Abstract
Low-density lattice codes (LDLC) designed for inter-symbol interference (ISI) channels are proposed in this paper, including the node-by-node belief propagation (BP) decoding algorithm and the construction of LDLC codes for ISI channels. A theorem is presented to illustrate that the nominal coding gain of LDLC codes can be increased by introducing ISI into the primary codes. Shaping operation must be used to minimize the power of transmitted lattice points and to utilize the potential nominal coding gain. By using a semi-analytical density evolution method based on all-zero lattice assumption elements of parity check matrix are optimized. Simulation results show that error performance of LDLC code at dimension 10,000 is 1.1 dB from the capacity when the spectral efficiency is 1 bps/Hz.
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