Group Complete-$\{s\}$ Pliable Index Coding
Sina Eghbal, Badri N. Vellambi, Lawrence Ong, Parastoo Sadeghi

TL;DR
This paper introduces a new class of pliable index coding problems called group complete-$S$ PICOD, providing optimal coding schemes and bounds for certain parameters, advancing the understanding of broadcast rate limits.
Contribution
It defines the group complete-$S$ PICOD problem, develops a multi-stage coding scheme, and establishes optimality bounds for specific parameter ranges.
Findings
Achieves optimal broadcast rates for singleton $S$ and certain $t$, $g$, $s$ values.
Provides lower bounds on broadcast rate using acyclic subgraph bounds.
Shows the scheme's optimality within restricted code classes for other parameters.
Abstract
This paper introduces a novel class of PICOD() problems referred to as -group complete- PICOD() problems. It constructs a multi-stage achievability scheme to generate pliable index codes for group complete PICOD problems when is a singleton set. Using the maximum acyclic induced subgraph bound, lower bounds on the broadcast rate are derived for singleton , which establishes the optimality of the achievability scheme for a range of values for and for any and . For all other values, it is shown that the achievability scheme is optimal among the restricted class of broadcast codes.
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Taxonomy
TopicsCooperative Communication and Network Coding · graph theory and CDMA systems · Coding theory and cryptography
