We show how to construct an algorithm to search for binary idempotents which may be used to construct binary LDPC codes. The algorithm, which allows control of the key properties of sparseness, code rate and minimum distance, is constructed in the Mattson-Solomon domain. Some of the new codes, found by using this technique, are displayed.
The Hamming weight enumerator function of the formally self-dual even, binary extended quadratic residue code of prime p = 8m + 1 is given by Gleason's theorem for singly-even code. Using this theorem, the Hamming weight distribution of the extended quadratic residue is completely determined once the number of codewords of Hamming weight j Aj, for 0 ≤ j ≤… (More)
—In this paper, we consider the primary user detection problem in cognitive radio systems by using multi antenna at the cognitive radio receiver. An optimal linear combiner multi antenna based spectrum sensing technique is proposed using the multitaper spectrum estimation method. A suboptimal square law combiner multi antenna based technique, using the… (More)
— Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2 m), where m > 0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this… (More)
— An algorithm of improving the performance of iterative decoding on perpendicular magnetic recording is presented. This algorithm follows on the authors' previous works on the parallel and serial concatenated turbo codes and low-density parity-check codes. The application of this algorithm with signal-to-noise ratio mismatch technique shows promising… (More)