Response to Quora Question: Are there any popular science books on information theory?

There are a small handful that may meet your requirements:

Information, Entropy, Life and the Universe: What We Know and What We Do Not Know by Arieh Ben-Naim
http://www.amazon.com/gp/product/9814651672/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=9814651672&linkCode=as2&tag=itbio-20&linkId=A67ICW76GUS5PBJ5

An Introduction to Information Theory: Symbols, Signals and Noise by John R. Pierce
http://www.amazon.com/gp/product/0486240614/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0486240614&linkCode=as2&tag=itbio-20&linkId=FXIGZDG722UWRA3D

The Information: A History, A Theory, A Flood by James Gleick
http://www.amazon.com/gp/product/1400096235/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=1400096235&linkCode=as2&tag=itbio-20&linkId=SH3QLZDFQKUFAILF

Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes by Charles Seife
http://www.amazon.com/gp/product/0143038397/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0143038397&linkCode=as2&tag=itbio-20&linkId=KAC3KXORX7PKWLP7

Complexity: A Guided Tour by Melanie Mitchell
http://www.amazon.com/gp/product/0199798109/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0199798109&linkCode=as2&tag=itbio-20&linkId=QPXNSL7NK4SQWKNM

Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos by Seth Lloyd
http://www.amazon.com/gp/product/B000GCFBP6/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B000GCFBP6&linkCode=as2&tag=itbio-20&linkId=SAUTIICZBWUIROVD

The Mathematical Theory of Communication by Claude E. Shannon and Warren Weaver
http://www.amazon.com/gp/product/0252725484/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0252725484&linkCode=as2&tag=itbio-20&linkId=KR7IE3CY2GDWRVH3

The Ben-Naim book is coming out at the end of May, and is probably the best popular science book on the topic that you're likely to find (I've read most of an early draft). Following that it's still very hard to beat Pierce's presentation all these years later. Seife wasn't too bad while Gleick comes at things from the most broad viewpoint and covers more history than anything else. Lloyd's book mentions it tangentially. Mitchell's book is excellent, and though it only has one chapter on information theory, some of the other areas it covers are tangential to the subject and very interesting in their own right.

Finally, after Ben-Naim and Robinson, I'd really recommend the UofI Press edition of Shannon/Weaver. Though you can get a copy of Shannon's paper for free online, the introduction by Warren Weaver is really excellent (and similar to Robinson's presentation) and then one can delve into a bit of Shannon's actual math, which isn't too difficult and should be able to be followed by most reasonable high school students. Shannon's text is the only one I've listed that has any mathematical equations, but the Weaver half of the book is certainly a popular science presentation without any math.