Quasi-Cyclic Generalized LDPC Codes With Low Error Floors

Abstract

Abstract-In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

Low-Density Parity-Check Code Constructions

“…This illustrates that these ensembles can be viewed as protograph-based ensembles. Protograph code properties and design methods were studied in [17,18,30,31], among many other works. Some examples of popular designs are shown in Figure 8; many of these designs incorporate additional accumulator structures.…”

Joint iterative decoding for simple-encoding systematic irregular-LDPC-based coded cooperation in non-ideal relay channel

“…(1) is an irregular systematic LDPC code. Although some other methods [13][14][15] can be used to define the irregular LDPC codes, however, this simple-encoding solution is quite suitable for the design of double irregular systematic LDPC codes adopted in an one-relay cooperation, where the joint iterative decoding is performed in the destination. In this paper, we use the notation ( , , , ) v c C N M d d to denote the ensemble of these irregular systematic LDCP codes.…”

“…To further improve the performance of wireless system, channel coding is naturally applied to relay cooperation called coded cooperation, where cooperative signaling is integrated with channel coding in order to obtain benefits from both diversity and error correction codes. The previous studies [9][10][11][12] have investigated coded relay cooperation using turbo and LDPC codes, especially for LDPC codes [13][14][15] due to the merits of low decoding complex and delay for the implementation. However, the encoding computation is high for irregular LDPC codes constructed by conventional method of extrinsic information distributed by Gaussian law, which also leads to high decoding complexity for multiple received signals in the destination.…”

Approach to the construction of regular low-density parity-check codes from group permutation matrices

“…In this direction, several algebraic constructions for LDPC codes can be found in the literature. From among these constructions we refer to those given in [3][4][5][6][7][8][9][10][13][14][15][16][17][18][19][20][21][22][23][24]. These constructions can be divided into two types.…”

“…These constructions can be divided into two types. One type is based on finite geometries ( [3,5,[13][14][15][16][17][18][19]) and another type, which initially proposed by Gallager [6], is based on circulant matrices [4,[6][7][8][9][10][20][21][22][23][24].…”