Low-complexity coded-modulation for ISI-constrained channels

We propose a low-complexity PAM-based transmission scheme that is well suited for channels constrained by inter-symbol interference (ISI) and colored Gaussian noise. The scheme consists of coset-codes constructed on multi-dimensional lattices with a combination of low-density parity-check (LDPC) codes and classical Reed-Solomon (RS) codes. To approach the capacity of an ISI-constrained channel, the code is easy to employ in conjunction with spectral shaping, Tomlinson- Harashima precoding and decision-feedback equalization (DFE). The scheme performs within 2-2.5 dB of un-shaped channel capacity (the sphere-bound) at very low BER´s, even with regular LDPC codes of modest block lengths. We investigate dense multidimensional lattices such as the Schlafli, Gosset, Barnes-Wall, and Leech lattices, besides simple one-dimensional lattices. Via the density evolution technique, we show that the lattices reduce the noise threshold of belief-propagation decoders. We investigate the practical application of the proposed schemes to 10G-Base-T, an emerging Ethernet standard over twisted-pairs at 10 Gbit/sec. A simple 1-dimensional scheme improves upon recent proposals by 0.5-1 dB at BER´s approaching 10^-11, with half the LDPC coding complexity. Multi-dimensional schemes are seen to reduce the complexity further.