Low-Complexity Decoding of Best Known Quasi-Cyclic Linear Codes

Abstract

Error-correcting codes are widely used in modern communications to detect and correct errors that can occur during the transmission of digital information. These codes help ensure reliable transmission by enabling the receiver to reconstruct the original information even if some bits of data were lost or corrupted during transmission. This thesis focuses on improving the decoding schemes of quasi-cyclic error-correcting codes. A classical theoretical framework is provided for understanding error-correcting codes. Quasi-cyclic codes which have the best parameters for given length are considered as generalized low-density parity-check codes to perform decoding. Exhaustive search for parity-check matrices of these codes is done to find ones as suitable as possible for iterative decoding. A new low-complexity decoding algorithm is proposed that uses multiple sub-decoders for the same code. It is shown that for a length 24 quasi-cyclic error-correcting code, this algorithm approaches the best achievable error rates and is competitive with previous results.