Concatenated codes for class IV partial response channels

We present the design and analysis of parallel and serial concatenated codes with iterative decoding for class IV partial response (PR4) signaling. Code rates of the form K₀/(K₀+1), for K₀=4, 8, 16, 32, and 64, are considered. We show that the 1/(1⊕D²) (Tomlinson) precoder, first proposed by Wolf and Ungerboeck (1991) for trellis coded PR4 channels, is effective for both parallel and serial concatenations, but the error-rate “floor” is relatively high for the serial case. This leads to new interleaver and precoder designs for serial concatenations, the latter involving an examination of the conditional distance enumerator of each precoded PR4 channel. The new precoders substantially reduce the floors of the serial concatenated codes, but degrade the performance of the parallel concatenated codes. For a bit-error rate of 10^-5, the best parallel and serial concatenated codes come within 1.7 dB of a lower bound on the capacity limit for PR4 signaling on an additive white Gaussian noise channel