Innovative designs and deployments of erasure codes in communication systems

This dissertation is concerned with the design and application of erasure codes in non-conventional settings. Erasure coding has the potential to improve overall reliability and power efficiency of communication systems which has not yet been fully utilized. With these motivations, this dissertation presents three main contributions that employ the concept of erasure coding.Secondly, an unconventional application of erasure codes in the reduction of high peak-to-average power ratios (PAPRs) in orthogonal frequency division multiplexing (OFDM) systems is presented. This dissertation proposes a new method based on constellation expansion and intentional injection of erasures at the transmitter for PAPR reduction in OFDM signals. The expanded constellation is comprised of a conventional modulation scheme and an external circle or square of alternative signalling points. The advantage of the design is that the location of the alternative signalling points is radially symmetric to the original signalling points in the conventional constellation, which has been demonstrated to maximize the probability of reducing the PAPR. Erasure coding is proposed to address the issue of ambiguous symbol representation resulting from the mapping of more than one point to the same alternative point.Finally, an analytical bound for post-decoding erasure loss rates in binary product codes (PC) is developed in this dissertation. The bound is established by finding the exact number of unrecoverable erasure patterns for a given number of erasures in the received codeword matrix. Development of the improved bound for post-decoding erasure rates has been motivated by the applicability of such codes for combating packet loss in communication networks where retransmission is not always feasible.By interpreting erasure coding as a versatile element in the design of reliable communication networks and power efficient transceivers, this dissertation is addressing current trends in cross-layered protocol designs and exploits the principles of combined channel coding and modulation design. The results presented are applicable to real-time networking applications and multicasting, and to OFDM-based systems with non-linear power amplifiers such as digital audio and video broadcasting.First, innovative linear block code designs are presented to recover from loss and erroneous packets in a communication network. These designs are packet-based as opposed to conventional designs based on bits or symbols. The basis of the new codes is a Vandermonde matrix with elements comprised of different shift operators. The key concept of the designs is that each coded packet is a parity check for the information packets, or a shifted version of them. As a result of the code designs, a new class of single packet error correcting codes is introduced. The erasure recovery and error correction capabilities of the design are investigated individually with a binary erasure channel (BEC) and a binary symmetric channel (BSC) respectively, and Monte Carlo simulations show good agreement with the corresponding theoretical results. Also, the joint error and erasure capabilities of these designs are evaluated over an error-erasure channel (EEC).