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A statistical mechanical framework for analyzing random linear vectorchannels is presented in a large system limit. The framework is based on theassumptions that the left and right singular value bases of the rectangularchannel matrix $\bH$ are generated independently from uniform distributionsover Haar measures and the eigenvalues of $\bH^{\rm T}\bH$ asymptoticallyfollow a certain specific distribution. These assumptions make it possible tocharacterize the communication performance of the channel utilizing an integralformula with respect to $\bH$, which is analogous to the one introduced byMarinari {\em et. al.} in {\em J. Phys. A} {\bf 27}, 7647 (1994) for largerandom square (symmetric) matrices. A computationally feasible algorithm forapproximately decoding received signals based on the integral formula is alsoprovided.

An integral formula for large random rectangular matrices and its application to analysis of linear vector channels