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Secure Decentralized Pliable Index Coding for Target Data Size

Anjali Padmanabhan, Danya Arun Bindhu, Nujoom Sageer Karat, Shanuja Sasi

TL;DR

This work addresses securing decentralized pliable index coding (DPIC) in networks where clients hold heterogeneous side-information under the linearly progressive sets with fixed overlap (LPS-FO) model. It develops a recursive transmission scheme that drives all $C$ clients to a common target knowledge level $T = K + C$ while guaranteeing that no client ends up with more than $T$ messages, thus enforcing a strict security constraint. The achievability is realized via Algorithm 1, with a general-case Algorithm 2 and a special-case Algorithm 3, under conditions $K \ge 2P$, $P \ge r_{\max}-2$, and a combinatorial bound on $C$ determining $r_{\max}$; the total number of transmissions obeys $N(C) = C + N(C - r_{\max})$, with base cases $N(1)=1$ and $N(2)=3$. The authors prove the correctness of the schemes, preserve the LPS-FO structure at every recursive step, and show optimality for $C \in \{3,4\}$, highlighting a trade-off between security and transmission overhead $N(C - r_{\max})$ relative to non-secure lower bounds. This work enables secure, scalable, decentralized content distribution in heterogeneous networks where side-information is unevenly distributed.

Abstract

Decentralized Pliable Index Coding (DPIC) problem addresses efficient information exchange in distributed systems where clients communicate among themselves without a central server. An important consideration in DPIC is the heterogeneity of side-information and demand sizes. Although many prior works assume homogeneous settings with identical side-information cardinality and single message demands, these assumptions limit real-world applicability where clients typically possess unequal amounts of prior information. In this paper, we study DPIC problem under heterogeneous side-information cardinalities. We propose a transmission scheme that coordinates client broadcasts to maximize coding efficiency while ensuring that each client achieves a common target level $T$. In addition, we impose a strict security constraint that no client acquires more than the target $T$ number of messages, guaranteeing that each client ends up with exactly $T$ messages. We analyze the communication cost incurred by the proposed scheme under this security constraint.

Secure Decentralized Pliable Index Coding for Target Data Size

TL;DR

This work addresses securing decentralized pliable index coding (DPIC) in networks where clients hold heterogeneous side-information under the linearly progressive sets with fixed overlap (LPS-FO) model. It develops a recursive transmission scheme that drives all clients to a common target knowledge level while guaranteeing that no client ends up with more than messages, thus enforcing a strict security constraint. The achievability is realized via Algorithm 1, with a general-case Algorithm 2 and a special-case Algorithm 3, under conditions , , and a combinatorial bound on determining ; the total number of transmissions obeys , with base cases and . The authors prove the correctness of the schemes, preserve the LPS-FO structure at every recursive step, and show optimality for , highlighting a trade-off between security and transmission overhead relative to non-secure lower bounds. This work enables secure, scalable, decentralized content distribution in heterogeneous networks where side-information is unevenly distributed.

Abstract

Decentralized Pliable Index Coding (DPIC) problem addresses efficient information exchange in distributed systems where clients communicate among themselves without a central server. An important consideration in DPIC is the heterogeneity of side-information and demand sizes. Although many prior works assume homogeneous settings with identical side-information cardinality and single message demands, these assumptions limit real-world applicability where clients typically possess unequal amounts of prior information. In this paper, we study DPIC problem under heterogeneous side-information cardinalities. We propose a transmission scheme that coordinates client broadcasts to maximize coding efficiency while ensuring that each client achieves a common target level . In addition, we impose a strict security constraint that no client acquires more than the target number of messages, guaranteeing that each client ends up with exactly messages. We analyze the communication cost incurred by the proposed scheme under this security constraint.
Paper Structure (20 sections, 7 theorems, 16 equations, 3 tables, 3 algorithms)

This paper contains 20 sections, 7 theorems, 16 equations, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. System Model
  4. Transmission Scheme for Secure DPIC with LPS-FO Side-information Sets
  5. Proof of Correctness of Algorithm 1
  6. Proof of Correctness of Algorithm 2
  7. Phase 1: Intermediate Clients Transmission Structure
  8. Phase 2: Client $\mathcal{C}_{r_{\max}^l-1}^l$ Transmission Strategy
  9. Phase 3: Client $\mathcal{C}_{r_{\max}^l}^l$ Transmission Strategy
  10. Proof of Correctness of Algorithm 3
  11. Phase 1: Intermediate Clients Transmission Structure
  12. Phase 2: Client $\mathcal{C}_{r_{\max}^l-1}^l$ Transmission Strategy
  13. Phase 3: Client $\mathcal{C}_{r_{\max}^l}^l$ Transmission Strategy
  14. Recursive Structure Preservation
  15. Initial Level ($l = 1$)
  16. ...and 5 more sections

Key Result

Theorem 1

For a DPIC problem with LPS-FO side-information sets, the optimal number of transmissions required to achieve the target knowledge level $T = K + C$ for all clients is given by $S_{\text{opt}}=C$, if $C \geq 3$, and $S_{\text{opt}}=3$, if $C = 2$.

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 1: Lower Bound NCCpaper
  • Example 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Example 2
  • Lemma 1
  • Lemma 2
  • ...and 3 more