Blind Reconstruction of BCH and RS Codes Using Single-Error Correction

In this paper, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes is proposed, which aims to reconstruct the generator polynomials of BCH and RS codes from the intercepted noisy bitstream in non-cooperative environments. The previous blind reconstruction methods try to select correct (or noiseless) codewords or extract code information from the received bitstream. However, they need to have sufficiently correct codewords for successful reconstruction. Therefore, the existing methods are highly dependent on the channel conditions because a sufficient number of correct codewords should be available for achieving good reconstruction performance. To overcome such high dependency on channel conditions, the proposed blind reconstruction method performs error correction of single-error codewords through the proposed single-error correction method (SCM). Then, both the correct codewords and the corrected single-error codewords are utilized for blind reconstruction. Specifically, the correct codewords are selected based on the algebraic property of BCH and RS codes that codeword polynomials have consecutive roots. At the same time, the codewords presumably with a single error are selected and corrected based on the fact that the most of BCH and RS codeword polynomials with either a single error or double errors do not have consecutive roots. Based on this fact, SCM is devise, which selects and corrects the codewords with a single error with high probability. Finally, it is verified that the proposed blind reconstruction method shows much better reconstruction performance by using only one-tenth of the received codewords compared to the existing best methods even under harsh channel conditions.