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Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping

Shadi Abu‐Surra, Gianluigi Liva, W.E. Ryan

Published Jan 1, 2006• 6 citations
OpenAlex

Abstract

We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders.

Related papers

Design and performance of selected classes of Tanner codes

Shadi Abu‐Surra, Gianluigi Liva, W.E. Ryan

We study the design of structured Tanner codes with low error-rate floors on the binary additive white Gaussian noise channel (BAWGNC) and the binary erasure channel (BEC). The design technique involves the “doping of standard LDPC protographs, meaning Hamming or recursive systematic convolutional (RSC) code constraints are used together with singleparity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult.

•Feb 10, 2006•8 citations

Short Low-Error-Floor Tanner Codes with Hamming Nodes

Gianluigi Liva, W.E. Ryan

While it is fairly easy to design good low-density parity-check codes with medium or large block lengths, and with code rates 1/2 or greater, much more effort is required for short lengths and low rates. We propose a code structure which incorporates Hamming codes into a code's graph, leading to a type of a Tanner code. The incorporation of Hamming codes into the graph, which we call "Hamming code doping", tends to lead to larger minimum distances and hence low error-rate floors. We present an iterative decoding algorithm tailored to graphs possessing "Hamming nodes". Further, a density evolution analysis based on the Gaussian approximation is presented, which is a useful tool for finding good codes. Finally, we present numerical results of some Hamming-doped Tanner codes simulated on the AWGN channel. The simulated codes exhibit remarkably low error floors, while simultaneously displaying good decoding thresholds

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Gianluigi Liva, W.E. Ryan, Marco Chiani

Tanner codes represent a broad class of graph-based coding schemes, including low-density parity-check (LDPC) and turbo codes. Whereas many different classes of LDPC and turbo codes have been proposed and studied in the past decade, very little work has been performed on the broader class of Tanner codes. In this paper we propose a design technique which leads to efficiently encodable quasi-cyclic Tanner codes based on both Hamming and single parity check (SPC) nodes. These codes are characterized by fast message-passing decoders and can be encoded using shift-register-based circuits. The resulting schemes exhibit excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel. 1

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Gianluigi Liva, W.E. Ryan, Marco Chiani

In this paper, a novel methodology for designing structured generalized low-density parity-check (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 low-density parity-check (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.

IEEE Transactions on Communications•Dec 1, 2007•9 citations

Quasi-cyclic generalized ldpc codes with low error floors

Gianluigi Liva, W.E. Ryan, Marco Chiani

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.

IEEE Transactions on Communications•Jan 1, 2008•136 citations

Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds

Roxana Smarandache, Pascal O. Vontobel

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds depend on graph structure parameters (like variable degrees, check node degrees, girth) of the Tanner graph and of the underlying proto-graph. Moreover, for several classes of proto-graphs we present explicit QC LDPC code constructions that achieve (or come close to) the respective minimum Hamming distance upper bounds. Because of the tight algebraic connection between QC codes and convolutional codes, we can state similar results for the free Hamming distance of convolutional codes. In fact, some QC code statements are established by first proving the corresponding convolutional code statements and then using a result by Tanner that says that the minimum Hamming distance of a QC code is upper bounded by the free Hamming distance of the convolutional code that is obtained by “unwrapping” the QC code.

arXiv:0901.4129•IEEE Transactions on Information Theory•Feb 1, 2012•127 citations
We study the design of structured Tanner codes with low error-rate floors on the AWGN channel. The design technique involves the “doping” of standard LDPC (proto-)graphs, by which we mean Hamming or recursive systematic convolutional (RSC) code constraints are used together with single-parity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good” graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult. Lastly, we perform a simple complexity analysis of our Tanner codes and examine the performance of lower-complexity, suboptimal Hamming-node decoders.
We study the design of structured Tanner codes with low error-rate floors on the binary additive white Gaussian noise channel (BAWGNC) and the binary erasure channel (BEC). The design technique involves the “doping of standard LDPC protographs, meaning Hamming or recursive systematic convolutional (RSC) code constraints are used together with singleparity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult.
While it is fairly easy to design good low-density parity-check codes with medium or large block lengths, and with code rates 1/2 or greater, much more effort is required for short lengths and low rates. We propose a code structure which incorporates Hamming codes into a code's graph, leading to a type of a Tanner code. The incorporation of Hamming codes into the graph, which we call "Hamming code doping", tends to lead to larger minimum distances and hence low error-rate floors. We present an iterative decoding algorithm tailored to graphs possessing "Hamming nodes". Further, a density evolution analysis based on the Gaussian approximation is presented, which is a useful tool for finding good codes. Finally, we present numerical results of some Hamming-doped Tanner codes simulated on the AWGN channel. The simulated codes exhibit remarkably low error floors, while simultaneously displaying good decoding thresholds
Tanner codes represent a broad class of graph-based coding schemes, including low-density parity-check (LDPC) and turbo codes. Whereas many different classes of LDPC and turbo codes have been proposed and studied in the past decade, very little work has been performed on the broader class of Tanner codes. In this paper we propose a design technique which leads to efficiently encodable quasi-cyclic Tanner codes based on both Hamming and single parity check (SPC) nodes. These codes are characterized by fast message-passing decoders and can be encoded using shift-register-based circuits. The resulting schemes exhibit excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel. 1
In this paper, a novel methodology for designing structured generalized low-density parity-check (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 low-density parity-check (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, 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.
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds depend on graph structure parameters (like variable degrees, check node degrees, girth) of the Tanner graph and of the underlying proto-graph. Moreover, for several classes of proto-graphs we present explicit QC LDPC code constructions that achieve (or come close to) the respective minimum Hamming distance upper bounds. Because of the tight algebraic connection between QC codes and convolutional codes, we can state similar results for the free Hamming distance of convolutional codes. In fact, some QC code statements are established by first proving the corresponding convolutional code statements and then using a result by Tanner that says that the minimum Hamming distance of a QC code is upper bounded by the free Hamming distance of the convolutional code that is obtained by “unwrapping” the QC code.