The amount of information required to transmit some information content over a lossless channel is equal to the amount of information content. If you have a 2 megabyte disk file on your computer then it will take 2 megabytes of information to transmit that file over a lossless channel.
The latter sentence cannot be right. Not every 2 megabyte disk file contains 2 megabytes of information. For example, a compressed text file contains the same information in both the compressed and uncompressed format. Yet the rules governing the translation from one format to another might require only a few bytes to transmit.
I'll note that the latter quoted statement does not follow from the former statement above regarding the amount information required to transmit an amount of information across a channel.
I have a vague recollection that we have discussed this issue before.
Of course the above should suggest that information and entropy cannot be inversely related as the entropy in a compressed and uncompressed file
are different.
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