Very Pliable Index Coding

In the pliable variant of index coding, receivers are allowed to decode any new message not known a priori. Optimal code design for this variant involves identifying each receiver's choice of a new message that minimises the overall transmission rate. This paper proposes a formulation that further relaxes the decoding requirements of pliable index coding by allowing receivers to decode different new messages depending on message realisations. Such relaxation is shown to offer no rate benefit when linear codes are used, but can achieve strictly better rates in general. Scenarios are demonstrated for which the transmission rates are better when the message size is finite than when it is asymptotically large. This is in stark contrast to traditional communication setups.