Analysis of the Block Error Probability of Concatenated Polar Code Ensembles

In this paper, we provide an analysis of the performance of concatenation of polar codes with outer cyclic redundancy check (CRC) codes, separated by an interleaver, in the short and moderate block length regimes. The analysis addresses maximum likelihood decoding as a proxy to the code performance under successive cancellation list decoding. The analysis is carried out by introducing the concatenated polar code (CPC) ensembles, whose distance properties can be analyzed (for sufficiently short block lengths) by means of the uniform interleaver approach. At moderate block lengths, we resort to the Monte Carlo simulations. Results show that if the inner polar code possesses a low minimum distance and the outer CRC code has a sufficiently large amount of redundancy, then the choice of the outer code generator polynomial and the interleaver may yield to a large variability in the performance of the resulting CPC

Forward Error Correction for Optical Transponders

Forward error correction is an essential technique required in almost all communication systems to guarantee reliable data transmission close to the theoretical limits. In this chapter, we discuss the state-of-the-art forward error correction (FEC) schemes for fiber-optic communications. Following a historical overview of the evolution of FEC schemes, we first introduce the fundamental theoretical limits of common communication channel models and show how to compute them. These limits provide the reader with guidelines for comparing different FEC codes under various assumptions. We then provide a brief introduction to the general basic concepts of FEC, followed by an in-depth introduction to the main classes of codes for soft decision decoding and hard decision decoding. We include a wide range of performance curves, compare the different schemes, and give the reader guidelines on which FEC scheme to use. We also introduce the main techniques to combine coding and higher-order modulation (coded modulation), including constellation shaping. Finally, we include a guide on how to evaluate the performance of FEC in transmission experiments. We conclude the chapter with an overview of the properties of some state-of-the-art FEC schemes used in optical communications and an outlook