Finite-Alphabet Message Passing using only Integer Operations for Highly Parallel LDPC Decoders

Monsees, Tobias; Wübben, Dirk; Dekorsy, Armin; Griebel, Oliver; Herrmann, Matthias; Wehn, Norbert

doi:10.1109/spawc51304.2022.9833953

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…For the special case where the relevant source

is a binary random variable (i.e.,

), the algorithm that finds the optimal quantizer via dynamic programming has been derived in [ 24 ]. We denote the LLRs of the quantizer output

An important property of the MI maximizing quantizer for binary input is that any two different sets of LLRs

and

for

and

are separated by a single threshold [ 19 , 24 , 25 ]. This property will be exploited in the design of the MIC decoder in Section 4 .…”

Section: Preliminariesmentioning

confidence: 99%

“…It should be noted that the CFU implementation is identical for the MIC, Min-mLUT and Min-sLUT decoders. Compared to the corresponding NMS, the CFU implementation is less complex [ 19 ] due to: (i) a 1 bit smaller message quantization, (ii) the omission of the scaling unit, and (iii) the omission of the sign-magnitude to two’s complement conversion. Hence, the CFU complexity of the FA-MP is always lower than that of the NMS independent of the respective CN degree.…”

Section: Finite Alphabet Message Passing (Fa-mp) Decoder Implementationmentioning

confidence: 99%

“…Based on the framework of MIM-QBP and RCQ, the proposed MIC decoder [ 19 ] realizes CN updates by a minimum search and VN updates by integer computations that are designed to realize the information maximizing mLUT mappings either exactly or approximately. In this paper, we provide more detailed explanations, extend the discussion to irregular LDPC codes and present a comprehensive implementation analysis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

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et al. 2022

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In Message Passing (MP) decoding of Low-Density Parity Check (LDPC) codes, extrinsic information is exchanged between Check Node (CNs) and Variable Node (VNs). In a practical implementation, this information exchange is limited by quantization using only a small number of bits. In recent investigations, a novel class of Finite Alphabet Message Passing (FA-MP) decoders are designed to maximize the Mutual Information (MI) using only a small number of bits per message (e.g., 3 or 4 bits) with a communication performance close to high-precision Belief Propagation (BP) decoding. In contrast to the conventional BP decoder, operations are given as discrete-input discrete-output mappings which can be described by multidimensional LUT (mLUTs). A common approach to avoid exponential increases in the size of mLUTs with the node degree is given by the sequential LUT (sLUT) design approach, i.e., by using a sequence of two-dimensional Lookup-Table (LUTs) for the design, leading to a slight performance degradation. Recently, approaches such as Reconstruction-Computation-Quantization (RCQ) and Mutual Information-Maximizing Quantized Belief Propagation (MIM-QBP) have been proposed to avoid the complexity drawback of using mLUTs by using pre-designed functions that require calculations over a computational domain. It has been shown that these calculations are able to represent the mLUT mapping exactly by executing computations with infinite precision over real numbers. Based on the framework of MIM-QBP and RCQ, the Minimum-Integer Computation (MIC) decoder design generates low-bit integer computations that are derived from the Log-Likelihood Ratio (LLR) separation property of the information maximizing quantizer to replace the mLUT mappings either exactly or approximately. We derive a novel criterion for the bit resolution that is required to represent the mLUT mappings exactly. Furthermore, we show that our MIC decoder has exactly the communication performance of the corresponding mLUT decoder, but with much lower implementation complexity. We also perform an objective comparison between the state-of-the-art Min-Sum (MS) and the FA-MP decoder implementations for throughput towards 1 Tb/s in a state-of-the-art 28 nm Fully-Depleted Silicon-on-Insulator (FD-SOI) technology. Furthermore, we demonstrate that our new MIC decoder implementation outperforms previous FA-MP decoders and MS decoders in terms of reduced routing complexity, area efficiency and energy efficiency.

show abstract

“…For the special case where the relevant source

is a binary random variable (i.e.,

), the algorithm that finds the optimal quantizer via dynamic programming has been derived in [ 24 ]. We denote the LLRs of the quantizer output

An important property of the MI maximizing quantizer for binary input is that any two different sets of LLRs

and

for

and

are separated by a single threshold [ 19 , 24 , 25 ]. This property will be exploited in the design of the MIC decoder in Section 4 .…”

Section: Preliminariesmentioning

confidence: 99%

Section: Finite Alphabet Message Passing (Fa-mp) Decoder Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

Monsees

Griebel

Herrmann

et al. 2022

Entropy

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show abstract

Deep Learning-Based Forward-Aware Quantization for Satellite-Aided Communications via Information Bottleneck Method

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Hassanpour,

Wübben

et al. 2024

2024 Joint European Conference on Networks and Communications &Amp;amp; 6G Summit (EuCNC/6G Summit)

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Deep FAVIB: Deep Learning-Based Forward-Aware Quantization via Information Bottleneck Method

Hummert,

Hassanpour,

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et al. 2024

ICC 2024 - IEEE International Conference on Communications

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Finite-Alphabet Message Passing using only Integer Operations for Highly Parallel LDPC Decoders

Cited by 4 publications

References 15 publications

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

Deep Learning-Based Forward-Aware Quantization for Satellite-Aided Communications via Information Bottleneck Method

Deep FAVIB: Deep Learning-Based Forward-Aware Quantization via Information Bottleneck Method

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