Alzubi, Jafar A.; Alzubi, Omar A.; Chen, Thomas M. Forward error correction based on algebraic-geometric theory. (English) Zbl 1347.94076 SpringerBriefs in Electrical and Computer Engineering. Cham: Springer (ISBN 978-3-319-08292-9/pbk; 978-3-319-08293-6/ebook). xii, 70 p. (2014). Publisher’s description: This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time. Cited in 1 Document MSC: 94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory 94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory 14G50 Applications to coding theory and cryptography of arithmetic geometry Keywords:design; construction; implementation; algebraic-geometric codes from Hermitian curves; Matlab simulations; Reed-Solomon codes; bit error rate; different modulation schemes; additive white Gaussian noise channel model; algebraic-geometric codes bit error rate performance; quadrature amplitude modulation; Chase-Pyndiah’s algorithm; algebraic-geometric irregular block turbo codes (AG-IBTC) Software:Matlab PDFBibTeX XMLCite \textit{J. A. Alzubi} et al., Forward error correction based on algebraic-geometric theory. Cham: Springer (2014; Zbl 1347.94076) Full Text: DOI