Non-binary codes with applications to satellite and space communications

The dissertation investigates the design of error correcting codes for modern communication systems, with emphasis on satellite and space communication. A novel design methodology for capacity-approaching codes (low-density parity-check codes over non-binary finite fields) is introduced and analyzed. In particular, the finite-length design for erasure channels, under maximum a posteriori decoding, is addressed. A key feature of the proposed code design strategy is the careful control of the amount and of the connectivity of the variable nodes of small degrees. The identified family of codes provides a remarkable trade-off between decoding complexity, waterfall and error-floor performances, representing de-facto a universal solution to most of the erasure correcting problems.