In this paper we investigate the minimum code distance of QC LDPC codes [1], [2], [3]. These codes form an important subclass of LDPC codes [4], [5]. These codes also are a subclass of protograph-based LDPC codes [6]. QC LDPC codes can be easily stored as their parity-check matrices can be easily described. Besides such codes have efficient encoding [7] and decoding [8] algorithms. All of these...

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projectiv...

Trapping sets have been identified as one of the main factors causing error floors of low-density parity-check (LDPC) codes at high SNR values. By adding several new rows to the original parity-check matrix, a novel method is proposed to eliminate small trapping sets in the LDPC code’s Tanner graph. Based on this parity-check matrix extension, we design new codes with low error floors from the ...

A statistical theory of turbo-codes, treated as a special family of convolutional codes with a low-density parity-check matrix, is developed. The basic ideas are: the representation of the transposed parity-check matrix of turbo-codes as a product of a sparse (multiple) scrambler matrix and the transposed parity-check matrix of the basic code, the introduction of a special statistical ensemble ...

In this paper we propose a new class of irregular low-density parity check (LDPC) codes with linear encoding complexity. We show that these codes offer performances compatible with irregular LDPC codes with randomly generated parity-check matrices. The non-systematic part of the paritycheck matrix has a simple triangular structure, which enables linear encoding, while the systematic part of the...

We study recovering parity check relations for an unknown code from intercepted bitstream received from Binary Symmetric Channel in this paper. An iterative column elimination algorithm is introduced which attempts to eliminate parity bits in codewords of noisy data. This algorithm is very practical due to low complexity and use of XOR operator. Since, the computational complexity is low, searc...

In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the rst row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We also present an O(nd) algorithm to solve the problem of deciding whether codes satisfying given con...

A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

•We observed that Low-Density ParityCheck (LDPC) codes based on partial geometries have superior performance to randomly constructed codes when decoded iteratively with the sum-product algorithm. •The reason for this good performance are redundant rows in the parity-check matrix. •We compared a parity-check matrix with redundant rows (Hredundant) with a matrix with full rank (Hfull) representin...

A particular class of low-density parity-check codes referred to as cylinder-type BC-LDPC codes is proposed by Gholami and Eesmaeili. In this paper We represent a double cylinder-type parity-check matrix H by a graph called the block-structure graph of H and denoted by BSG(H). Using the properties of BSG(H) we propose some mother matrices with column-weight two such that the rate of correspondi...