Codes on Sparse Graphs for Satellite and Space Communications

This work considers novel low-density parity-check (LDPC) code designs and decoding algorithms for various types of channels. Amongst, efficient maximum likelihood (ML) decoding on both correlated and uncorrelated erasure channels is investigated. Code designs with good performance in terms of codeword error rate (CER) and low decoding complexity are presented. An extension of the ML erasure decoding algorithm to correct additional, sporadic errors is provided. Thereby, the inherent LDPC code structure is exploited. A further development of the decoding algorithm able to cope with erasures and multiple errors within a codeword is presented. Likewise, non-binary LDPC codes for additive white Gaussian noise (AWGN) channels are considered. Amongst others, non-binary protograph-based LDPC codes with block-circulant parity-check matrices are introduced allowing simpler code designs and decoder implementations. Efficient encoding and girth optimization are treated by presenting non-binary irregular repeat-accumulate (IRA) codes based on cycle graphs. It is illustrated that already for block lengths in the order of a few hundred bits excellent CER results may be obtained without the presence of an error floor for practical CERs. Finally, low-rate coding schemes are investigated on both coherent and blockwise non-coherent AWGN channels. Low rates are achieved by concatenating outer non-binary LDPC codes with low-rate inner binary codes, such as Hadamard or Reed-Muller (RM) codes. The concatenated scheme may be decoded efficiently thanks to fast Hadamard transforms (FHTs) applied both on the outer and the inner code. Composite capacity results are derived to cast light on the code construction for the concatenated scheme bringing to finite-length designs with remarkable coding gains w.r.t. conventional low-rate schemes.