Turbo Lattices: Construction and Performance Analysis

In this paper a new class of lattices called turbo lattices is introduced and established. We use the lattice Construction D to produce turbo lattices. This method needs a set of nested linear codes as its underlying structure. We benefit from turbo codes as our basis codes. Therefore, a set of nested turbo codes based on nested interleavers and nested convolutional codes is built. To this end, we employ both tail-biting and zero-tail convolutional codes. Using these codes, along with construction D, turbo lattices are created. Several properties of Construction D lattices and fundamental characteristics of turbo lattices including the minimum distance, coding gain, kissing number and an upper bound on the probability of error under a maximum likelihood decoder over AWGN channel are investigated. Furthermore, a multi-stage turbo lattice decoding algorithm based on iterative turbo decoding algorithm is given. Finally, simulation experiments provide strong agreement with our theoretical results. More precisely, for example, it is shown by simulation that turbo lattices attain good error performance within ∼ 1.25 dB from capacity at block length of n = 1035. Also an excellent performance of only ∼ .5 dB away from capacity at SER of 10 is achieved for size n = 10131.