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

arXiv:1910.06574 · IEEE Information Theory Workshop (ITW)

On Generalized LDPC Codes for 5G Ultra Reliable Communication

Yanfang Liu, Pablo M. Olmos, David G. M. Mitchell

Published Nov 1, 2018• 9 citations
arXivHTMLPDF

Abstract

Generalized low-density parity-check (GLDPC) codes, where single parity-check (SPC) constraint nodes are replaced with generalized constraint (GC) nodes, are a promising class of codes for low latency communication. In this paper, a practical construction of quasi-cyclic (QC) GLDPC codes is proposed, where the proportion of generalized constraints is determined by an asymptotic analysis. We analyze the message passing process and complexity of a GLDPC code over the additive white gaussian noise (AWGN) channel and present a constraint-to-variable update rule based on the specific codewords of the component code. The block error rate (BLER) performance of the GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art code and decoder designs with suitable lengths and rates for the 5G Ultra Reliable Communication (URC) regime over an additive white gaussian noise (AWGN) channel with quadrature PSK (QPSK) modulation.

DOI
10.1109/itw.2018.8613515

Related papers

Structural Analysis of Generalized Quasi-Cyclic LDPC Codes: Rank, Design, and Generator Matrices

Roxana Smarandache, David G. M. Mitchell, Anthony Gómez-Fonseca

Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication. The block error rate performance of the GLDPC codes, combined with a complementary outer code, has been shown to outperform a variety of state-of-the-art code and decoder designs with suitable lengths and rates for the 5G ultra-reliable low-latency communication (URLLC) regime. A major drawback of these codes is that it is not known how to construct appropriate polynomial matrices to encode them efficiently. In this paper, we analyze practical constructions of quasi-cyclic GLDPC (QC-GLDPC) codes and show how to construct polynomial generator matrices in various forms using minors of the polynomial matrix. The approach can be applied to fully generalized matrices or partially generalized (with mixed constraint node types) to find better performance/rate trade-offs. The resulting encoding matrices are presented in useful forms that facilitate efficient implementation. The rich substructure displayed also provides us with new methods of determining low weight codewords, providing lower and upper bounds on the minimum distance and often giving those of weight equal to the minimum distance. Based on the minors of the polynomial parity-check matrix, we also give a formula for the rank of any parity-check matrix representing a QC-LDPC or QC-GLDPC code, and hence, the dimension of the code. Finally, we show that by applying double graph-liftings, the code parameters can be improved without affecting the ability to obtain a polynomial generator matrix.

IEEE Transactions on Information Theory•Oct 27, 2025•3 citations

Quasi-Cyclic LDPC Codes from Generalized Behrend Sequences for Space Applications

Suresh Kumar Venkataramanappa, P. Vijay Kumar, Deepak Mishra +1 more

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.

Globecom•Dec 8, 2025•0 citations

Performance Simulation of a Layered QC-LDPC Decoder for URLLC Applications

Bilal Mejmaa, Chakir Aqil, Ismail Akharraz +1 more

This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10 −2 , the decoder outperforms reference shorter codes (K40, K64) with an E b /N o gain of up to 0.9 dB.

EPJ Web of Conferences•Jan 1, 2026•0 citations

Performance Simulation of a Layered QC-LDPC Decoder for URLLC Applications

Bilal Mejmaa, Chakir Aqil, Ismail Akharraz +1 more

This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10−2, the decoder outperforms reference shorter codes (K40, K64) with an Eb/No gain of up to 0.9 dB.

•Jul 1, 2026•0 citations

On the Design of Generalized LDPC Codes with Component BCJR Decoding

Yanfang Liu, Pablo M. Olmos, David G. M. Mitchell

Generalized low-density parity-check (GLDPC) codes, where the single parity-check (SPC) nodes are replaced by generalized constraint (GC) nodes, are known to offer a reduced gap to capacity when compared with conventional LDPC codes, while also maintaining linear growth of minimum distance. However, for certain classes of practical GLDPC codes, there remains a gap to capacity even when utilizing blockwise decoding algorithm at GC nodes. In this work, we propose to optimize the design of GLDPC codes where the GC nodes are decoded with a trellis-based bit-wise Bahl-Cocke-Jelinek- Raviv (BCJR) component decoding algorithm. We analyze the asymptotic threshold behavior of GLDPC codes and determine the optimal proportion of the GC nodes in the GLDPC Tanner graph.We show significant performance improvements compared to existing designs with the same order of decoding complexity.

Globecom•Dec 1, 2020•6 citations

Quasi-Cyclic LDPC Codes for Short Block-Lengths

Muhammad Nauman Danish, Syed Ahmed Pasha, Ali Javed Hashmi

In wireless communication, transmission error can be caused by multi-path fading, shadowing, scattering, interference and noise. As a result, errors generated in digital communication can be classified as burst errors, random bit errors, crosstalk and echo. For reliable communication, channel coding is used which adds redundancy to the information bits. Reliable and low latency communication are crucial for future communication systems involving satellite constellations and 5G communication systems, which underscores the importance of channel coding. Various codes exist for channel coding, among which low-density parity-check (LDPC) codes, polar codes and tail biting convolution codes are mentioned for 5G ultra-reliable low latency communication and enhanced mobile broadband systems. In the literature, the performance of large block-length codes has been well-studied. But these codes lead to high latency. The design of short block-length codes remains an open problem due to the trade-off between latency and performance. In this paper, we develop a systematic procedure for construction of hybrid quasi-cyclic LDPC (QC-LDPC) codes and compare the performance of the proposed approach with random LDPC and existing QC-LDPC codes for short block-lengths and phase shift keying (PSK) signal characteristics. The proposed method exploits Euclidean geometry and circulant decomposition resulting in a QC-LDPC matrix that avoids shorter girths for iterative decoding cycles. We emphasize that the proposed approach is different from the protographic construction method, masking method, identity matrix replacement method, algebraic based construction method, and base graph method used for the construction of QC-LDPC codes.

IEEE Aerospace Conference (AERO)•Mar 6, 2021•6 citations
Generalized low-density parity-check (GLDPC) codes, where single parity-check (SPC) constraint nodes are replaced with generalized constraint (GC) nodes, are a promising class of codes for low latency communication. In this paper, a practical construction of quasi-cyclic (QC) GLDPC codes is proposed, where the proportion of generalized constraints is determined by an asymptotic analysis. We analyze the message passing process and complexity of a GLDPC code over the additive white gaussian noise (AWGN) channel and present a constraint-to-variable update rule based on the specific codewords of the component code. The block error rate (BLER) performance of the GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art code and decoder designs with suitable lengths and rates for the 5G Ultra Reliable Communication (URC) regime over an additive white gaussian noise (AWGN) channel with quadrature PSK (QPSK) modulation.
Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication. The block error rate performance of the GLDPC codes, combined with a complementary outer code, has been shown to outperform a variety of state-of-the-art code and decoder designs with suitable lengths and rates for the 5G ultra-reliable low-latency communication (URLLC) regime. A major drawback of these codes is that it is not known how to construct appropriate polynomial matrices to encode them efficiently. In this paper, we analyze practical constructions of quasi-cyclic GLDPC (QC-GLDPC) codes and show how to construct polynomial generator matrices in various forms using minors of the polynomial matrix. The approach can be applied to fully generalized matrices or partially generalized (with mixed constraint node types) to find better performance/rate trade-offs. The resulting encoding matrices are presented in useful forms that facilitate efficient implementation. The rich substructure displayed also provides us with new methods of determining low weight codewords, providing lower and upper bounds on the minimum distance and often giving those of weight equal to the minimum distance. Based on the minors of the polynomial parity-check matrix, we also give a formula for the rank of any parity-check matrix representing a QC-LDPC or QC-GLDPC code, and hence, the dimension of the code. Finally, we show that by applying double graph-liftings, the code parameters can be improved without affecting the ability to obtain a polynomial generator matrix.
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.
This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10 −2 , the decoder outperforms reference shorter codes (K40, K64) with an E b /N o gain of up to 0.9 dB.
This research investigates the simulation performance of a layered Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) decoder intended for Ultra-Reliable Low-Latency Communication (URLLC) applications in 5G New-Radio (NR) standards. The proposed work focuses on short block-length QC-LDPC codes (280,176) to meet the dual challenge of achieving ultra-low latency (<1ms) while maintaining high reliability. LDPC codes have traditionally excelled at longer code lengths; this study demonstrates the effectiveness of LDPC codes in short-length contexts through architectural optimization utilizing a layered decoding approach, which provides improved convergence speed and reduced latency compared to traditional flooding techniques. The baseline QC-LDPC decoder performs better in terms of Bit Error Rate (BER) and Block Error Rate (BLER) with only 7 iterations. For a target BLER of 10−2, the decoder outperforms reference shorter codes (K40, K64) with an Eb/No gain of up to 0.9 dB.
Generalized low-density parity-check (GLDPC) codes, where the single parity-check (SPC) nodes are replaced by generalized constraint (GC) nodes, are known to offer a reduced gap to capacity when compared with conventional LDPC codes, while also maintaining linear growth of minimum distance. However, for certain classes of practical GLDPC codes, there remains a gap to capacity even when utilizing blockwise decoding algorithm at GC nodes. In this work, we propose to optimize the design of GLDPC codes where the GC nodes are decoded with a trellis-based bit-wise Bahl-Cocke-Jelinek- Raviv (BCJR) component decoding algorithm. We analyze the asymptotic threshold behavior of GLDPC codes and determine the optimal proportion of the GC nodes in the GLDPC Tanner graph.We show significant performance improvements compared to existing designs with the same order of decoding complexity.
In wireless communication, transmission error can be caused by multi-path fading, shadowing, scattering, interference and noise. As a result, errors generated in digital communication can be classified as burst errors, random bit errors, crosstalk and echo. For reliable communication, channel coding is used which adds redundancy to the information bits. Reliable and low latency communication are crucial for future communication systems involving satellite constellations and 5G communication systems, which underscores the importance of channel coding. Various codes exist for channel coding, among which low-density parity-check (LDPC) codes, polar codes and tail biting convolution codes are mentioned for 5G ultra-reliable low latency communication and enhanced mobile broadband systems. In the literature, the performance of large block-length codes has been well-studied. But these codes lead to high latency. The design of short block-length codes remains an open problem due to the trade-off between latency and performance. In this paper, we develop a systematic procedure for construction of hybrid quasi-cyclic LDPC (QC-LDPC) codes and compare the performance of the proposed approach with random LDPC and existing QC-LDPC codes for short block-lengths and phase shift keying (PSK) signal characteristics. The proposed method exploits Euclidean geometry and circulant decomposition resulting in a QC-LDPC matrix that avoids shorter girths for iterative decoding cycles. We emphasize that the proposed approach is different from the protographic construction method, masking method, identity matrix replacement method, algebraic based construction method, and base graph method used for the construction of QC-LDPC codes.