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IEEE/CIC International Conference on Communications in China (ICCC)

An Improved 5G NR LDPC Decoding Algorithm Based On Box-Plus Operation

Liming Lu, Yi Li, Li Fang

Published Aug 11, 2022• 2 citations
Publisher

Abstract

Iterative box-plus operation is an equivalent function of BP algorithm used in fifth generation(5G) new radio Low-Density Parity-Check (LDPC) decoders, which has gathered significant interest in the past few years. However, it is very challenging to approximate iterative Box-Plus operation effectively since it contains continuous logarithmic and exponential operation. In this paper, the problem is solved gracefully by proposing a simple yet efficient approximate function. The corresponding optimal parameters are given by density evolution and Monte Carlo simulation, which could greatly reduce the unreliability of check-to-variable messages. The extensive experiments in error-correction performance have show the feasibility of the proposed method, compared to existing NMS and OMS algorithms, which makes it more attractive in practical 5G LDPC decoding applications.

DOI
10.1109/iccc55456.2022.9880684

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IEEE Communications Letters•Oct 20, 2015•10 citations
Iterative box-plus operation is an equivalent function of BP algorithm used in fifth generation(5G) new radio Low-Density Parity-Check (LDPC) decoders, which has gathered significant interest in the past few years. However, it is very challenging to approximate iterative Box-Plus operation effectively since it contains continuous logarithmic and exponential operation. In this paper, the problem is solved gracefully by proposing a simple yet efficient approximate function. The corresponding optimal parameters are given by density evolution and Monte Carlo simulation, which could greatly reduce the unreliability of check-to-variable messages. The extensive experiments in error-correction performance have show the feasibility of the proposed method, compared to existing NMS and OMS algorithms, which makes it more attractive in practical 5G LDPC decoding applications.
The high complexity of the Belief Propagation (BP) decoding algorithm in LDPC decoding leads to greater resource consumption and increased communication link latency. This has become a critical challenge in designing efficient communication systems. The Box-Plus operation can effectively transform the nonlinear equations in check nodes into an addition operation of the minimum and the logarithmic functions, but the logarithmic function still has high complexity. In this paper, we propose an Approximate Box-Plus (ABP) decoding algorithm, which reduces decoding complexity while maintaining decoding performance. We first deduced that the logarithmic function in addition operations essentially represents the error between the BP decoding algorithm and the Min-Sum (MS). Based on this insight, a low-complexity, high-precision substitute function is designed. This function utilizes the boundary control ability and symmetry of the min and max functions to effectively express the relative size changes, thereby reducing the unreliability in check node message passing. The proposed decoding algorithm based on the above function reduces the complexity by 38.9% compared to the BP algorithm, and the mean square error of the substitute function and logarithmic function is only 0.0018. Simulation results demonstrate that the decoding performance improves by approximately 0.4 dB compared to the classical Normalized Min-Sum (NMS) and Offset Min-Sum (OMS) algorithms, and the complexity is increased by only three and two new operations per operation compared to NMS and OMS, respectively.
Day by day the internet traffic is increasing rapidly. Challenges to improve these internet traffic requirements leads to evolution of 5G NR LDPC (New Radio Low Density Parity Check) codes which provides high coding gain and energy efficiency. BER Vs Eb/No dB curve defines the energy efficiency and coding gain of the any error correcting codes. LDPC codes which are adopted by 5G Standard are called 5G NR LDPC codes.In the design of the decoder,Message Passing Approach reduces the decoding complexity due to the sparsity of the parity check matrix. An efficient decoding algorithm is the key to the successful code. In this paper an iterative minsum approximation message passing decoding algorithm has been implemented for both BG1 and BG2. Results show that the coding gain can be improved up to 9dB.
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.
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.
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 problem of how to approximate effectively the box-plus operation used in sum-product algorithm (SPA) decoding of low-density parity-check (LDPC) codes has been widely investigated over the past years of research. This letter deals, for the first time, with a totally different approach where a very simple, yet efficient, decoding algorithm for LDPC codes is proposed. The tremendous savings, in terms of required number of operations, offered by the proposed algorithm and its near optimal SPA performance are making it appealing in practical applications requiring very low complexity LDPC decoding architectures.