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Decoding of Non-Binary LDPC Codes using the Information Bottleneck Method

Maximilian Stark, Gerhard Bauch, Jan Lewandowsky, Souradip Saha

Published May 1, 2019• 9 citations
OpenAlex

Abstract

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information-maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.

Related papers

Decoding of Non-Binary LDPC Codes using the Information Bottleneck Method

Maximilian Stark, Gerhard Bauch, Jan Lewandowsky +1 more

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information-maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.

arXiv:1810.08921•International Conference on Communications•May 1, 2019•6 citations

Information-Optimum LDPC Decoders Based on the Information Bottleneck Method

Jan Lewandowsky, Gerhard Bauch

The Information Bottleneck method is a powerful and generic tool from the field of machine learning. It compresses an observation to a quantized variable while attempting to preserve the mutual information shared with a relevant random variable. This paper describes a new application of the Information Bottleneck method in communications. It explains in detail, how the Information Bottleneck method can be applied to construct discrete message passing decoders for regular low-density parity-check codes. The obtained decoders process only unsigned integers and use only simple lookup tables as node operations. As a consequence, the decoders can be implemented using only unsigned integer arithmetic which makes them significantly simpler and faster than the state-of-the-art decoders which process real valued log-likelihood ratios. Anyway, included results show that the considered discrete message passing decoders perform surprisingly close to optimum message passing decoders and even outperform state-of-the-art decoders, such as the min-sum decoder. We aim to take the reader on a journey from the theoretical idea of the Information Bottleneck method to a complete design framework for the considered discrete decoders. Several included figures and examples illustrate the decoder construction process and its analysis.

IEEE Access•Jan 1, 2018•84 citations

Design and Evaluation of Information Bottleneck LDPC Decoders for Software Defined Radios

Jan Lewandowsky, Gerhard Bauch, Matthias Tschauner +1 more

The Information Bottleneck method allows to construct information-optimum message passing decoders for low-density parity-check codes. In such decoders lookup tables replace the classical node operations of the variable and the check nodes. These lookup tables are designed using the Information Bottleneck principle of maximizing the relevant information. Unlike state-of-the-art decoders which use real valued log-likelihood ratios for decoding, the considered decoders do not process any real values, but only quantization indices. Nevertheless, they have performance extremely close to belief propagation decoding. Since hardware representation of unsigned integers is efficient and lookup table implementations have low complexity, it is reasonable to assume that the designed decoders offer advantages over their conventional counterparts in practice. In this paper, we evaluate, quantify and discuss these advantages in a practical experiment. Our focus lies on a software defined radio application, where the channel decoder is implemented on a digital signal processor. We present several implementations of the considered decoders and compare them with state-of-the-art decoders. Our results show considerable gains of the Information Bottleneck decoders in terms of bit error rate performance and net decoding throughput.

International Conference on Signal Processing and Communication Systems•Dec 1, 2018•5 citations

On Bit-Level Decoding of Nonbinary LDPC Codes

Mu Zhang, Kui Cai, Qin Huang +1 more

This paper addresses binary message-passing (MP) decoding for nonbinary low-density parity-check (NB-LDPC) codes based on the binary image of Galois field symbols. The parity-check matrix of NB-LDPC codes in binary form is used to perform MP. The corresponding nonbinary check node (CN) update and variable node (VN) update can thus be decomposed to a set of binary sub-CN updates and sub-VN updates with much lower computational complexity. In particular, we start from adapting the binary parity-check matrix with Gaussian elimination. Then, we add redundant rows to the parity-check matrix instead of adaptation to further improve the performance. A min-max operation based on the expanded matrix is proposed for the CN update. It not only decreases the computational complexity incurred by Gaussian elimination but also improves the error performance. Simulation results show that the bit-level decoding with min-max operation can achieve similar error performance as the extended min-sum algorithm, but the computational complexity can be lower than the min-sum algorithm for binary LDPC codes.

IEEE Transactions on Communications•Apr 17, 2018•15 citations

Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes.

Peng Kang, Kui Cai, Xuan He +1 more

In this paper, we propose a general framework of the mutual infomration-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes, which can outperform the state-of-the-art lookup table (LUT) decoder by using simple mappings and fixed-point additions for the node updates. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and it can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm, leading to the MIM quantized BP (MIM-QBP) decoder and the MIM quantized MS (MIM-QMS) decoder, respectively. In particular, we approximate the check node (CN) update of the MIM-QBP decoder by a max-product operation and obtain the MIM-QMS decoder, which simplifies the decoder design and requires less resource consumption. To avoid the precision degradation, we introduce a dynamic reconstruction method to optimize the variable node update for different iterations. Some practical aspects of the proposed decoders such as the design and decoding complexity are also discussed. Simulation results show that the MIM-QBP decoder outperforms the LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-QMS decoder can even surpass the floating-point BP decoder in the error-floor region.

•Nov 26, 2020•1 citation

Information Bottleneck Decoding of Rate-Compatible 5G-LDPC Codes

Maximilian Stark, Gerhard Bauch, Linfang Wang +1 more

The new 5G communications standard increases data rates and supports low-latency communication that places constraints on the computational complexity of channel decoders. 5G low-density parity-check (LDPC) codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. Practical LDPC decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. Performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing lookup tables that replace conventional finite-precision node computations. The IB approach exchanges messages represented by integers with very small bit width. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include puncturing and rate-compatible IB decoder design. As an example of the new approach, a 4-bit information bottleneck decoder is evaluated for PBRL LDPC codes over a typical range of rates. Frame error rate simulations show that the proposed scheme outperforms offset min-sum decoding algorithms and operates very close to double-precision sum-product belief propagation decoding.

arXiv:1906.08985•International Conference on Communications•Jun 1, 2020•15 citations
Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information-maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.
Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information-maximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.
The Information Bottleneck method is a powerful and generic tool from the field of machine learning. It compresses an observation to a quantized variable while attempting to preserve the mutual information shared with a relevant random variable. This paper describes a new application of the Information Bottleneck method in communications. It explains in detail, how the Information Bottleneck method can be applied to construct discrete message passing decoders for regular low-density parity-check codes. The obtained decoders process only unsigned integers and use only simple lookup tables as node operations. As a consequence, the decoders can be implemented using only unsigned integer arithmetic which makes them significantly simpler and faster than the state-of-the-art decoders which process real valued log-likelihood ratios. Anyway, included results show that the considered discrete message passing decoders perform surprisingly close to optimum message passing decoders and even outperform state-of-the-art decoders, such as the min-sum decoder. We aim to take the reader on a journey from the theoretical idea of the Information Bottleneck method to a complete design framework for the considered discrete decoders. Several included figures and examples illustrate the decoder construction process and its analysis.
The Information Bottleneck method allows to construct information-optimum message passing decoders for low-density parity-check codes. In such decoders lookup tables replace the classical node operations of the variable and the check nodes. These lookup tables are designed using the Information Bottleneck principle of maximizing the relevant information. Unlike state-of-the-art decoders which use real valued log-likelihood ratios for decoding, the considered decoders do not process any real values, but only quantization indices. Nevertheless, they have performance extremely close to belief propagation decoding. Since hardware representation of unsigned integers is efficient and lookup table implementations have low complexity, it is reasonable to assume that the designed decoders offer advantages over their conventional counterparts in practice. In this paper, we evaluate, quantify and discuss these advantages in a practical experiment. Our focus lies on a software defined radio application, where the channel decoder is implemented on a digital signal processor. We present several implementations of the considered decoders and compare them with state-of-the-art decoders. Our results show considerable gains of the Information Bottleneck decoders in terms of bit error rate performance and net decoding throughput.
This paper addresses binary message-passing (MP) decoding for nonbinary low-density parity-check (NB-LDPC) codes based on the binary image of Galois field symbols. The parity-check matrix of NB-LDPC codes in binary form is used to perform MP. The corresponding nonbinary check node (CN) update and variable node (VN) update can thus be decomposed to a set of binary sub-CN updates and sub-VN updates with much lower computational complexity. In particular, we start from adapting the binary parity-check matrix with Gaussian elimination. Then, we add redundant rows to the parity-check matrix instead of adaptation to further improve the performance. A min-max operation based on the expanded matrix is proposed for the CN update. It not only decreases the computational complexity incurred by Gaussian elimination but also improves the error performance. Simulation results show that the bit-level decoding with min-max operation can achieve similar error performance as the extended min-sum algorithm, but the computational complexity can be lower than the min-sum algorithm for binary LDPC codes.
In this paper, we propose a general framework of the mutual infomration-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes, which can outperform the state-of-the-art lookup table (LUT) decoder by using simple mappings and fixed-point additions for the node updates. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and it can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm, leading to the MIM quantized BP (MIM-QBP) decoder and the MIM quantized MS (MIM-QMS) decoder, respectively. In particular, we approximate the check node (CN) update of the MIM-QBP decoder by a max-product operation and obtain the MIM-QMS decoder, which simplifies the decoder design and requires less resource consumption. To avoid the precision degradation, we introduce a dynamic reconstruction method to optimize the variable node update for different iterations. Some practical aspects of the proposed decoders such as the design and decoding complexity are also discussed. Simulation results show that the MIM-QBP decoder outperforms the LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-QMS decoder can even surpass the floating-point BP decoder in the error-floor region.
The new 5G communications standard increases data rates and supports low-latency communication that places constraints on the computational complexity of channel decoders. 5G low-density parity-check (LDPC) codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. Practical LDPC decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. Performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing lookup tables that replace conventional finite-precision node computations. The IB approach exchanges messages represented by integers with very small bit width. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include puncturing and rate-compatible IB decoder design. As an example of the new approach, a 4-bit information bottleneck decoder is evaluated for PBRL LDPC codes over a typical range of rates. Frame error rate simulations show that the proposed scheme outperforms offset min-sum decoding algorithms and operates very close to double-precision sum-product belief propagation decoding.