Shaping for Construction D Lattices
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In this paper we propose a practical and general method for shaping a coding lattice Λ_c obtained by the construction D. The proposal assumes only that the coarse/shaping lattice Λ_s is an integer lattice. To achieve this, a new way to encode and index a construction-D Voronoi lattice code is presented which has linear complexity in the block length. We test the performance of our proposal using a construction-D lattice obtained from an extended BCH code, and shaping is performed by a Gosset Lattice (E_8). This results in a shaping gain of 0.54 dB, which is close to the expected gain of the E_8, 0.65 dB.
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