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)

Waterfall region performance of punctured LDPC codes over the BEC

Iryna Andriyanova, Rudiger L. Urbanke

Published Jun 1, 2009• 9 citations
Publisher

Abstract

This paper is devoted to the analysis of finite-length iterative performance of punctured LDPC ensembles in the waterfall region, assuming the transmission over the binary erasure channel (BEC). The analysis is carried out using the scaling approach proposed in. Two punctured ensembles are considered: (a) randomly punctured ensembles, in the sense that each bit of a codeword is punctured with some puncturing probability; (b) ensembles with a fixed puncturing fraction of bits of each degree. In both cases, parameters of the scaling approximation are completely determined in terms of the ensemble parameters such as left, right and puncturing degree distributions.

DOI
10.1109/isit.2009.5205927

Related papers

Randomly Punctured LDPC Codes

David G. M. Mitchell, Michael Lentmaier, Alí Emre Pusane +1 more

In this paper, we present a random puncturing analysis of low-density parity-check (LDPC) code ensembles. We derive a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary-input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate, and we show how the prediction can be improved with knowledge of the BI-AWGNC threshold. We also perform an asymptotic minimum distance analysis of randomly punctured code ensembles and present simulation results that confirm the robust decoding performance promised by the asymptotic results. Protograph-based LDPC block code and spatially coupled LDPC code ensembles are used throughout as examples to demonstrate the results.

IEEE Journal on Selected Areas in Communications•Dec 11, 2015•48 citations

Finite-length analysis of the TEP decoder for LDPC ensembles over the BEC

Pablo M. Olmos, Fernando Pérez‐Cruz, Luis Salamanca +1 more

In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•2 citations

Waterfall Performance Analysis of Finite-Length LDPC Codes on Symmetric Channels

Raman Yazdani, Masoud Ardakani

An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.

IEEE Transactions on Communications•Nov 1, 2009•24 citations

Finite-length scaling of non-binary (c, d) LDPC codes for the BEC

Iryna Andriyanova, Kenta Kasai

This paper provides a performance analysis of the regular (c, d) LDPC code ensemble of codelength n with parity-check matrices defined over the general linear group GL(2m). The transmission is assumed to take place over the binary erasure channel with erasure probability ε. In this work, the scaling approximation of the block erasure rate is generalized to the non-binary case, and the scaling parameter α of the approximation is derived. The proposed estimation is then compared with numerical results, showing that it predicts well the slope of the block erasure rate vs. channel erasure probability.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2010•4 citations

Further results on finite-length scaling for iteratively decoded LDPC ensembles

Ala Eddine Kaddour Amraoui, Andrea Montanari A, T. Richardson +1 more

The behavior of iteratively decoded low-density parity-check (LDPC) codes over the binary erasure channel in the so-called "waterfall region" is investigated and shows that the performance curves in this region follow a very basic scaling law. This scaling law, combined with previously known expressions for the error floor, yields a promising direction for analyzing the performance of irregular LDPC codes of practical lengths.

IEEE International Symposium on Information Theory (ISIT)•Dec 23, 2004•19 citations

Rate-Compatible Puncturing of Finite-Length Low-Density Parity-Check Codes

Badri N. Vellambi, R. Badri, Faramarz Fekri

In this paper, we study rate-compatible puncturing of finite-length Low-Density Parity-Check (LDPC) codes. First, we derive simple and yet good bounds on the expected performance of punctured codes (constructed by random puncturing) over Binary Erasure Channel (BEC) as a function of the performance of their parent LDPC code. We then present a novel rate-compatible puncturing scheme that is very easy to implement. Our scheme uses the idea that a more uniform distribution of punctured bits across the Tanner graph results in punctured codes with better performance. Although the puncturing scheme tailored to regular codes is presented, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over BEC and Additive White Gaussian Noise (AWGN) Channel.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2006•5 citations
This paper is devoted to the analysis of finite-length iterative performance of punctured LDPC ensembles in the waterfall region, assuming the transmission over the binary erasure channel (BEC). The analysis is carried out using the scaling approach proposed in. Two punctured ensembles are considered: (a) randomly punctured ensembles, in the sense that each bit of a codeword is punctured with some puncturing probability; (b) ensembles with a fixed puncturing fraction of bits of each degree. In both cases, parameters of the scaling approximation are completely determined in terms of the ensemble parameters such as left, right and puncturing degree distributions.
In this paper, we present a random puncturing analysis of low-density parity-check (LDPC) code ensembles. We derive a simple analytic expression for the iterative belief propagation (BP) decoding threshold of a randomly punctured LDPC code ensemble on the binary erasure channel (BEC) and show that, with respect to the BP threshold, the strength and suitability of an LDPC code ensemble for random puncturing is completely determined by a single constant that depends only on the rate and the BP threshold of the mother code ensemble. We then provide an efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary-input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate, and we show how the prediction can be improved with knowledge of the BI-AWGNC threshold. We also perform an asymptotic minimum distance analysis of randomly punctured code ensembles and present simulation results that confirm the robust decoding performance promised by the asymptotic results. Protograph-based LDPC block code and spatially coupled LDPC code ensembles are used throughout as examples to demonstrate the results.
In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.
An efficient method for analyzing the performance of finite-length low-density parity-check (LDPC) codes in the waterfall region, when transmission takes place on a memoryless binary-input output-symmetric channel is proposed. This method is based on studying the variations of the channel quality around its expected value when observed during the transmission of a finite-length codeword. We model these variations with a single parameter. This parameter is then viewed as a random variable and its probability distribution function is obtained. Assuming that a decoding failure is the result of an observed channel worse than the codeiquests decoding threshold, the block error probability of finite-length LDPC codes under different decoding algorithms is estimated. Using an extrinsic information transfer chart analysis, the bit error probability is obtained from the block error probability. Different parameters can be used for modeling the channel variations. In this work, two of such parameters are studied. Through examples, it is shown that this method can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.
This paper provides a performance analysis of the regular (c, d) LDPC code ensemble of codelength n with parity-check matrices defined over the general linear group GL(2m). The transmission is assumed to take place over the binary erasure channel with erasure probability ε. In this work, the scaling approximation of the block erasure rate is generalized to the non-binary case, and the scaling parameter α of the approximation is derived. The proposed estimation is then compared with numerical results, showing that it predicts well the slope of the block erasure rate vs. channel erasure probability.
In this paper, we study rate-compatible puncturing of finite-length Low-Density Parity-Check (LDPC) codes. First, we derive simple and yet good bounds on the expected performance of punctured codes (constructed by random puncturing) over Binary Erasure Channel (BEC) as a function of the performance of their parent LDPC code. We then present a novel rate-compatible puncturing scheme that is very easy to implement. Our scheme uses the idea that a more uniform distribution of punctured bits across the Tanner graph results in punctured codes with better performance. Although the puncturing scheme tailored to regular codes is presented, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over BEC and Additive White Gaussian Noise (AWGN) Channel.