Source Coding with Unreliable Side Information in the Finite Blocklength Regime

This paper studies a special case of the problem of source coding with side information. A single transmitter describes a source to a receiver that has access to a side information observation that is unavailable at the transmitter. While the source and true side information sequences are dependent, stationary, memoryless random processes, the side information observation at the decoder is unreliable, which here means that it may or may not equal the intended side information and therefore may or may not be useful for decoding the source description. The probability of side information observation failure, caused, for example, by a faulty sensor or source decoding error, is non-vanishing but is bounded by a fixed constant independent of the blocklength. This paper proposes a coding system that uses unreliable side information to get efficient source representation subject to a fixed error probability bound. Results include achievability and converse bounds under two different models of the joint distribution of the source, the intended side information, and the side information observation.