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IEEE Wireless Communications Letters

Improved Layered Normalized Min-Sum Algorithm for 5G NR LDPC

Beeshanga Abewardana Jayawickrama, Ying He

Published Jul 20, 2022• 15 citations
Publisher

Abstract

Layered Normalised Min-Sum algorithm is a widely used message passing algorithm for decoding Low Density Parity Check codes. The decoding performance heavily depends on the normalisation factor. Firstly, we leverage the bit structure present in 5G transport blocks to develop an improved decoding algorithm for 5G. Secondly, we determine the optimal normalisation factors of the proposed algorithm using a Deep Neural Network. Performance evaluations show an improvement of 0.3-1.9 dB, with no extra cost on multiplier resources on hardware. Hence, the proposed method is highly attractive for practical 5G decoder implementations.

DOI
10.1109/lwc.2022.3192518

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Layered Normalised Min-Sum algorithm is a widely used message passing algorithm for decoding Low Density Parity Check codes. The decoding performance heavily depends on the normalisation factor. Firstly, we leverage the bit structure present in 5G transport blocks to develop an improved decoding algorithm for 5G. Secondly, we determine the optimal normalisation factors of the proposed algorithm using a Deep Neural Network. Performance evaluations show an improvement of 0.3-1.9 dB, with no extra cost on multiplier resources on hardware. Hence, the proposed method is highly attractive for practical 5G decoder implementations.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
Abstract In order to cater to the needs of the 5G standard, one of the prominent solutions in terms of high coding gain, high throughput and low power dissipation is the 5G NR LDPC (New Radio Low Density Parity Check) codes which have been adopted by 5G Standard. LDPC codes are the successful Third Generation Forward Error Correcting codes. An Efficient decoder is the key to the success of any Error Correcting Code. LDPC codes are one whose parity check matrix have a very few non zero entries. 5G NR LDPC codes are constructed by Protographs or base graphs and are block structured. This paper improves the performance of Layered Iterative minsum Approximation Message Passing decoding Algorithm using Rate Matching, Fixed Point Quantization and Offset minsum techniques. Rate Matching is to maintain the exact number of encoded blocks with in the TTI. Simulation of this algorithm with BPSK encoding over AWGN channel shows that BER of 10-3 gives Eb/No of~2 dB for the block length of 105.
5G new radio low density parity check (5G-NR LDPC) codes specified by the 3rd generation partnership project (3GPP), a representative class of multi-edge-type, quasi-cyclic and raptor-like LDPC codes with rate-compatible and length-scalable capability, could meet with high-throughput demands. The corresponding decoding algorithm and implementation should support low complexity, high performance and scaleinvariance to channel variations and receiver imperfections. Flooding scheduling is usually used for the prevalent decoding algorithms and architecture of LDPC codes, but it is inefficient and inflexible compared with layered scheduling. This paper proposes a new simplification method where the sub-groups with similar fitting functions of normalization factors are incorporated into the same type, and enhanced adaptive normalized min-sum algorithm (enhanced ANMSA) for layered scheduling is further proposed for the implementation of 5G-NR LDPC codes. Based on the new simplification method, the proposed algorithm defines three types of check nodes for base graph 2 (BG2) in 5G-NR LDPC codes, and then obtains three look-up tables for BG2 by training. Simulation results demonstrate that the proposed algorithm can achieve excellent performance for 5G-NR LDPC codes of different rates and lengths over Binary-input AWGN channel and Rayleigh channel.
The development of the Fifth Generation (5G) New Radio (NR) provides several significant advantages when compared to the fourth generation (4G) Long Term Evolution (LTE) in mobile communications. Due to the outstanding characteristics of Low-Density Parity-Check (LDPC) codes such as high decoding performance, high throughput, low complexity, they have been accepted as the standard codes for the 5G NR. In this paper, we propose two LDPC decoding algorithms: Hybrid Offset Min-Sum (HOMS) and Variable Offset Min-Sum (VOMS), which are aimed at improving the error correction performance. The main idea of the HOMS/VOMS algorithm is to apply modified factors to both variable-nodes and check-nodes updated processing in order to compensate the extrinsic messages overestimation of the MS-based algorithms and increase the protection ability for degree-1 variable-nodes. The simulation results show that at the Bit-Error-Rate (BER) of 10-5, the proposed HOMS/VOMS algorithm achieves the decoding gain up to 0.2 dB compared to the Offset Min-Sum (OMS) algorithm, with a slight increase in decoding complexity.
The paper presents a detailed analysis of the minsum decoding algorithm as applied to low-density parity-check (LDPC) codes used in 5G new radio (NR) systems. With the increasing demand for higher data rates and improved reliability in next-generation wireless communications, LDPC codes have emerged as a pivotal component in 5G NR's coding strategy. The minsum algorithm, known for its simplicity and efficiency in message passing, is evaluated in the context of its performance and practical implementation for these codes. Minsum decoding reduces complexity by approximating the soft-decision values using the minimum of the incoming messages, rather than applying the more computationally expensive operations such as hyperbolic tangent functions. In the context of 5G NR, this approximation makes minsum decoding particularly attractive for hardware implementation, providing a good trade-off between error-correction performance and computational efficiency. The algorithm iteratively updates messages passed along the edges of the Tanner graph, leveraging the sparsity of LDPC codes. This abstract reviews the relevance of minsum decoding to 5G NR LDPC codes, emphasizing its role in balancing performance with low computational requirements, critical in mobile and high-throughput applications.
In this letter, a neural self-corrected min-sum (NSCMS) decoder is proposed for 5G new radio (NR) low-density parity-check (LDPC) codes. Training in real-time on a rapidly changing channel requires low latency and minimal resource utilization. Unfortunately, typical neural decoders for LDPC codes use large and deep neural networks proportional to the code length, leading to latency and resource problems. In the network of NSCMS similar to network model pruning, certain nodes meeting the self correction condition are deleted and excluded from learning. This reduces the computational complexity of learning, compared to conventional networks. Thus, the NSCMS decoder has high practicality in real-time training using machine learning. Furthermore, self-correction allows for more reliable message-based learning and significantly improves performance. Simulation results demonstrate that NSCMS decoders exhibit lower error rates than previously proposed min-sum decoders.