This paper introduces a novel class of PICOD($t$) problems referred to as $g$-group complete-$S$ PICOD($t$) problems. It constructs a multi-stage achievability scheme to generate pliable index codes for group complete PICOD problems when $S = \{s\}$ is a singleton set. Using the maximum acyclic induced subgraph bound, lower bounds on the broadcast rate are derived for singleton $S$, which establishes the optimality of the achievability scheme for a range of values for $t$ and for any $g$ and $s$. For all other values, it is shown that the achievability scheme is optimal among the restricted class of broadcast codes.

翻译：本文介绍了一类新颖的PICOD($t$)问题，称为$g$-group complete-$S$ PICOD($t$)问题。针对$S = \{s\}$为单元素集的情况，本文构建了一种多阶段可达性方案，用于生成group complete PICOD问题的可塑索引编码。利用最大无环诱导子图界，推导了单元素$S$情形下广播率的下界，从而证明了该可达性方案在特定$t$值范围以及任意$g$和$s$下的最优性。对于其余参数值，证明该可达性方案在受限广播编码类中是最优的。