  An online shaping technique for high performance communication over Gaussian
channels with Inter-Symbol Interference (ISI) and receiver Analog to Digital
Converter (ADC) noise is presented. The technique uses online transmitter
precoding over Pulse Amplitude Modulation (PAM) constellation, designed to
shape the symbols distribution so that peak power constraint at the channel
output is satisfied. An iterative decoder shares information between a modified
M-BCJR module, which computes online the trellis transition probabilities of
the shaped distribution, and turbo decoder. The result is a reduction in the
required ADC Effective Number Of Bits (ENOB), which is in particular attractive
in modern high-speed wireline links. Theoretical bounds are analytically
derived which enable to assess the possible gain using shaping. On practical
scenarios aim to transmit 200 Gbps and 400 Gbps over printed circuit board, we
demonstrate in simulations an overall ENOB gains as high as 1.43 bit and 1.78
bit, respectively, compared to uniform 4-PAM transmission with turbo
equalization at the receiver side.
