3 research outputs found
On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods
The evaluation of the minimum distance of linear block codes remains an open
problem in coding theory, and it is not easy to determine its true value by
classical methods, for this reason the problem has been solved in the
literature with heuristic techniques such as genetic algorithms and local
search algorithms. In this paper we propose two approaches to attack the
hardness of this problem. The first approach is based on genetic algorithms and
it yield to good results comparing to another work based also on genetic
algorithms. The second approach is based on a new randomized algorithm which we
call Multiple Impulse Method MIM, where the principle is to search codewords
locally around the all-zero codeword perturbed by a minimum level of noise,
anticipating that the resultant nearest nonzero codewords will most likely
contain the minimum Hamming-weight codeword whose Hamming weight is equal to
the minimum distance of the linear code
An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes
In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM).
In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders