Information Theory On extrinsic information of good binary codes operating over Gaussian channels

We show that the extrinsic information about the coded bits of any good (capacity achieving) binary code operating over a Gaussian channel is zero when the channel capacity is lower than the code rate and unity when capacity exceeds the code rate, that is, the extrinsic information transfer (EXIT) chart is a step function of the signal to noise ratio and independent of the code. It follows that, for a common class of iterative receivers where the error correcting decoder must operate at first iteration at rate above capacity (such as in turbo equalization, iterative channel estimation, parallel and serial concatenated coding and the like), classical good codes which achieve capacity over the Additive White Gaussian Noise Channel are not effective and should be replaced by different new ones. Copyright © 2006 AEIT