  This paper introduces the ${\it decentralized}$ Pliable Index CODing (PICOD)
problem: a variant of the Index Coding (IC) problem, where a central
transmitter serves ${\it pliable}$ users with message side information; here,
pliable refers to the fact that a user is satisfied by decoding ${\it any}$ $t$
messages that are not in its side information set. In the decentralized PICOD,
a central transmitter with knowledge of all messages is not present, and
instead users share among themselves massages that can only depend on their
local side information set. This paper characterizes the capacity of two
classes of decentralized complete--$S$ PICOD$(t)$ problems with $m$ messages
(where the set $S\subset[m]$ contains the sizes of the side information sets,
and the number of users is $n=\sum_{s\in S}\binom{m}{s}$, with no two users
having the same side information set): (i) the consecutive case:
$S=[s_\min:s_\max]$ for some $0 \leq s_\min\leq s_\max \leq m-t$, and (ii) the
complement-consecutive case: $S=[0:m-t]\backslash[s_\min:s_\max]$, for some $0
< s_\min\leq s_\max < m-t$. Interestingly, the optimal code-length for the
decentralized PICOD in those cases is the same as for the classical
(centralized) PICOD counterpart, except when the problem is no longer pliable,
that is, it reduces to an IC problem where every user needs to decode all
messages not in its side information set. Although the optimal code-length may
be the same in both centralized and decentralized settings, the actual optimal
codes are not. For the decentralized PICOD, sparse Maximum Distance Separable
(MDS) codes and vector linear index codes are used (as opposed to scalar linear
codes).
