Shaping Gain of Lattices Based on Convolutional Codes and Construction A

This paper studies the shaping gain and the performance-complexity trade-off of convolutional code lattices, lattices that are based on convolutional codes and Construction A. Generator polynomials for convolutional codes which provide the best-found shaping gain are presented, for various code rates, memory orders and lattice dimensions. Results are based on exhaustive searches. The obtained shaping gains usually exceed that of convolutional codes good for coding. Convolutional code lattices with memory order 7 can provide a shaping gain of 1.20 dB (up to a possible 1.53 dB theoretical maximum) at dimension 256, which is higher than the 1.03 dB shaping gain of the Leech lattice. While convolutional code lattices based on rate 1/2 convolutional codes have the best shaping gain for a fixed memory order, we show that using rate 1/3 convolutional codes produces a more favorable performance-complexity trade-off.