On quasi-cyclic interleavers for parallel turbo codes

We present an interleaving scheme that yields quasi-cyclic turbo codes. We prove that randomly chosen members of this family yield with probability almost 1 turbo codes with asymptotically optimum minimum distance, i.e. growing as a logarithm of the interleaver size. These interleavers are also very practical in terms of memory requirements and their decoding error probabilities for small block lengths compare favorably with previous interleaving schemes.Comment: 15 pages, 2 eps figure

Minimum-Delay Decoding of Turbo-Codes for Upper-Layer FEC

In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first symbols are received. This algorithm compares with the iterative decoding of codes defined on graphs, in that it propagates in the trellises of the turbo code by removing transitions in the same way edges are removed in a bipartite graph under message-passing decoding. Performance comparison with LDPC codes for different coding rates is shown.Comment: 5 pages, submitted SPAWC0

Cycle structure of permutation functions over finite fields and their applications

In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $\mathbb{F}_q$. For the first time M\"{o}bius and R\'edei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of R\'edei functions an exact formula for the inverse function is derived. The cycle structure of R\'edei functions is also investigated. The self-inverse and non-self-inverse versions of these permutation functions can be used to construct new interleavers.Comment: Accepted to appear in AM

Turbo Lattices: Construction and Error Decoding Performance

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 (block 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 and kissing number are investigated. Furthermore, a multi-stage turbo lattice decoding algorithm based on iterative turbo decoding algorithm is given. We show, by simulation, that turbo lattices attain good error performance within $\sim1.25 dB$ from capacity at block length of $n=1035$. Also an excellent performance of only $\sim.5 dB$ away from capacity at SER of $10^{-5}$ is achieved for size $n=10131$.Comment: Submitted to IEEE Trans. on Inform. Theory since Dec 201