitioning algorithms play a key role in machine learning, signal processing, and communications. They are used in many well-known NP-hard problems such as k-means clustering and vector quantization. The goodness of a partition scheme is measured by a given impurity function over the resulted partitions. The optimal partition is one(s) with the minimum impurity. Practical algorithms for finding an optimal partitioning are approximate, heuristic, and often assume certain properties of the given impurity function such as concavity/convexity. In this paper, we propose a heuristic, efficient (linear time) algorithm for finding the minimum impurity for a broader class of impurity functions which includes popular impurities such as Gini index and entropy. We also make a connection to a well-known result which states that the optimal partitions correspond to the regions separated by hyperplane cuts in the probability space of the posterior distribution.
Proceedings of the 17th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems - MSWiM '14, 2014
Recent advances in free-space optical technology promise a complementary approach to increasing w... more Recent advances in free-space optical technology promise a complementary approach to increasing wireless capacity with minimal changes to the existing wireless technologies. This paper puts forth the hypothesis that it is possible to simultaneously achieve high capacity and high mobility by developing a communication system called WiFiFO (WiFi Free space Optic) that seamlessly integrates the recent freespace optics technologies and the current WiFi technologies. We briefly describe the WiFIFO architecture then discuss the main contribution of this paper that is optimizing the capacity of the proposed WiFiFO system. Specifically, we consider the problem of power allocation for multiple FSO and WiFi transmitters in order to achieve maximum system capacity for given budget power. A mathematical model of the combined capacity of FSO and WiFi channel is derived. We show that the power allocation problem for WiFiFO can be approximated well as a convex optimization problem. To that end, an algorithm based on gradient decent method is developed. Simulation results indicate that the proposed algorithm, together with system architecture can provide an order-of-magnitude increase in capacity over the existing WiFi systems.
Glucosinolates (GSLs) are secondary plant metabolites abundantly found in plant order Brassicales... more Glucosinolates (GSLs) are secondary plant metabolites abundantly found in plant order Brassicales. GSLs are constituted by an S-β-d-glucopyrano unit anomerically connected to O-sulfated (Z)-thiohydroximate moiety. The side-chain of the O-sulfate thiohydroximate moiety, which is derived from a different amino acid, contributes to the diversity of natural GSL, with more than 130 structures identified and validated to this day. Both the structural diversity of GSL and their biological implication in plants have been biochemically studied. Although chemical syntheses of GSL have been devised to give access to these secondary metabolites, direct extraction from biomass remains the conventional method to isolate natural GSL. While intact GSLs are biologically inactive, various products, including isothiocyanates, nitriles, epithionitriles, and cyanides obtained through their hydrolysis of GSLs, exhibit many different biological activities, among which several therapeutic benefits have bee...
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