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This paper introduces the ${\it decentralized}$ Pliable Index CODing (PICOD)problem: a variant of the Index Coding (IC) problem, where a centraltransmitter 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, andinstead users share among themselves massages that can only depend on theirlocal side information set. This paper characterizes the capacity of twoclasses 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 usershaving 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) thecomplement-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 thedecentralized 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 allmessages not in its side information set. Although the optimal code-length maybe the same in both centralized and decentralized settings, the actual optimalcodes are not. For the decentralized PICOD, sparse Maximum Distance Separable(MDS) codes and vector linear index codes are used (as opposed to scalar linearcodes).

Decentralized Pliable Index Coding