Spatially coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform close to the Shannon limit. In this paper we investigate the suitability of coupled regular LDPC code ensembles with respect to rate-flexibility. Regular ensembles with good performance and low complexity exist for a variety of specific code rates. On the other hand it can be observed that outside this set of favorable rational rates the complexity and performance penalty become unreasonably high. We therefore propose ensembles with slight irregularity that allow us to smoothly cover the complete range of rational rates. Our simple construction allows a performance with negligible gap to the Shannon limit while maintaining complexity as low as for the best regular code ensembles. At the same time the construction guarantees that asymptotically the minimum distance grows linearly with the length of the coupled blocks.

We investigate a family of protograph based ratecompatible LDPC convolutional codes. The code family shows improved thresholds close to the Shannon limit compared to their uncoupled versions for the binary erasure channel as well as the AWGN channel. In fact, the gap to Shannon limit is almost uniform for all members of the code family ensuring good performance for all subsequent incremental redundancy transmissions. Compared to similar code families based on regular LDPC codes [1] the complexity of our approach grows slower for the considered rates.

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Spatially-coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform arbitrarily close to the Shannon limit without requiring irregular graph structures. In this paper, we are concerned with the performance and complexity of spatially-coupled ensembles with a rate-compatibility constraint. Spatially-coupled regular ensembles that support rate-compatibility through extension have been proposed before and show very good performance if the node degrees and the coupling width are chosen appropriately. But due to the strict constraint of maintaining a regular degree, there exist certain unfavorable rates that exhibit bad performance and high decoding complexity. We introduce an altered LDPC ensemble construction that changes the evolution of degrees over subsequent incremental redundancy steps in such a way, that the degrees can be kept low to achieve outstanding performance close to Shannon limit for all rates. These ensembles always outperform their regular counterparts at small coupling width.