ACE Spectrum of LDPC Codes

Construction of Irregular LDPC Code Using ACE Algorithm

The Low Density Parity Check (LDPC) codes have been widely acclaimed in recent years for their nearcapacity performance, they have not found their way into many important applications. For some cases, this is due to their increased decoding complexity relative to the classical coding techniques. For other cases, this is due to their inability to reach very low bit error rates at low signal-to-n...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

An Efficient Algorithm for Finding Dominant Trapping Sets of LDPC Codes

This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. The algorithm can be used to estimate the error floor of LDPC codes or to be used as a tool to design LDPC codes with low error floors. For regular codes, the algorithm is initiated with a set of short cycles as the input. For irregular codes, in addition to short cycles,...

The New Multi-Edge Metric-Constrained PEG/QC-PEG Algorithms for Designing the Binary LDPC Codes With Better Cycle-Structures

To obtain a better cycle-structure is still a challenge for the low-density parity-check (LDPC) code design. This paper formulates two metrics firstly so that the progressive edge-growth (PEG) algorithm and the approximate cycle extrinsic message degree (ACE) constrained PEG algorithm are unified into one integrated algorithm, called the metric-constrained PEG algorithm (M-PEGA). Then, as an im...

Expansion Properties of Generalized ACE Codes

This work presents a generalization of the ACE algorithm proposed by Tian et. al [1] (called Generalized ACE GACE) for irregular LDPC code construction. We show that if the minimum left degree of a (dACE , η) compliant GACEconstrained LDPC code is lmin and the number of check nodes M is large enough, it is a [ α, 1 − 1+2 lmin ] , 2 > 0 expander with probability 1− O(f(M)) where f(M) = max [ 1/M...