The random energy model in a magnetic field and joint source–channel coding

We demonstrate that there is an intimate relationship between the magnetic properties of Derrida’s random energy model (REM) of spin glasses and the problem of joint source–channel coding in Information Theory. In particular, typical patterns of erroneously decoded messages in the coding problem have “magnetization” properties that are analogous to those of the REM in certain phases, where the non-uniformity of the distribution of the source in the coding problem plays the role of an external magnetic field applied to the REM. We also relate the ensemble performance (random coding exponents) of joint source–channel codes to the free energy of the REM in its different phases.