On Extrinsic Information of Good Codes Operating Over Memoryless Channels with Incremental Noisiness

We show that the Extrinsic Information about the coded bits of any good (capacity achieving) code operating over a binary symmetric channel is zero when the code operates at code rate above capacity and a positive constant otherwise, that is, the Extrinsic Information Transfer (EXIT) chart is a step function of channel quality, for any capacity achieving code. This extends similar previous results proved over the erasure channel and over the AWGN channel, indicating the step function property of the EXIT chart is rather general. It follows that, for a common class of iterative receivers where the error correcting decoder must operate at the first iterations at rate above capacity (such as in turbo equalization, turbo channel estimation, parallel and serial concatenated coding and the like), classical good codes which achieve capacity over the relevant channels are not effective and should be replaced by different new ones. The authors are with the Department of Electrical Engineering, Technion¿Israel Institute of Technology, 32000 Haifa, Israel. M. Peleg is also with Rafael ltd. The work was supported by the US-Israel Binational Science Foundation (BSF).