Erasure Corrections in Tensor Product DFT Codes

摘要

A new class of long codes that encode numerical values into codewords with numerical symbols is constructed using a Kronecker product of two shorter discrete Fourier transform (DFT) code-checking matrices. These tensor product codes can correct declared erasures up to the capabilities of the two underlying DFT codes. The erasure correction procedures are done in two stages. The first involves pre-syndromes that correct some of the items that are affected by codeword erasures. The newly corrected pre-syndromes, in turn, establish corrections for erased codeword symbols. Some comparisons with long standard DFT codes are included.