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

Asilomar Conference on Signals, Systems and Computers (ACSSC)

Quantization, absorbing regions and practical message passing decoders

Behzad Amiri, Shayan Garani Srinivasa, Lara Dolecek

Published Nov 1, 2012• 0 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes and accompanying message passing decoding algorithms are a popular choice for data encoding and decoding in modern communications and storage systems. To reduce implementation complexity, the messages in a practical message passing decoder are necessarily quantized. It is well known that the performance of practical, quantized message passing decoders in the high-reliability regime is governed by non-codeword decoding errors, typically described via trapping/absorbing sets. Absorbing regions act as “decoding regions” around absorbing sets. In this work, we take a closer look at the interplay between quantization and absorbing regions. We provide a study of a range of quantization choices, describe the impact of quantization on the candidate absorbing regions, and derive guidelines for practical finite-precision decoders. In particular, we show that, depending on the choice of the quantization allocation, different absorbing sets emerge as dominant: even though the overall performance of two quantization schemes can be similar, the distribution of decoding errors across possible absorbing sets can be substantially different. We take the advantage of disjointness of error profiles of two carefully chosen quantized decoders to design a decoder that is a series of these two decoders. The result is a performance improvement of at least an order magnitude relative to constituent decoders without increase in complexity.

DOI
10.1109/acssc.2012.6489224

Related papers

Absorbing Set Distributions, Quantization and Practical Message Passing Decoders

Behzad Amiri

It is well recognized that low-density parity-check (LDPC) codes can suffer from an error floor when decoded iteratively. This performance degradation is often attributed to the class of objects known as trapping sets. As a subset of the trapping set collection, there exists a class of graphical structures called the absorbing sets. An absorbing set is a combinatorially-defined object; in particular a fully absorbing set is stable under bit-flipping decoding. By construction, there can exist trapping sets that are not stable under such a decoder. As a result, for finite-precision, iterative decoding algorithms used over additive channels, absorbing sets can describe decoding errors more accurately than the broader class of trapping sets. In the first part of this thesis, we compute the normalized logarithmic asymptotic distributions of absorbing sets and fully absorbing sets, including elementary (fully) absorbing sets. We compare distributions of absorbing and trapping sets for representative code parameters of interest, and quantify the (lack of) discrepancies between the two. Good absorbing set properties are implied for known structured LDPC codes, including repeat accumulate codes and protograph-based constructions. Establishing the distribution of fully absorbing sets (especially when the discrepancy with the trapping set distribution is significant) allows one to further refine the estimates of the error rates under bit-flipping and related decoders.To reduce implementation complexity, the messages in a practical message passing decoder are necessarily quantized. Absorbing regions act as "decoding regions" around absorbing sets. In the second part of this thesis, we take a closer look at the interplay between quantization and absorbing regions. We provide a study of a range of quantization choices, the impact of quantization on the candidate absorbing regions, and derive guidelines for practical decoders. We show that, due to the non-linear dynamics of message passing decoders, coarser quantization may in fact perform better than finer quantization. Results of this type of work can be particularly useful in designing high performance decoders for very high-reliability storage systems, such as emerging data storage hard disk and solid state drives.

•Jan 1, 2012•0 citations

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

Zhengya Zhang, Lara Dolecek, Borivoje Nikolić +2 more

Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders

IEEE Transactions on Communications•Nov 1, 2009•113 citations

Transactions Papers Design of LDPC Decoders for Improved Low Error Rate Performance: Quantization and Algorithm Choices

Zhengya Zhang, Lara Dolecek, Venkat Anantharam +1 more

Abstract—Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders

•Jan 1, 2009•1 citation

Performance bounds for quantized LDPC decoders based on absorbing sets

Homayoon Hatami, David G. M. Mitchell, Daniel J. Costello +1 more

A code-independent performance bound for a given absorbing set is derived for quantized low-density parity-check (LDPC) decoders. The analysis demonstrates that each absorbing set in the Tanner graph imposes a specific lower bound on the frame error rate (FER) of any code containing that absorbing set under a given quantization scheme. This approach is applicable to any message-passing (MP) decoding algorithm and any uniform or non-uniform quantization scheme for LDPC codes. Simulation results using the sum-product algorithm (SPA) provide FERs that are consistent with the obtained bounds. In addition, the bounds demonstrate that the conventional quantized SPA is not capable of achieving very low FERs if the LDPC codes contain certain absorbing sets.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2016•5 citations

Quantized Iterative Message Passing Decoders with Low Error Floor for LDPC Codes

Xiaojie Zhang, Paul H. Siegel

The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures - variously referred to as near-codewords, trapping sets, absorbing sets, or pseudocodewords - in a Tanner graph representation of the code. Many approaches have been proposed to lower the error floor by designing new LDPC codes with fewer such substructures or by modifying the decoding algorithm. Using a theoretical analysis of iterative MP decoding in an idealized trapping set scenario, we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used. We then propose a new quantization method - (q+1)-bit quasi-uniform quantization - that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes. Finally, we use the quasi-uniform quantizer to decode several LDPC codes that suffer from high error floors with traditional fixed-point decoder implementations. The performance simulation results provide evidence that the proposed quantization scheme can, for a wide variety of codes, significantly lower error floors with minimal increase in decoder complexity.

arXiv:1212.6465•IEEE Transactions on Communications•Jan 1, 2014•90 citations

Quantization Effects in Low-Density Parity-Check Decoders

Zhengya Zhang, Lara Dolecek, Martin J. Wainwright +2 more

A. class of combinatorial structures, called absorbing sets, strongly influences the performance of low-density parity- check (LDPC) decoders. In particular, the quantization scheme strongly affects which absorbing sets dominate in the error-floor region. Absorbing sets may be characterized as weak or strong. They are a characteristic of the parity check matrix of a code. Conventional quantization schemes applied to a (2209,1978) array-based LDPC code can induce low-weight weak absorbing sets and, as a result, elevate the error floor. Adaptive quantization schemes alleviate the effects of weak absorbing sets, and, as a result, only the strong ones dominate the error floor of an optimized decoder implementation. Another benefit of an adaptive quantization scheme is that it performs well even in very few iterations.

International Conference on Communications•Jun 1, 2007•45 citations
Low-density parity-check (LDPC) codes and accompanying message passing decoding algorithms are a popular choice for data encoding and decoding in modern communications and storage systems. To reduce implementation complexity, the messages in a practical message passing decoder are necessarily quantized. It is well known that the performance of practical, quantized message passing decoders in the high-reliability regime is governed by non-codeword decoding errors, typically described via trapping/absorbing sets. Absorbing regions act as “decoding regions” around absorbing sets. In this work, we take a closer look at the interplay between quantization and absorbing regions. We provide a study of a range of quantization choices, describe the impact of quantization on the candidate absorbing regions, and derive guidelines for practical finite-precision decoders. In particular, we show that, depending on the choice of the quantization allocation, different absorbing sets emerge as dominant: even though the overall performance of two quantization schemes can be similar, the distribution of decoding errors across possible absorbing sets can be substantially different. We take the advantage of disjointness of error profiles of two carefully chosen quantized decoders to design a decoder that is a series of these two decoders. The result is a performance improvement of at least an order magnitude relative to constituent decoders without increase in complexity.
It is well recognized that low-density parity-check (LDPC) codes can suffer from an error floor when decoded iteratively. This performance degradation is often attributed to the class of objects known as trapping sets. As a subset of the trapping set collection, there exists a class of graphical structures called the absorbing sets. An absorbing set is a combinatorially-defined object; in particular a fully absorbing set is stable under bit-flipping decoding. By construction, there can exist trapping sets that are not stable under such a decoder. As a result, for finite-precision, iterative decoding algorithms used over additive channels, absorbing sets can describe decoding errors more accurately than the broader class of trapping sets. In the first part of this thesis, we compute the normalized logarithmic asymptotic distributions of absorbing sets and fully absorbing sets, including elementary (fully) absorbing sets. We compare distributions of absorbing and trapping sets for representative code parameters of interest, and quantify the (lack of) discrepancies between the two. Good absorbing set properties are implied for known structured LDPC codes, including repeat accumulate codes and protograph-based constructions. Establishing the distribution of fully absorbing sets (especially when the discrepancy with the trapping set distribution is significant) allows one to further refine the estimates of the error rates under bit-flipping and related decoders.To reduce implementation complexity, the messages in a practical message passing decoder are necessarily quantized. Absorbing regions act as "decoding regions" around absorbing sets. In the second part of this thesis, we take a closer look at the interplay between quantization and absorbing regions. We provide a study of a range of quantization choices, the impact of quantization on the candidate absorbing regions, and derive guidelines for practical decoders. We show that, due to the non-linear dynamics of message passing decoders, coarser quantization may in fact perform better than finer quantization. Results of this type of work can be particularly useful in designing high performance decoders for very high-reliability storage systems, such as emerging data storage hard disk and solid state drives.
Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders
Abstract—Many classes of high-performance low-density parity-check (LDPC) codes are based on parity check matrices composed of permutation submatrices. We describe the design of a parallel-serial decoder architecture that can be used to map any LDPC code with such a structure to a hardware emulation platform. High-throughput emulation allows for the exploration of the low bit-error rate (BER) region and provides statistics of the error traces, which illuminate the causes of the error floors of the (2048, 1723) Reed-Solomon based LDPC (RS-LDPC) code and the (2209, 1978) array-based LDPC code. Two classes of error events are observed: oscillatory behavior and convergence to a class of non-codewords, termed absorbing sets. The influence of absorbing sets can be exacerbated by message quantization and decoder implementation. In particular, quantization and the log-tanh function approximation in sum-product decoders
A code-independent performance bound for a given absorbing set is derived for quantized low-density parity-check (LDPC) decoders. The analysis demonstrates that each absorbing set in the Tanner graph imposes a specific lower bound on the frame error rate (FER) of any code containing that absorbing set under a given quantization scheme. This approach is applicable to any message-passing (MP) decoding algorithm and any uniform or non-uniform quantization scheme for LDPC codes. Simulation results using the sum-product algorithm (SPA) provide FERs that are consistent with the obtained bounds. In addition, the bounds demonstrate that the conventional quantized SPA is not capable of achieving very low FERs if the LDPC codes contain certain absorbing sets.
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures - variously referred to as near-codewords, trapping sets, absorbing sets, or pseudocodewords - in a Tanner graph representation of the code. Many approaches have been proposed to lower the error floor by designing new LDPC codes with fewer such substructures or by modifying the decoding algorithm. Using a theoretical analysis of iterative MP decoding in an idealized trapping set scenario, we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used. We then propose a new quantization method - (q+1)-bit quasi-uniform quantization - that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes. Finally, we use the quasi-uniform quantizer to decode several LDPC codes that suffer from high error floors with traditional fixed-point decoder implementations. The performance simulation results provide evidence that the proposed quantization scheme can, for a wide variety of codes, significantly lower error floors with minimal increase in decoder complexity.
A. class of combinatorial structures, called absorbing sets, strongly influences the performance of low-density parity- check (LDPC) decoders. In particular, the quantization scheme strongly affects which absorbing sets dominate in the error-floor region. Absorbing sets may be characterized as weak or strong. They are a characteristic of the parity check matrix of a code. Conventional quantization schemes applied to a (2209,1978) array-based LDPC code can induce low-weight weak absorbing sets and, as a result, elevate the error floor. Adaptive quantization schemes alleviate the effects of weak absorbing sets, and, as a result, only the strong ones dominate the error floor of an optimized decoder implementation. Another benefit of an adaptive quantization scheme is that it performs well even in very few iterations.