We consider the private information retrieval (PIR) problem from decentralized uncoded caching da... more We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the K files, where each file is of size L bits, and several databases with storage size constraint μKL bits exist in the system. Each database independently chooses μKL bits out of the total KL bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses N databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum\nolimits_{n = 1}^{N + 1} {\binom{N } {{n - 1} }{\mu ^{n - 1}}{{(1 - \mu )}^{N + 1 - n}}\left( {1 + \frac{1}{n} + \cdots + \frac{1}{{{n^{K - 1}}}}} \right)} $. We show that uniform and random caching scheme which is originally propose...
We consider the private information retrieval (PIR) problem from decentralized uncoded caching da... more We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the $K$ files, where each file is of size $L$ bits, and several databases with storage size constraint $\mu K L$ bits exist in the system. Each database independently chooses $\mu K L$ bits out of the total $KL$ bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses $N$ databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum_{n=1}^{N+1} \binom{N}{n-1} \mu^{n-1} (1-\mu)^{N+1-n} \left( 1+ \frac{1}{n} + \dots+ \frac{1}{n^{K-1}} \right)$. We show that uniform and random caching scheme which is originally proposed for decentralized coded c...
We consider the two-user multiple-input multiple- output (MIMO) interference channel with confide... more We consider the two-user multiple-input multiple- output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.
We investigate the problem of semantic private information retrieval (PIR) from coded databases, ... more We investigate the problem of semantic private information retrieval (PIR) from coded databases, where a user requires to download a message out of $M$ independent messages, without revealing its identity to the databases. These messages are coded using an (N, K) MDS code and stored in $N$ non-colluding databases. The $M$ messages are allowed to have different semantics, e.g., different sizes and different probabilities of retrieval. We characterize the exact capacity of semantic PIR with coded databases, and provide an achievable scheme with non-uniform subpacketization. We show that the retrieval rate of semantic PIR with coded databases outperforms that of classical PIR with coded databases when the effects of zero padding shorter messages are taken into account.
We consider the problem of private information retrieval (PIR) over a distributed storage system.... more We consider the problem of private information retrieval (PIR) over a distributed storage system. The storage system consists of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> non-colluding databases, each storing an MDS-coded version of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> messages. In the PIR problem, the user wishes to retrieve one of the available messages without revealing the message identity to any individual database. We derive the information-theoretic capacity of this problem, which is defined as the maximum number of bits of the desired message that can be privately retrieved per one bit of downloaded information. We show that the PIR capacity in this case is <inline-formula> <tex-math notation="LaTeX">$C=(1+{K}/{N}+{K^{2}}/{N^{2}}+\cdots +{K^{M-1}}/{N^{M-1}})^{-1}=(1+R_{c}+R_{c}^{2}+\cdots +R_{c}^{M-1})^{-1}=({1-R...
Balancing traffic among network installed radio base stations is one of the main challenges facin... more Balancing traffic among network installed radio base stations is one of the main challenges facing mobile operators because of the unhomogeneous geographical distribution of mobile subscribers in addition to practical and environmental limitations preventing acquiring the best locations to build radio sites. This increases the challenge of satisfying the increasing data speed demand for smartphone users. In this paper, we present a reinforcement learning framework for optimizing neighbor cell relational parameters that can better balance the traffic between different cells within a defined geographical cluster. We present a comprehensive design of the learning framework that includes key system performance indicators and the design of a general reward function. System level simulations show that reinforcement learning based optimization for neighbor cell borders can significantly improve overall system performance; in particular, with a reward function defined as throughput, an impr...
We consider the problem of private information retrieval (PIR) from $N$ non-colluding and replica... more We consider the problem of private information retrieval (PIR) from $N$ non-colluding and replicated databases when the user is equipped with a cache that holds an uncoded fraction $r$ from each of the $K$ stored messages in the databases. We assume that the databases are unaware of the cache content. We investigate $D^{\ast}(r)$ the optimal download cost normalized with the message size as a function of K, N, r. We develop inner and outer bounds for the optimal download cost. Both inner and outer bounds are piece-wise linear functions in $r$ (for fixed N, K) that consist of $K$ line segments. The inner and the outer bounds match in general for the cases of very low caching ratios and very high caching ratios. As a corollary, we fully characterize the optimal download cost caching ratio tradeoff for K = 3. For general K, N, and r, we show that the largest additive gap between the achievability and the converse bounds is $\frac{1}{6}$.
We consider the problem of privately updating a message out of K messages from N replicated and n... more We consider the problem of privately updating a message out of K messages from N replicated and non-colluding databases. In this problem, a user has an outdated version of the message Ŵθ of length L bits that differ from the current version Wθ in at most f bits. The user needs to retrieve Wθ correctly using a private information retrieval (PIR) scheme with the least number of downloads without leaking any information about the message index θ to any individual database. To that end, we propose a novel achievable scheme based on syndrome decoding. Specifically, the user downloads the syndrome corresponding to Wθ, according to a linear block code with carefully designed parameters, using the optimal PIR scheme for messages with a length constraint. We derive lower and upper bounds for the optimal download cost that match if the term ${\log _2}\left( \sum\nolimits_{i = 0}^f \binom L i \right)$ is an integer. Our results imply that there is a significant reduction in the download cost i...
We consider private information retrieval (PIR) of a single file out of K files from N non-collud... more We consider private information retrieval (PIR) of a single file out of K files from N non-colluding databases with heterogeneous storage constraints m = (m1, ⋯, mN). The aim of this work is to jointly design the content placement phase and the retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint $\mu = \frac{1}{N}\sum\nolimits_{n = 1}^N {{m_n}} $. We show the optimum content placement explicitly for N = 3.
We consider the problem of private information retrieval from N storage-constrained databases. In... more We consider the problem of private information retrieval from N storage-constrained databases. In this problem, a user wishes to retrieve a single message out of M messages (of size L) without revealing any information about the identity of the message to individual databases. Each database stores μML symbols, i.e., a μ fraction of the entire library, where
We consider the problem of private information retrieval (PIR) of a single message out of K messa... more We consider the problem of private information retrieval (PIR) of a single message out of K messages from N non-colluding and non-replicated databases. Different from the majority of the existing literature, here, we consider the case of non-replicated databases under a special non-replication structure where each database stores M out of K messages and each message is stored across R different databases. This generates an R-regular graph structure for the storage system where the vertices of the graph are the messages and the edges are the databases. We derive a general upper bound for M = 2 that depends on the graph structure. We then specialize the problem to storage systems described by two special types of graph structures: cyclic graphs and fully-connected graphs. We prove that the PIR capacity for the case of cyclic graphs is $\frac{2}{{K + 1}}$, and the PIR capacity for the case of fully-connected graphs is $\min \left\{ {\frac{2}{K},\;\frac{1}{2}} \right\}$. In both cases, ...
We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II).... more We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single message (file) privately out of M messages, which are stored in N replicated and non-communicating databases. An external eavesdropper observes a fraction <inline-formula> <tex-math notation="LaTeX">$\mu _{\text {n}}$ </tex-math></inline-formula> (of its choice) of the traffic exchanged between the nth database and the user. In addition to the privacy constraint, the databases should encode the returned answer strings such that the eavesdropper learns absolutely nothing about the <italic>contents</italic> of the databases. We aim at characterizing the capacity of the PIR-WTC-II under the combined privacy and security constraints. We obtain a general upper bound for the problem in the form of a max-min optimization problem, which extends the converse proof of the PIR problem under asymmetric tr...
A status updating communication system is examined, in which a transmitter communicates with a re... more A status updating communication system is examined, in which a transmitter communicates with a receiver over a noisy channel. The goal is to realize timely delivery of fresh data over time, which is assessed by an age-of-information (AoI) metric. Channel coding is used to combat the channel errors, and feedback is sent to acknowledge updates' reception. In case decoding is unsuccessful, a hybrid ARQ protocol is employed, in which incremental redundancy (IR) bits are transmitted to enhance the decoding ability. This continues for some amount of time in case decoding remains unsuccessful, after which a new (fresh) status update is transmitted instead. In case decoding is successful, the transmitter has the option to idly wait for a certain amount of time before sending a new update. A general problem is formulated that optimizes the codeword and IR lengths for each update, and the waiting times, such that the long term average AoI is minimized. Stationary deterministic policies ar...
We consider the problem of private information retrieval (PIR) of a single message (file) out of ... more We consider the problem of private information retrieval (PIR) of a single message (file) out of <tex>$M$</tex> messages from <tex>$N$</tex> distributed databases under asymmetric traffic from databases. In this problem, the ratios between the traffic from the databases are constrained, i.e., the ratio of the length of the answer string that the user receives from the nth database to the total length of all answer strings from all databases is constrained to be <tex>$\tau_{n}$</tex>. For this problem, for fixed <tex>$M, N$</tex>, we develop a general upper bound <tex>$\bar{C}(\tau)$</tex>. Our converse bound is a piece-wise affine function in the traffic ratio vector <tex>$\tau=(\tau_{1}, \cdots, \tau_{N})$</tex>. For the lower bound, we explicitly show the achievability of <tex>$\begin{pmatrix} M+N-1\\ M \end{pmatrix}$</tex> corner points. For the remaining traffic ratio vectors, we perform time-sha...
We introduce the problem of timely private information retrieval (PIR) from $N$ non-colluding and... more We introduce the problem of timely private information retrieval (PIR) from $N$ non-colluding and replicated servers. In this problem, a user desires to retrieve a message out of $M$ messages from the servers, whose contents are continuously updating. The retrieval process should be executed in a timely manner such that no information is leaked about the identity of the message. To assess the timeliness, we use the age of information (AoI) metric. Interestingly, the timely PIR problem reduces to an AoI minimization subject to PIR constraints under asymmetric traffic. We explicitly characterize the optimal tradeoff between the PIR rate and the AoI metric (peak AoI or average AoI) for the case of $N=2,\ M=3$. Further, we provide some structural insights on the general problem with arbitrary $N,\ M$.
2017 IEEE International Symposium on Information Theory (ISIT)
We consider the problem of multi-message private information retrieval (MPIR) from N non-communic... more We consider the problem of multi-message private information retrieval (MPIR) from N non-communicating replicated databases. In MPIR, the user is interested in retrieving P messages out of M stored messages without leaking the identity of the retrieved messages. The information-theoretic sum capacity of MPIR C P s is the maximum number of desired message symbols that can be retrieved privately per downloaded symbol. For the case P ≥ M 2 , we determine the exact sum capacity of MPIR as C P s = 1 1+ M −P P N. For P ≤ M 2 , we develop lower and upper bounds for all M, P, N. These bounds match if the number of messages M is an integer multiple of the number of desired messages P , in which case, C P s = 1− 1 N 1−(1 N) M/P. Our results indicate that joint retrieval of desired messages is more efficient than successive use of single-message retrieval schemes.
We study the problem of private set intersection (PSI). In this problem, there are two entities E... more We study the problem of private set intersection (PSI). In this problem, there are two entities E i , for i = 1, 2, each storing a set P i , whose elements are picked from a finite field F K , on N i replicated and non-colluding databases. It is required to determine the set intersection P 1 ∩ P 2 without leaking any information about the remaining elements to the other entity, and to do this with the least amount of downloaded bits. We first show that the PSI problem can be recast as a multi-message symmetric private information retrieval (MM-SPIR) problem with certain added restrictions. Next, as a stand-alone result, we derive the information-theoretic sum capacity of MM-SPIR,
We consider the private information retrieval (PIR) problem from decentralized uncoded caching da... more We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the K files, where each file is of size L bits, and several databases with storage size constraint μKL bits exist in the system. Each database independently chooses μKL bits out of the total KL bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses N databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum\nolimits_{n = 1}^{N + 1} {\binom{N } {{n - 1} }{\mu ^{n - 1}}{{(1 - \mu )}^{N + 1 - n}}\left( {1 + \frac{1}{n} + \cdots + \frac{1}{{{n^{K - 1}}}}} \right)} $. We show that uniform and random caching scheme which is originally propose...
We consider the private information retrieval (PIR) problem from decentralized uncoded caching da... more We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the $K$ files, where each file is of size $L$ bits, and several databases with storage size constraint $\mu K L$ bits exist in the system. Each database independently chooses $\mu K L$ bits out of the total $KL$ bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses $N$ databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be $\frac{D}{L} = \sum_{n=1}^{N+1} \binom{N}{n-1} \mu^{n-1} (1-\mu)^{N+1-n} \left( 1+ \frac{1}{n} + \dots+ \frac{1}{n^{K-1}} \right)$. We show that uniform and random caching scheme which is originally proposed for decentralized coded c...
We consider the two-user multiple-input multiple- output (MIMO) interference channel with confide... more We consider the two-user multiple-input multiple- output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.
We investigate the problem of semantic private information retrieval (PIR) from coded databases, ... more We investigate the problem of semantic private information retrieval (PIR) from coded databases, where a user requires to download a message out of $M$ independent messages, without revealing its identity to the databases. These messages are coded using an (N, K) MDS code and stored in $N$ non-colluding databases. The $M$ messages are allowed to have different semantics, e.g., different sizes and different probabilities of retrieval. We characterize the exact capacity of semantic PIR with coded databases, and provide an achievable scheme with non-uniform subpacketization. We show that the retrieval rate of semantic PIR with coded databases outperforms that of classical PIR with coded databases when the effects of zero padding shorter messages are taken into account.
We consider the problem of private information retrieval (PIR) over a distributed storage system.... more We consider the problem of private information retrieval (PIR) over a distributed storage system. The storage system consists of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> non-colluding databases, each storing an MDS-coded version of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> messages. In the PIR problem, the user wishes to retrieve one of the available messages without revealing the message identity to any individual database. We derive the information-theoretic capacity of this problem, which is defined as the maximum number of bits of the desired message that can be privately retrieved per one bit of downloaded information. We show that the PIR capacity in this case is <inline-formula> <tex-math notation="LaTeX">$C=(1+{K}/{N}+{K^{2}}/{N^{2}}+\cdots +{K^{M-1}}/{N^{M-1}})^{-1}=(1+R_{c}+R_{c}^{2}+\cdots +R_{c}^{M-1})^{-1}=({1-R...
Balancing traffic among network installed radio base stations is one of the main challenges facin... more Balancing traffic among network installed radio base stations is one of the main challenges facing mobile operators because of the unhomogeneous geographical distribution of mobile subscribers in addition to practical and environmental limitations preventing acquiring the best locations to build radio sites. This increases the challenge of satisfying the increasing data speed demand for smartphone users. In this paper, we present a reinforcement learning framework for optimizing neighbor cell relational parameters that can better balance the traffic between different cells within a defined geographical cluster. We present a comprehensive design of the learning framework that includes key system performance indicators and the design of a general reward function. System level simulations show that reinforcement learning based optimization for neighbor cell borders can significantly improve overall system performance; in particular, with a reward function defined as throughput, an impr...
We consider the problem of private information retrieval (PIR) from $N$ non-colluding and replica... more We consider the problem of private information retrieval (PIR) from $N$ non-colluding and replicated databases when the user is equipped with a cache that holds an uncoded fraction $r$ from each of the $K$ stored messages in the databases. We assume that the databases are unaware of the cache content. We investigate $D^{\ast}(r)$ the optimal download cost normalized with the message size as a function of K, N, r. We develop inner and outer bounds for the optimal download cost. Both inner and outer bounds are piece-wise linear functions in $r$ (for fixed N, K) that consist of $K$ line segments. The inner and the outer bounds match in general for the cases of very low caching ratios and very high caching ratios. As a corollary, we fully characterize the optimal download cost caching ratio tradeoff for K = 3. For general K, N, and r, we show that the largest additive gap between the achievability and the converse bounds is $\frac{1}{6}$.
We consider the problem of privately updating a message out of K messages from N replicated and n... more We consider the problem of privately updating a message out of K messages from N replicated and non-colluding databases. In this problem, a user has an outdated version of the message Ŵθ of length L bits that differ from the current version Wθ in at most f bits. The user needs to retrieve Wθ correctly using a private information retrieval (PIR) scheme with the least number of downloads without leaking any information about the message index θ to any individual database. To that end, we propose a novel achievable scheme based on syndrome decoding. Specifically, the user downloads the syndrome corresponding to Wθ, according to a linear block code with carefully designed parameters, using the optimal PIR scheme for messages with a length constraint. We derive lower and upper bounds for the optimal download cost that match if the term ${\log _2}\left( \sum\nolimits_{i = 0}^f \binom L i \right)$ is an integer. Our results imply that there is a significant reduction in the download cost i...
We consider private information retrieval (PIR) of a single file out of K files from N non-collud... more We consider private information retrieval (PIR) of a single file out of K files from N non-colluding databases with heterogeneous storage constraints m = (m1, ⋯, mN). The aim of this work is to jointly design the content placement phase and the retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint $\mu = \frac{1}{N}\sum\nolimits_{n = 1}^N {{m_n}} $. We show the optimum content placement explicitly for N = 3.
We consider the problem of private information retrieval from N storage-constrained databases. In... more We consider the problem of private information retrieval from N storage-constrained databases. In this problem, a user wishes to retrieve a single message out of M messages (of size L) without revealing any information about the identity of the message to individual databases. Each database stores μML symbols, i.e., a μ fraction of the entire library, where
We consider the problem of private information retrieval (PIR) of a single message out of K messa... more We consider the problem of private information retrieval (PIR) of a single message out of K messages from N non-colluding and non-replicated databases. Different from the majority of the existing literature, here, we consider the case of non-replicated databases under a special non-replication structure where each database stores M out of K messages and each message is stored across R different databases. This generates an R-regular graph structure for the storage system where the vertices of the graph are the messages and the edges are the databases. We derive a general upper bound for M = 2 that depends on the graph structure. We then specialize the problem to storage systems described by two special types of graph structures: cyclic graphs and fully-connected graphs. We prove that the PIR capacity for the case of cyclic graphs is $\frac{2}{{K + 1}}$, and the PIR capacity for the case of fully-connected graphs is $\min \left\{ {\frac{2}{K},\;\frac{1}{2}} \right\}$. In both cases, ...
We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II).... more We consider the problem of private information retrieval through wiretap channel II (PIR-WTC-II). In PIR-WTC-II, a user wants to retrieve a single message (file) privately out of M messages, which are stored in N replicated and non-communicating databases. An external eavesdropper observes a fraction <inline-formula> <tex-math notation="LaTeX">$\mu _{\text {n}}$ </tex-math></inline-formula> (of its choice) of the traffic exchanged between the nth database and the user. In addition to the privacy constraint, the databases should encode the returned answer strings such that the eavesdropper learns absolutely nothing about the <italic>contents</italic> of the databases. We aim at characterizing the capacity of the PIR-WTC-II under the combined privacy and security constraints. We obtain a general upper bound for the problem in the form of a max-min optimization problem, which extends the converse proof of the PIR problem under asymmetric tr...
A status updating communication system is examined, in which a transmitter communicates with a re... more A status updating communication system is examined, in which a transmitter communicates with a receiver over a noisy channel. The goal is to realize timely delivery of fresh data over time, which is assessed by an age-of-information (AoI) metric. Channel coding is used to combat the channel errors, and feedback is sent to acknowledge updates' reception. In case decoding is unsuccessful, a hybrid ARQ protocol is employed, in which incremental redundancy (IR) bits are transmitted to enhance the decoding ability. This continues for some amount of time in case decoding remains unsuccessful, after which a new (fresh) status update is transmitted instead. In case decoding is successful, the transmitter has the option to idly wait for a certain amount of time before sending a new update. A general problem is formulated that optimizes the codeword and IR lengths for each update, and the waiting times, such that the long term average AoI is minimized. Stationary deterministic policies ar...
We consider the problem of private information retrieval (PIR) of a single message (file) out of ... more We consider the problem of private information retrieval (PIR) of a single message (file) out of <tex>$M$</tex> messages from <tex>$N$</tex> distributed databases under asymmetric traffic from databases. In this problem, the ratios between the traffic from the databases are constrained, i.e., the ratio of the length of the answer string that the user receives from the nth database to the total length of all answer strings from all databases is constrained to be <tex>$\tau_{n}$</tex>. For this problem, for fixed <tex>$M, N$</tex>, we develop a general upper bound <tex>$\bar{C}(\tau)$</tex>. Our converse bound is a piece-wise affine function in the traffic ratio vector <tex>$\tau=(\tau_{1}, \cdots, \tau_{N})$</tex>. For the lower bound, we explicitly show the achievability of <tex>$\begin{pmatrix} M+N-1\\ M \end{pmatrix}$</tex> corner points. For the remaining traffic ratio vectors, we perform time-sha...
We introduce the problem of timely private information retrieval (PIR) from $N$ non-colluding and... more We introduce the problem of timely private information retrieval (PIR) from $N$ non-colluding and replicated servers. In this problem, a user desires to retrieve a message out of $M$ messages from the servers, whose contents are continuously updating. The retrieval process should be executed in a timely manner such that no information is leaked about the identity of the message. To assess the timeliness, we use the age of information (AoI) metric. Interestingly, the timely PIR problem reduces to an AoI minimization subject to PIR constraints under asymmetric traffic. We explicitly characterize the optimal tradeoff between the PIR rate and the AoI metric (peak AoI or average AoI) for the case of $N=2,\ M=3$. Further, we provide some structural insights on the general problem with arbitrary $N,\ M$.
2017 IEEE International Symposium on Information Theory (ISIT)
We consider the problem of multi-message private information retrieval (MPIR) from N non-communic... more We consider the problem of multi-message private information retrieval (MPIR) from N non-communicating replicated databases. In MPIR, the user is interested in retrieving P messages out of M stored messages without leaking the identity of the retrieved messages. The information-theoretic sum capacity of MPIR C P s is the maximum number of desired message symbols that can be retrieved privately per downloaded symbol. For the case P ≥ M 2 , we determine the exact sum capacity of MPIR as C P s = 1 1+ M −P P N. For P ≤ M 2 , we develop lower and upper bounds for all M, P, N. These bounds match if the number of messages M is an integer multiple of the number of desired messages P , in which case, C P s = 1− 1 N 1−(1 N) M/P. Our results indicate that joint retrieval of desired messages is more efficient than successive use of single-message retrieval schemes.
We study the problem of private set intersection (PSI). In this problem, there are two entities E... more We study the problem of private set intersection (PSI). In this problem, there are two entities E i , for i = 1, 2, each storing a set P i , whose elements are picked from a finite field F K , on N i replicated and non-colluding databases. It is required to determine the set intersection P 1 ∩ P 2 without leaking any information about the remaining elements to the other entity, and to do this with the least amount of downloaded bits. We first show that the PSI problem can be recast as a multi-message symmetric private information retrieval (MM-SPIR) problem with certain added restrictions. Next, as a stand-alone result, we derive the information-theoretic sum capacity of MM-SPIR,
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Papers by Karim Banawan