Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Design and Analysis of a Family of Complexity-Constrained LDPC Codes

Massimo Battaglioni, Matteo Amagliani, Marco Baldi, Franco Chiaraluce, Giovanni Cancellieri

Published Jul 7, 2024• 2 citations
Publisher

Abstract

In this paper we study a special family of Low-Density Parity-Check (LDPC) codes, called Primitive Rate-Compatible (PRC) LDPC codes, obtained by applying puncturing to some properly chosen simplex codes. We investigate their minimum distance properties and give insights on the design of PRC-LDPC codes for use in scenarios where constraints on hardware and software resources require maintaining a low level of complexity. We numerically assess the error rate performance of these codes in such a setting, showing that they also demonstrate good performance under belief propagation decoding, in addition to low decoding complexity.

DOI
10.1109/isit57864.2024.10619325

Related papers

Rate-Compatible LDPC Codes Based on Primitive Polynomials and Golomb Rulers

Massimo Battaglioni, Marco Baldi, Franco Chiaraluce +1 more

We introduce and study a family of rate-compatible Low-Density Parity-Check (LDPC) codes. The design of these codes starts from simplex codes, defined by parity-check matrices having a simple form stemming from the coefficients of a primitive polynomial. For this reason, we call the new codes Primitive Rate-Compatible LDPC (PRC-LDPC) codes. By applying puncturing to these codes, we obtain a bit-level granularity of the code rate. We show that, in order to achieve good LDPC codes, the underlying polynomials, besides being primitive, must meet some more stringent conditions with respect to those of classical punctured simplex codes. We leverage non-modular Golomb rulers to take these new requirements into account. We characterize the minimum distance properties of PRC-LDPC codes, and study and discuss their encoding and decoding complexity. Finally, we assess the error rate performance of high rate PRC-LDPC codes under iterative decoding.

arXiv:2309.14917•IEEE Transactions on Communications•Jun 17, 2024•9 citations

Rate-Adaptive LDPC Codes Obtained from Simplex Codes

Massimo Battaglioni, Marco Baldi, Franco Chiaraluce +1 more

In this paper we show that, when a binary primitive polynomial can be associated to a sparse Golomb ruler, the simplex code obtained by taking it as the code parity-check polynomial exhibits good distance properties and performance. We define some conditions under which the obtained codes are also Low-Density Parity-Check (LDPC) codes, and can hence be decoded through efficient iterative algorithms. We perform code puncturing, leading to a family of rate-adaptive codes, and we predict some of their structural properties in terms of minimum distance and weight distribution. We show that, in addition to having some useful properties, these codes achieve good performance in terms of error rate under LDPC decoding.

International Conference on Communications•May 28, 2023•6 citations

Punctured Binary Simplex Codes as LDPC codes

Massimo Battaglioni, Giovanni Cancellieri

Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their performance and flexibility of operation, in wireless and mobile radio channels, as well as in cable transmission systems. In this paper, we present a class of rate-adaptive LDPC codes, obtained as properly punctured simplex codes. These codes allow for the use of an efficient soft-decision decoding algorithm, provided that a condition called row-column constraint is satisfied. This condition is tested on small-length codes, and then extended to medium-length codes. The puncturing operations we apply do not influence the satisfaction of the row-column constraint, assuring that a wide range of code rates can be obtained. We can reach code rates remarkably higher than those obtainable by the original simplex code, and the price in terms of minimum distance turns out to be relatively small, leading to interesting trade-offs in the resulting asymptotic coding gain.

arXiv:2210.03537•FITCE Congress•Sep 29, 2022•7 citations

Multiple-rate low-density parity-check codes with constant blocklength

Andres I. Vila Casado, Wen-Yen Weng, Stefano Valle +1 more

This paper describes and analyzes low-density parity-check code families that support variety of different rates while maintaining the same fundamental decoder architecture. Such families facilitate the decoding hardware design and implementation for applications that require communication at different rates, for example to adapt to changing channel conditions. Combining rows of the lowest-rate parity-check matrix produces the parity-check matrices for higher rates. An important advantage of this approach is that all effective code rates have the same blocklength. This approach is compatible with well known techniques that allow low-complexity encoding and parallel decoding of these LDPC codes. This technique also allows the design of programmable analog LDPC decoders. The proposed design method maintains good graphical properties and hence low error floors for all rates.

IEEE Transactions on Communications•Jan 1, 2009•43 citations

Construction of Optimal Puncturing of Low-Density Parity-Check Codes

S. Suresh Kumar, Manju Rajaram

Low-density parity-check with Length-compatible and low error floors (LDPC-LCLEF) on the binary symmetric channel is presented in this paper. These codes can support a wide range of lengths for a given rate and also the Tanner graphs are free of small trapping sets. This can be obtained by applying the schemes of shortening and puncturing to good LDPC codes and the trapping sets are selected using the trapping set ontology based on their relative harmfulness for the given decoding algorithm. The conventional approach does not guarantee to have a good performance as the degree distributions may be wildly varied. In this paper, a modified algorithm is presented to generate LDPC codes of a given rate with almost their degree distributions are same as the mother code degree distribution. Also the relative harmfulness for different trapping sets are evaluated and decoding failures of one trapping set in presence or absence of other trapping sets are analyzed. To facilitate this discussion, a new description of structured LDPC codes with arrays of permutation matrices as parity-check matrices is given. Numerical results show that the LDPC code constructed by this approach performed much better than the conventional approach.

CiiT international journal of fuzzy systems•Jan 1, 2014•0 citations

Fast Decoding of Rate-Compatible Punctured LDPC Codes

Jini Kwon, Demijan Klinc, Jeongseok Ha +1 more

While rate-compatible punctured low-density parity-check (RCP-LDPC) codes offer high flexibility in terms of code rate at a relatively low cost in implementation complexity, they are reported to require more decoding iterations than unpunctured LDPC codes. In this paper1we consider layered belief propagation decoding and propose efficient check node layering that significantly accelerates the decoding convergence of RCP-LDPC codes. We show that the proposed layering outperforms both random layering and conventional BP decoding. The performance improvements become more distinctive at high rates and they come at no additional implementation cost.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2007•7 citations
In this paper we study a special family of Low-Density Parity-Check (LDPC) codes, called Primitive Rate-Compatible (PRC) LDPC codes, obtained by applying puncturing to some properly chosen simplex codes. We investigate their minimum distance properties and give insights on the design of PRC-LDPC codes for use in scenarios where constraints on hardware and software resources require maintaining a low level of complexity. We numerically assess the error rate performance of these codes in such a setting, showing that they also demonstrate good performance under belief propagation decoding, in addition to low decoding complexity.
We introduce and study a family of rate-compatible Low-Density Parity-Check (LDPC) codes. The design of these codes starts from simplex codes, defined by parity-check matrices having a simple form stemming from the coefficients of a primitive polynomial. For this reason, we call the new codes Primitive Rate-Compatible LDPC (PRC-LDPC) codes. By applying puncturing to these codes, we obtain a bit-level granularity of the code rate. We show that, in order to achieve good LDPC codes, the underlying polynomials, besides being primitive, must meet some more stringent conditions with respect to those of classical punctured simplex codes. We leverage non-modular Golomb rulers to take these new requirements into account. We characterize the minimum distance properties of PRC-LDPC codes, and study and discuss their encoding and decoding complexity. Finally, we assess the error rate performance of high rate PRC-LDPC codes under iterative decoding.
In this paper we show that, when a binary primitive polynomial can be associated to a sparse Golomb ruler, the simplex code obtained by taking it as the code parity-check polynomial exhibits good distance properties and performance. We define some conditions under which the obtained codes are also Low-Density Parity-Check (LDPC) codes, and can hence be decoded through efficient iterative algorithms. We perform code puncturing, leading to a family of rate-adaptive codes, and we predict some of their structural properties in terms of minimum distance and weight distribution. We show that, in addition to having some useful properties, these codes achieve good performance in terms of error rate under LDPC decoding.
Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their performance and flexibility of operation, in wireless and mobile radio channels, as well as in cable transmission systems. In this paper, we present a class of rate-adaptive LDPC codes, obtained as properly punctured simplex codes. These codes allow for the use of an efficient soft-decision decoding algorithm, provided that a condition called row-column constraint is satisfied. This condition is tested on small-length codes, and then extended to medium-length codes. The puncturing operations we apply do not influence the satisfaction of the row-column constraint, assuring that a wide range of code rates can be obtained. We can reach code rates remarkably higher than those obtainable by the original simplex code, and the price in terms of minimum distance turns out to be relatively small, leading to interesting trade-offs in the resulting asymptotic coding gain.
This paper describes and analyzes low-density parity-check code families that support variety of different rates while maintaining the same fundamental decoder architecture. Such families facilitate the decoding hardware design and implementation for applications that require communication at different rates, for example to adapt to changing channel conditions. Combining rows of the lowest-rate parity-check matrix produces the parity-check matrices for higher rates. An important advantage of this approach is that all effective code rates have the same blocklength. This approach is compatible with well known techniques that allow low-complexity encoding and parallel decoding of these LDPC codes. This technique also allows the design of programmable analog LDPC decoders. The proposed design method maintains good graphical properties and hence low error floors for all rates.
Low-density parity-check with Length-compatible and low error floors (LDPC-LCLEF) on the binary symmetric channel is presented in this paper. These codes can support a wide range of lengths for a given rate and also the Tanner graphs are free of small trapping sets. This can be obtained by applying the schemes of shortening and puncturing to good LDPC codes and the trapping sets are selected using the trapping set ontology based on their relative harmfulness for the given decoding algorithm. The conventional approach does not guarantee to have a good performance as the degree distributions may be wildly varied. In this paper, a modified algorithm is presented to generate LDPC codes of a given rate with almost their degree distributions are same as the mother code degree distribution. Also the relative harmfulness for different trapping sets are evaluated and decoding failures of one trapping set in presence or absence of other trapping sets are analyzed. To facilitate this discussion, a new description of structured LDPC codes with arrays of permutation matrices as parity-check matrices is given. Numerical results show that the LDPC code constructed by this approach performed much better than the conventional approach.
While rate-compatible punctured low-density parity-check (RCP-LDPC) codes offer high flexibility in terms of code rate at a relatively low cost in implementation complexity, they are reported to require more decoding iterations than unpunctured LDPC codes. In this paper1we consider layered belief propagation decoding and propose efficient check node layering that significantly accelerates the decoding convergence of RCP-LDPC codes. We show that the proposed layering outperforms both random layering and conventional BP decoding. The performance improvements become more distinctive at high rates and they come at no additional implementation cost.