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IEEE Vehicular Technology Conference

Quasi-Cyclic Doubly Generalized LDPC Codes

Raffaele Soloperto, Giuliano Garrammone, Gianluigi Liva, Oreste Andrisano

Published Jun 1, 2013• 1 citation
Publisher

Abstract

We introduce a class of structured (protograph-based) doubly generalized low-density parity-check (DGLDPC) codes. The proposed class leads to quasi-cyclic codes for which efficient encoder and decoder implementations are possible. In particular, we illustrate that on the additive white Gaussian noise (AWGN) channel, the introduced structured DGLDPC codes do not lose in performance with respect to unstructured DGLDPC codes. Furthermore, a sufficient condition on the code graph is derived, which allows unveiling the quasi-cyclic nature of the designed codes.

DOI
10.1109/vtcspring.2013.6692727

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We introduce a class of structured (protograph-based) doubly generalized low-density parity-check (DGLDPC) codes. The proposed class leads to quasi-cyclic codes for which efficient encoder and decoder implementations are possible. In particular, we illustrate that on the additive white Gaussian noise (AWGN) channel, the introduced structured DGLDPC codes do not lose in performance with respect to unstructured DGLDPC codes. Furthermore, a sufficient condition on the code graph is derived, which allows unveiling the quasi-cyclic nature of the designed codes.
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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.
In this paper, the design of doubly generalized low-density parity-check (DGLDPC) codes is proposed. This approach generalizes the structure of LDPC codes at both check and variable nodes. The performance of DGLDPC codes over the AWGN channel is analyzed using EXIT charts. Combined with differential evolution optimization, this analysis provides thresholds for DGLDPC codes that are better than that of LDPC and GLDPC codes with the same maximum variable degree. These theoretical thresholds are verified via simulations. Furthermore DGLDPC codes exhibit a lower error floor compared with their LDPC and GLDPC counterparts.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.
In this contribution, we investigate the attainable performance of quasi-cyclic (QC) protograph low-density parity-check (LDPC) codes for transmission over both Additive White Gaussian noise (AWGN) and uncorrelated Rayleigh channels. The codes presented are constructed using the Vandermonde matrix and benefit from both low- complexity encoding and decoding, low memory requirements as well as hardware-friendly implementations. Our simulation results demonstrate that the advantages offered by this family of QC protograph LDPC codes accrue without any compromise in the attainable bit error ratio (BER) and block error ratio (BER) performance. In fact, it is also shown that despite their implementational benefits, the proposed codes exhibit slight BER/BLER gains when compared to some of their more complex counterparts of the same length.