Abstract
In this letter, we show how to construct low-density lattice code (LDLC) lattices shaped using convolutional code lattices. First, we give an explicit method to find the generator matrices of convolutional code lattices. The shaping gain of convolutional code lattices based on rate 1/2 convolutional codes for short block length is found by evaluating the normalized second moment; a shaping gain as high as 1.24 dB for dimension $n=200$ was found. Then, nested LDLC lattices are constructed. We design LDLC lattices that satisfy conditions necessary for forming nested lattice codes, and give a specific example. For an $n=36$ dimensional lattice, a lattice code based on LDLC lattices, shaped using convolutional code lattices, has a shaping gain of 0.87 dB, over hypercube shaping.
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