Can Structure Beat Random? - The Story of Lattice Codes

At the birth of information theory, Shannon surprised the communication world with the concept of random coding, which he used for proving the ultimate limits of his theory. This powerful tool is, however, nonconstructive. In Shannon’s words: “An attempt to obtain a good approximation to ideal coding by following the method of the proof is generally impractical... related to the difficulty of giving an explicit construction for a good approximation to a random sequence.” A practical substitute to random coding are structured codes (one example of which the Hamming code appeared already in Shannon’s paper from 1948). Multiterminal information theory provides us now with a new surprise: for some distributed coding problems structured codes seem to be better than random codes! This summary of my ISIT 2010 plenary talk discusses how lattice codes are used in Gaussian multiterminal settings, and the intuition they provide for the question in the title.