  The genetic code maps the sixty-four nucleotide triplets (codons) to twenty
amino-acids. While the biochemical details of this code were unraveled long
ago, its origin is still obscure. We review information-theoretic approaches to
the problem of the code's origin and discuss the results of a recent work that
treats the code in terms of an evolving, error-prone information channel. Our
model - which utilizes the rate-distortion theory of noisy communication
channels - suggests that the genetic code originated as a result of the
interplay of the three conflicting evolutionary forces: the needs for diverse
amino-acids, for error-tolerance and for minimal cost of resources. The
description of the code as an information channel allows us to mathematically
identify the fitness of the code and locate its emergence at a second-order
phase transition when the mapping of codons to amino-acids becomes nonrandom.
The noise in the channel brings about an error-graph, in which edges connect
codons that are likely to be confused. The emergence of the code is governed by
the topology of the error-graph, which determines the lowest modes of the
graph-Laplacian and is related to the map coloring problem.
