Abstract
We introduce an information measure that reflects the intrinsic perspective of a receiver or sender of a single symbol, who has no access to the communication channel and its source or target. The measure satisfies three desired properties—causality, specificity, intrinsicality—and is shown to be unique. Causality means that symbols must be transmitted with probability greater than chance. Specificity means that information must be transmitted by an individual symbol. Intrinsicality means that a symbol must be taken as such and cannot be decomposed into signal and noise. It follows that the intrinsic information carried by a specific symbol increases if the repertoire of symbols increases without noise (expansion) and decreases if it does so without signal (dilution). An optimal balance between expansion and dilution is relevant for systems whose elements must assess their inputs and outputs from the intrinsic perspective, such as neurons in a network.
Highlights
We introduce an information measure that reflects the intrinsic perspective of a receiver or sender of a single symbol, who has no access to the communication channel and its source or target
Information measures were originally designed to optimize artificial communication channels (Fig. 1A), where a sender and a receiver can freely agree upon a code, implemented by a channel designer, in order to optimize the amount of information transmitted between them[1]
We introduced a novel information measure, which we called the intrinsic difference (ID; Eq 1) because it captures the difference between Pn and Qn from the intrinsic perspective
Summary
We introduce an information measure that reflects the intrinsic perspective of a receiver or sender of a single symbol, who has no access to the communication channel and its source or target. Standard measures of information imply that, from the extrinsic perspective of a channel designer, the input channels of the first and third enclosures are equivalent, since both can potentially transmit one bit per symbol when using proper error correction. While in the first enclosure the input channel transmits the correct symbol on every transmission, in the third enclosure the information from the noiseless wire is irreparably contaminated by the noise in the other wires.
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