Interestingly, Erwin Schrödinger's seminal paper "What is Life?" came out in 1944, almost contemporaneously with the creation of information theory in 1948. Unbeknownst to most Claude Shannon's (the researcher who created the field of information theory and whose Masters thesis literally launched the digital revolution) Ph.D. thesis (1940) was entitled: "An Algebra for Theoretical Genetics," so he could certainly be said to be the god-father of the entire area.

Since then, certainly dozens of researchers have looked at the potential of using information theory to create a better hard core definition of what life really is (certainly the place where any self-respecting Platonist would begin.)

One of the best definitions and frameworks I've seen thus far has to be that of Christoph Adami. To start, and depending on your level of sophistication, take a look at his recent arXiv paper (Information-theoretic considerations concerning the origin of life) and then take a crack at this popular press article about it in Medium. If it's something that blows your skirt up, then you can certainly begin to delve more deeply into some of his journal articles over the past decade or so.

For further references, I maintain a nice list of resources at Information Theory and Biology Resources, as well as a "journal club" of sorts at Mendeley: ITBio: Information Theory, Microbiology, Evolution, and Complexity.

If you really want to blow the top off of your definitions, you might also consider taking a much broader look at the universe (a distant reading, so-to-speak) and read through David Christian's conceptualization (Maps of Time: An Introduction to Big History: David Christian, William H. McNeill of the relatively new area known as "Big History." There, he posits the universe, the stars, and other structures as living things. Admittedly their structures are much simpler than what we might "traditionally" think of as life, but which when considered deeply, certainly are living by the broadest definition - they have less "complexity" but are far longer lived than human beings.