Channel Blurredness

Abstract

In this chapter we introduce a new information-theoretic notion, termed channel blurredness, which, in contrast to channel capacity, is defined as the infimum of mutual information (rate) between the noise and output of the channel. Intuitively, this measure lends a more direct relationship between the channel noise and the channel output. Three classes of channels are considered, including AWGN channels, ACGN channels, and fading channels. For each of the channel class, we examine the relation between channel blurredness and channel capacity. We show that to attain channel blurredness of MIMO channels, the channel power is mandated to be allocated with totally new “fire-quenching” policies, in stark contrast to the classical “water-filling” according to channel capacity.

As the signal power is increased from zero, we allot the power to the channels with the lowest noise. When the available power is increased still further, some of the power is put into noisier channels. The process by which the power is distributed among the various bins is identical to the way in which water distributes itself in a vessel, hence this process is sometimes referred to as “water-filling”.

—T. M. Cover, J. A. Thomas, “Elements of Information Theory,” 1991 [34]