Bounds on the Mutual Information for Bit-Linear Linear-Dispersion Codes

In this paper, we derive the relationship between the bit error probability (BEP) of maximum a posteriori (MAP) bit detection and the bit minimum mean square error (MMSE), that is, the BEP is greater than a quarter of the bit MMSE and less than a half of the bit MMSE. By using this result, the lower and upper bounds of the derivative of the mutual information are derived from the BEP in the multiple-input multiple-output (MIMO) communication systems with the bit-linear linear- dispersion (BLLD) codes in the Gaussian channel.