On Blahut's decoding algorithms for two-dimensional BCH codes

Abstract

It is shown that decoding of cyclic codes in the DFT domain is equivalent to an appropriate deconvolution problem. A two-dimensional (2-D) generalization of Blahut's (1979) one-dimensional (1-D) linear complexity theorem is obtained and utilized to determine the error-correcting capability of 2-D BCH codes, as afforded by code's defining array of zeros, with regard to correction of burst-errors. The 2-D linear complexity theorem is further utilized to present a new approach for decoding of cyclic codes, in general, and 2-D BCH codes in particular. An alternative exposition of Blahut's decoding algorithms, in the DFT domain, for random and burst error correction in 2-D BCH codes is given from a deconvolution viewpoint. Some modifications for efficient implementation of Blahut's decoding algorithms for random and burst error correction are suggested and improved decoding algorithms are presented. It is shown that the improved decoding algorithm requires at most half the number of passes through the Berlekamp-Massey algorithm compared to the Blahut's decoding algorithm. It is shown that Blahut's decoding algorithms have optimal error-correcting capability and improved decoding algorithms have less computational complexity. A comparative study of various time- and spectral-domain implementations of 2-D BCH decoding algorithms is also given.