Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Error Control Coding, Second Edition
Error Control Coding, Second Edition
Modulation and coding for linear Gaussian channels
IEEE Transactions on Information Theory
Multilevel codes: theoretical concepts and practical design rules
IEEE Transactions on Information Theory
Sphere-bound-achieving coset codes and multilevel coset codes
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Regular and irregular progressive edge-growth tanner graphs
IEEE Transactions on Information Theory
On the dimensionality of multilevel coded modulation in the high SNR regime
IEEE Communications Letters
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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 multi-dimensional lattices such as the Schläfli, 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.