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Journal of Automatic Control

ACE spectrum of LDPC codes

Dejan Vukobratović, Aleksandar Djurendic, V. Šenk

Published Jan 1, 2006• 1 citation
Publisher

Abstract

Construction of short-length LDPC codes with good, both waterfall and error-floor, behavior is still an attractive research problem. Recently proposed construction algorithms in this field are based on remarkably simple ideas, but yet, their effectiveness can still be questioned. In this paper we investigate a novel measure of goodness of a given LDPC code namely its ACE spectrum, based on a previously introduced ACE metrics associated with each cycle in LDPC code graph.

DOI
10.2298/jac0601033v

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Construction of short-length LDPC codes with good, both waterfall and error-floor, behavior is still an attractive research problem. Recently proposed construction algorithms in this field are based on remarkably simple ideas, but yet, their effectiveness can still be questioned. In this paper we investigate a novel measure of goodness of a given LDPC code namely its ACE spectrum, based on a previously introduced ACE metrics associated with each cycle in LDPC code graph.
The construction of good, finite-length, LDPC codes is currently an attractive research area. Reducing attention to the binary erasure channel (BEC), this problem translates into the problem of finding elements of selected (irregular) LDPC code ensemble with the size of the minimal stopping set being maximized. Faced with the lack of analytical solution to this problem, simple but powerful heuristic design algorithm, an ACE constrained design algorithm, was recently introduced. Building upon the ACE metric associated with every cycle in the code graph, we introduce the ACE spectrum of LDPC code as a useful measure of success in selection of the LDPC code from selected ensemble. Using ACE spectrum, we farther generalize ACE constrained design, making it more flexible and efficient.
The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we introduce the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. Using the ACE spectrum, we generalize the ACE constrained design algorithm, making it more flexible and efficient. We justify the ACE spectrum approach through examples and simulation results.
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes
Quasi-cyclic low-density parity-check (QC-LDPC) codes constructed by using algebraic approaches, such as finite geometry and finite field, generally have good structural properties and very low error-floors, and facilitate hardware implementation. Irregular QC-LDPC codes constructed from such QC-LDPC codes by using the masking technique, when decoded with the sum-product algorithm (SPA), have low decoding complexity, but often show early error-floors. In this paper, the relationship of cycle, girth and approximate cycle EMD (ACE) between the masking matrix and masked matrix is investigated, and the ACE algorithm is modified and used to construct the masking matrix for irregular QC-LDPC codes. Simulations demonstrate that the codes constructed by masking with ACE optimization exhibit much improved waterfall performance and lower error floors.
We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.