Ramon Ferrer i Cancho and Albert Díaz-Guilera J. Stat. Mech. (2007) P06009 doi:10.1088/1742-5468/2007/06/P06009
Ramon Ferrer i Cancho and Albert Díaz-Guilera
Show affiliationsUntil recently, models of communication have explicitly or implicitly assumed that the goal of a communication system is just maximizing the information transfer between signals and 'meanings'. Recently, it has been argued that a natural communication system not only has to maximize this quantity but also has to minimize the entropy of signals, which is a measure of the cognitive cost of using a word. The interplay between these two factors, i.e. maximization of the information transfer and minimization of the entropy, has been addressed previously using a Monte Carlo minimization procedure at zero temperature. Here we derive analytically the globally optimal communication systems that result from the interaction between these factors. We discuss the implications of our results for previous studies within this framework. In particular we prove that the emergence of Zipf's law using a Monte Carlo technique at zero temperature in previous studies indicates that the system had not reached the global optimum.
89.70.-a Information and communication theory
84.40.Ua Telecommunications: signal transmission and processing; communication satellites
Issue 06 (June 2007)
Received 19 March 2007, accepted for publication 16 May 2007
Published 12 June 2007
Ramon Ferrer i Cancho and Albert Díaz-Guilera J. Stat. Mech. (2007) P06009
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