Conveying individual source sequences over memoryless channels using finite-state decoders with source side information
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We study the following semi-deterministic setting of the joint source-channel coding problem: a deterministic source sequence (a.k.a. individual sequence) is transmitted via a memoryless channel, and decoded by a delay–limited, finite–state decoder with access to side information, which is a noisy version of the source sequence. We first prove a separation theorem with regard to the expected distortion between the source sequence and its reconstruction, which is an extension of earlier work of the same flavor (Ziv 1980, Merhav 2014), but without decoder side information. We then derive a lower bound to the best achievable excess-distortion probability and discuss situations where it is achievable. Here, of course, source coding and channel coding cannot be completely separated if one wishes to meet the bound. Finally, we outline a few variations and extensions of the model considered, such as: (i) incorporating a common reconstruction constraint, (ii) availability of side information at both ends, and (iii) extension to the Gel'fand-Pinsker channel.
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