In this letter, we propose a simplified step-by-step decoding algorithm for t-error-correcting binary Bose-ChaudhuriHocquenghem (BCH) codes based on logical analysis. Compared to the conventional stepby-step decoding algorithm, the computation complexity of this decoder is much less, since it significantly reduces the matrix calculation and the operations of multiplication. key words: BCH code,...

BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm, which requires about O(t) computational steps, where t is the error-correction capability of the BCH code. The evaluation of the errorlocator polynomial may also be computed using fast inversion techniques for Hankel matrices. It will be shown that only O(lt)...

Recommendations from the Pediatric Endocrine Society for Evaluation and Management of Persistent Hypoglycemia in Neonates, Infants, and Children Paul S. Thornton, MB, BCh, Charles A. Stanley, MD, Diva D. De Leon, MD, MSCE, Deborah Harris, PhD, Morey W. Haymond, MD, Khalid Hussain, MD, MPH, Lynne L. Levitsky, MD, Mohammad H. Murad, MD, MPH, Paul J. Rozance, MD, Rebecca A. Simmons, MD, Mark A. Sp...

Discovered by Bose, Chaudhuri and Hocquenghem [1], [4], the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performing codes, particularly when the number of errors being corrected is small relative to the code length. In this article we consider binary codes with minimum distance of 7. We construct new families of codes w...

In this paper we study a class of graph codes with BCH component codes as affine variety codes. We are able to find some optimal binary and ternary codes as Tanner codes with BCH component codes. We choose a special subgraph of the point-line incidence plane of P(2, q) as the Tanner graph, and we are able to describe the codes using Gröbner basis.

An interesting class of l inear error-correcting codes has been found by Goppa [3], [4]. This paper presents algebraic decoding algorithms for the Goppa codes. These algorithms are only a little more complex than Berlekamp’s well-known algorithm for BCH codes and, in fact, make essential use of his procedure. Hence the cost of decoding a Goppa code is similar to the cost of decoding a BCH code ...

In this paper, we evaluate the performance of an adaptive error correction scheme for Wireless ATM Networks (WATM). This scheme attempts to minimize the system throughput in order to satisfy the user defined Quality of Service (QoS) constraints. Indeed, error control for high speed wireless ATM networks is an important research topic even wireless communication channels are highly affected by u...

This paper focuses on the estimation of statistical atlases of 3D images by means of diffeomorphic transformations. Within a Log-Euclidean framework, the exponential and logarithm maps of diffeomorphisms need to be computed. In this framework, the Inverse Scaling and Squaring (ISS) method has been recently extended for the computation of the logarithm map, which is one of the most time demandin...

The structure of the twisted squaring construction, a generalization of the squaring construction, is studied with respect to trellis diagrams and complexity. We show that binary affine-invariant codes, which include the extended primitive BCH codes, and the extended binary quadratic-residue codes, are equivalent to twisted squaring construction codes. In particular, a recursive symmetric rever...

Our paper presents the prototyping of a BCH (Bose, Chaudhuri, and Hocquenghem) encoder and decoder using a Field Programmable Gate Array (FPGA) reconfigurable chip. The solutions implemented on FPGA lead to a high calculation rate using parallelization. We implemented the BCH code in a 3s400FG456 FPGA. In this implementation we used 15 bit-size word code and the results show that the circuits w...