Random quantization bounds for lattices over q-ary linear codes

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. The efficiency of the lattice-based quantization depends on a lattice parameter called the normalized second moment of Voronoi region. It is shown that there exist lattices over q -ary linear codes with normalized second moment value close to the theoretical limits. Particularly, the coding gain achievable by lattice over ternary codes is equal to 1.5321 dB which is less than 0.01 dB away from the coding gain provided by optimum non-structured vector quantizers.