Shannon Capacity of MIMO Systems and Metastability of Random Frustrated Spin Systems

A noiseless multiple-input multiple-output (MIMO) channel operating under a strict complexity constraint at the receiver is introduced. According to this constraint, detected bits, obtained by performing hard decisions directly on the channel’s matched filter output, must be the same as the transmitted binary inputs. An asymptotic analysis is carried out using mathematical tools originated from the study of metastable states of spin glasses. It is shown that such complexity-constrained channel exhibits a non-trivial Shannon-theoretic capacity, rigorously analyzed and corroborated using finite-size channel simulations. Index Terms Shannon capacity, metastability, MIMO, large-system analysis, statistical mechanics, spin glass. ∗ Corresponding Author. O. Shental is with the Center for Magnetic Recording Research (CMRR), University of California, San Diego (UCSD), 9500 Gilman Drive, La Jolla, CA 92093, USA (e-mail: [email protected]). I. Kanter is with the Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel (e-mail: [email protected]). November 29, 2007 DRAFT 2