Abstract
Cyclic codes were introduced as a classical result of coding theory. The relation between these codes and the algebra of polynomials allows us to obtain polynomial‐based procedures for decoding cyclic codes. The development of coding theory has been characterized by dealing with semicontinuous communication channels. Making use of turbo‐codes or low‐density parity check (LDPC) codes, coding schemes that are much more effective than classical cyclic codes with “hard” block‐to‐block decoding can be achieved. LDPC codes are particularly effective when used for transmission along an optical channel. LDPC codes are seen both as a powerful error correction technique used in many standards and as a fertile research topic with many potential applications. These codes are used in many places to transfer information through optical communication channels. Historically, the use of codes for transmission along optical channels can be divided into several stages or “generations”. .
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