Volume-Based Lower Bounds to the Capacity of the Gaussian Channel Under Pointwise Additive Input Constraints

We present a family of relatively simple and unified lower bounds on the capacity of the Gaussian channel under a set of pointwise additive input constraints. Specifically, the admissible channel input vectors <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> = (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.o