Reed-Solomon and BCH Coding for Digital Engineers

Reed-Solomon and BCH codes are used in a large number of the communication links a digital engineer will build or debug: high-speed SERDES and optical PHYs of 100G-800G Ethernet, automotive single-pair Ethernet, OTN, PON, DOCSIS and DVB, deep-space telemetry, optical discs and flash memory - even the QR codes in Appendix C - yet the textbooks and papers on the subject are written for mathematicians using graduate-level algebra, with the hardware left as an exercise for the engineer. This book takes a different approach. It starts from the representation an engineer already is familiar with - the LFSR and its transition matrices - and builds the Galois-field arithmetic, encoders and the decoders from there. All major approaches to BCH and Reed-Solomon encoding/decoding are explained, along with detailed machine-verified "step-by-step" examples - focusing on actual parallel hardware implementations, with the emphasis being minimizing latency. Next the book walks through some older codes that can be viewed as precursors to BCH, as well as covering the blocks required to build a real communications system: CRCs, scramblers, PRBS generators, and framers. The book concludes with an overview of how to approach real-world designs using RS and BCH, followed by practical design examples - including the 10GBASE-T1 PHY of IEEE 802.3 Clause 149. Practical considerations affecting lab-bringup, production test, and field debug are also discussed. To make this material easily usable by an engineer with an AI assistant, an appendix is provided that contains the book's distilled knowledge printed as QR codes, so a photograph of the desired pages becomes a verified starting point for your own implementation.