In Chapter 11, we address an alternative paradigm for erasure coding that exploits feedback from (multiple) receivers to the transmitter. Here, the receivers are assumed to be interested in the same content, and the transmission takes place over a broadcast channel. The feedback is employed to adapt “on the fly” the coding rate to the channel conditions. This approach, which shares several similarities with the framework of rate-compatible codes with hybrid automatic retransmission query ARQ, relies on the so-called fountain codes. Two well-established classes of fountain codes are discussed, namely the class of LT codes (strongly related to LDPC codes) and the class of Raptor codes.

Maximum-likelihood LDPC decoder analysis. In Chapter 8, the performance of LDPC codes under ML decoding is analyzed. ML decoding is intended here either as the block-wise or the symbol-wise decoding criterion (see Section 2.2). More specifically, the asymptotic analysis on the ML decoding threshold addresses the performance in terms of symbol-wise ML decoding, whereas finite-length bounds are provided for the block error probability under block-wise ML decoding. While the focus is on unstructured LDPC code ensembles, the results in this chapter can be considered to a large extent valid for other LDPC code ensembles.