Code Construction for Pliable Index Coding

Sasi, Shanuja; Rajan, B. Sundar

doi:10.1109/isit.2019.8849812

Cited by 11 publications

(19 citation statements)

References 5 publications

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“…This paper proposes both converse and achievable bounds. The proposed achievable scheme not only strictly outperforms the one in [8] for some values of the system parameters, but it is also information theoretically optimal in some settings. For the remaining cases, the proposed linear code is shown to require at most one more transmission than the converse bound derived by restricting the sender to only use linear codes.…”

mentioning

confidence: 90%

“…Recently, in [8], the Authors extended the private IC problem in [7] to the PICOD framework. Only the case where the side information structure is "circular", and where each user can decode one and only one message was considered in [8].…”

Section: Introductionmentioning

confidence: 99%

“…The first condition is a special case of the "circular-arc network topology hypergraph" class of PICOD studied in [6], for which an optimal solution was given without the privacy constraint. The second condition was first studied in [8] and was motivated by the need to keep content privacy is some distribution networks. This paper proposes both converse and achievable bounds.…”

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confidence: 99%

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Private Pliable Index Coding

Tuninetti

2019

2019 IEEE Information Theory Workshop (ITW)

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The Pliable Index CODing (PICOD) problem is a variant of the Index Coding (IC) problem, where the desired messages by the users, who are equipped with message side information, is part of the optimization. This paper studies the PICOD problem where users are subject to a privacy constraint. In particular, the following spacial class of private PICODs is investigated: 1) the side information structure is circular, and 2) each user can decode one and only one message. The first condition is a special case of the "circular-arc network topology hypergraph" class of PICOD studied in [6], for which an optimal solution was given without the privacy constraint. The second condition was first studied in [8] and was motivated by the need to keep content privacy is some distribution networks. This paper proposes both converse and achievable bounds. The proposed achievable scheme not only strictly outperforms the one in [8] for some values of the system parameters, but it is also information theoretically optimal in some settings. For the remaining cases, the proposed linear code is shown to require at most one more transmission than the converse bound derived by restricting the sender to only use linear codes.

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confidence: 90%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Private Pliable Index Coding

Tuninetti

2019

2019 IEEE Information Theory Workshop (ITW)

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“…Recently, the Authors of [14] studied the case of 'weak security against other users' in PICOD's with 's circular shift' side information set structure, namely, user u's side information set is the set of messages indexed by {u, u + 1, . .…”

Section: Introductionmentioning

confidence: 99%

“…. , u + s − 1} for some fixed s and where the indices are intended modulo the cardinality of the message set m. In [6] we generalized the problem setup of [14] and provided linear codes whose length is at most one more than a converse bound under the constraint of linear encoding. Our results for centralized PICOD with 's circular shift' side information structure demonstrate a multiplicative gap between secure and non-secure versions of the problem that is not bounded in general; in particular, for s ≥ m/2 the two cases have the same information theoretic optimal code-length; however, for 1 ≤ s < m/2 and under the constraint of linear encoding, the minimal number of transmissions for the secure PICOD is lowered bounded by essentially m/(2s), while the non-secure PICOD can always be satisfied by at most 2 transmissions.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Pliable Index Coding

Tuninetti

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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This paper studies a variant of the Pliable Index CODing (PICOD) problem, i.e., an index coding problem where a user can be satisfied by decoding any message that is not in its side information set, where communication is decentralized, i.e., it occurs among users rather than by the central server, and secure, i.e., each user is allowed to decode only one message outside its side information set and must not be able to collect any information about any other message that is not its decoded one. Given the difficulty of the general version of this problem, this paper focuses on the case where the side information sets are 's circular shifts', namely, user u's side information set is the set of messages indexed by {u, u + 1, . . . , u + s − 1} for some fixed s and where the indices are intended modulo the cardinality of the message set. This particular setting has been studied in the 'decentralized non-secure' and in the 'centralized secure' settings, thus allows one to quantify the cost of decentralized communication under security constraints on the number of transmissions. Interestingly, the decentralized vs the centralized secure setting incurs a multiplicative gap of approximately three. This is in contrast to the cases without security constraint, where the multiplicative gap is known to be at most two.

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Private Index Coding

Narayanan

Prabhakaran

Ravi

et al. 2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to it as side information. To enable such private communication, we allow the use of a collection of independent secret keys, each of which is shared amongst a subset of users and is known to the server. The goal is to study properties of the key access structures which make the problem feasible and then design encoding and decoding schemes efficient in the size of the server transmission as well as the sizes of the secret keys. We call this the private index coding problem.We begin by characterizing the key access structures that make private index coding feasible. We also give conditions to check if a given linear scheme is a valid private index code. For up to three users, we characterize the rate region of feasible server transmission and key rates, and show that all feasible rates can be achieved using scalar linear coding and time sharing; we also show that scalar linear codes are sub-optimal for four receivers. The outer bounds used in the case of three users are extended to arbitrary number of users and seen as a generalized version of the well-known polymatroidal bounds for the standard non-private index coding. We also show that the presence of common randomness and private randomness does not change the rate region. Furthermore, we study the case where no keys are shared among the users and provide some necessary and sufficient conditions for feasibility in this setting under a weaker notion of privacy. If the server has the ability to multicast to any subset of users, we demonstrate how this flexibility can be used to provide privacy and characterize the minimum number of server multicasts required.

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Code Construction for Pliable Index Coding

Cited by 11 publications

References 5 publications

Private Pliable Index Coding

Private Pliable Index Coding

Decentralized Pliable Index Coding

Private Index Coding

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