This sparsematrix is often randomly generated, subject to the sparsity constraints— LDPC code construction is discussed later. These codes were first designed by Robert Gallager in 1960.
Replace the default text in the Parity-check matrix Parameter box with a sparsematrix of the desired size. This sparsmatrix can be created with the MATLAB functions "sparse", "randi", and "eye".
In this article, a novel concatenated coding scheme is introduced consisting of an outer non-binary LDPC code and an inner sparse regression code, where the field size of the outer code equals the section size of the inner code.
We use Gaussian elimination to put the matrix in canonical form. Performing row and column operations does not change the code. Note that randomly generated matrices may not be full rank.
While sparsity of the check matrix makes the decoding of LDPC codes, the fact that they are defined in terms of parity check matrix makes their encoding complex.
Finally, reconstruction of the parity-check matrix of LDPC code was realized by making the parity-check matrixsparse. However, this method is only suitable for cases where the order of magnitude of the bit error rate (BER) of the bit sequence is less than 10−4.
In this paper, inspired by these observations, we propose to construct structured sparse binary matrices which are stable in orthogonality. The solution lies in the algorithms that construct parity-check matrices of low-density parity-check (LDPC) codes.
This example shows a simulation of the transmission of an image as a binary message through a gaussian white noise channel with an LDPC coding and decoding system.
We present the sparse binary matrix defined by low-density parity-check (LDPC) codes as measurement matrix in compressed sensing. This kind of matrix owns much stronger orthogonality than current other main measurement matrices.
