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VLSI implementation of a low-error-floor and capacity-approaching low-density parity-check code decoder with multi-rate capacity

Lei Yang, Hui Liu, C.-J.R. Shi

Published Jan 1, 2005• 3 citations
Publisher

Abstract

With the superior error correction capability, low-density parity-check (LDPC) codes have initiated wide scale interests in wireless communication and storage fields. In the past, various structures of single code-rate LDPC decoders have been reported. However, to cover a wide range of service requirements and diverse interference conditions in wireless applications, LDPC decoders that can operate at both high and low code rates are desirable. In this paper, a 9k code length multi-rate LDPC decoder architecture is presented and implemented on a Xilinx FPGA device. Using pin selection, three operating modes, namely, the irregular 1/2 code, the regular 5/8 code and the regular 7/8 code, are supported. Furthermore, to suppress the error floor level, a characterization on the conditions for short cycles in a LDPC code matrix expanded from a small base matrix is presented, and a cycle elimination algorithm is developed to detect and break such short cycles. The effectiveness of the cycle elimination algorithm has been verified by both simulation and hardware measurements, which show that the error floor is suppressed to a much lower level without incurring any performance penalty. The implemented decoder is tested in an experimental LDPC-OFDM system and achieves the superior measured performance of block error rate below 10/sup -7/ at SNR 1.8 dB.

DOI
10.1109/glocom.2005.1577854

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With the superior error correction capability, low-density parity-check (LDPC) codes have initiated wide scale interests in wireless communication and storage fields. In the past, various structures of single code-rate LDPC decoders have been reported. However, to cover a wide range of service requirements and diverse interference conditions in wireless applications, LDPC decoders that can operate at both high and low code rates are desirable. In this paper, a 9k code length multi-rate LDPC decoder architecture is presented and implemented on a Xilinx FPGA device. Using pin selection, three operating modes, namely, the irregular 1/2 code, the regular 5/8 code and the regular 7/8 code, are supported. Furthermore, to suppress the error floor level, a characterization on the conditions for short cycles in a LDPC code matrix expanded from a small base matrix is presented, and a cycle elimination algorithm is developed to detect and break such short cycles. The effectiveness of the cycle elimination algorithm has been verified by both simulation and hardware measurements, which show that the error floor is suppressed to a much lower level without incurring any performance penalty. The implemented decoder is tested in an experimental LDPC-OFDM system and achieves the superior measured performance of block error rate below 10/sup -7/ at SNR 1.8 dB.
With the superior error correction capability, low-density parity-check (LDPC) codes have initiated wide scale interests in satellite communication, wireless communication, and storage fields. In the past, various structures of single code-rate LDPC decoders have been reported. However, to cover a wide range of service requirements and diverse interference conditions in wireless applications, LDPC decoders that can operate at both high and low code rates are desirable. In this paper, a 9-k code length multi-rate LDPC decoder architecture is presented and implemented on a Xilinx field-programmable gate array device. Using pin selection, three operating modes, namely, the irregular 1/2 code mode, the regular 5/8 code mode, and the regular 7/8 code mode, are supported. Furthermore, to suppress the error floor level, a characterization on the conditions for short cycles in a LDPC code matrix expanded from a small base matrix is presented, and a cycle elimination algorithm is developed to detect and break such short cycles. The effectiveness of the cycle elimination algorithm has been verified by both simulation and hardware measurements, which show that the error floor is suppressed to a much lower level without incurring any performance penalty. The implemented decoder is tested in an experimental LDPC orthogonal frequency division multiplexing system and achieves the superior measured performance of block error rate below 10/sup -7/ at signal-to-noise ratio of 1.8 dB.
After the introduction of iterative coding, Low Density Parity Check (LDPC) codes have received a lot of attention due to their remarkable near Shannon-limit performance and practical decoder implementation. However, when employing an LDPC code for various applications, multiple issues do arise at the simulation, algorithm and implementation levels. The first issue is the performance evaluation of the iterative LDPC decoder in the very low Bit Error Rate (BER) regions. So far, no analytical tool has been developed to evaluate the performance of LDPC codes. Unfortunately standard Monte Carlo (MC) simulations cannot be used for performance estimation in these low BER regions due to prohibitive execution times. The second issue is the efficiency of the decoding algorithm. Due to the presence of short cycles in the bipartite graph, sum-product decoding algorithms lead to considerable performance loss for short block-length LDPC codes and produce error floors for longer codes. In addition, the iterative processing and estimation of soft probabilistic values with these algorithms result in very high computational complexity, which in turn impedes the adoption of LDPC codes for power constrained systems. Another prime objective is to design a high throughput decoder architecture which is capable of supporting multiple rates and variable code lengths within minimal area. This work aims to address and provide solutions to the above problems. As a solution to the performance estimation problem of LDPC codes, a highly efficient and novel fast BER simulation technique is developed. At the algorithm level, a performance improvement and error floor avoidance method is introduced, and a computationally efficient algorithm is developed for the sum-product decoding of LDPC codes. And finally, at the architecture level, a high throughput multi-rate variable code length implementation is presented which, when implemented, efficiently minimizes device resources while alleviating the routing complexity of the decoder.
Because of their excellent error-correcting performance, low-density parity-check (LDPC) codes have recently attracted a lot of attention. In this paper, we are interested in the practical LDPC code decoder hardware implementations. The direct fully parallel decoder implementation usually incurs too high hardware complexity for many real applications, thus partly parallel decoder design approaches that can achieve appropriate trade-offs between hardware complexity and decoding throughput are highly desirable. Applying a joint code and decoder design methodology, we develop a high-speed -regular LDPC code partly parallel decoder architecture based on which we implement a -bit, rate- -regular LDPC code decoder on Xilinx FPGA device. This partly parallel decoder supports a maximum symbol throughput of Mbps and achieves BER at 2 dB over AWGN channel while performing maximum decoding iterations.
The common approach for the design of an error correction system is first to construct a code and then to define the hardware structure of the encoder and decoder. However, in the case of LDPC codes (low-density parity-check) such a constructed code is generally not well suited for a hardware implementation. It has been recognized that the code construction and hardware design must be considered jointly to facilitate LDPC decoder and encoder implementation. In this paper, an efficient decoder structure for regular and irregular LDPC codes, based on TDMP (turbo-decoding message passing) scheme is designed first. The decoder has been implemented and verified in an FPGA device. Constraints for the parity check matrix of a code to be suitable for the decoder architecture are defined. Then an algorithm for LDPC parity check matrix construction subject to these constraints is presented. The algorithm aims at improving performance of the code in the low SNR region by employing irregular codes as well as in high SNR region by reducing the number of small Stopping Sets and Trapping Sets in the Tanner graph of the code making use of a computer search technique.
Low-density parity-check (LDPC) have been shown to have good error correcting performance approaching Shannon’s limit. Good error correcting performance enables efficient and reliable communication. However, a LDPC code decoding algorithm needs to be executed efficiently to meet cost , time, power and bandwidth requirements of target applications. Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important subclass of LDPC codes that are known as one of the most effective error controlling methods. Quasi cyclic codes are known to possess some degree of regularity. Many important communication standards such as DVB-S2 and 802.16e use these codes. The proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.Proposed decoder is well matched for VLSI implementation and will be implemented on Xilinx FPGA family
Low-density parity-check (LDPC) codes have been widely considered as error-correcting codes for next generation communication systems. A good LDPC decoder design requires both implementation friendly LDPC codes and efficient decoder architectures. The quality of LDPC code is crucial in determining the coding gain and implementation complexity of LDPC hardware decoders. This paper presented a genetic algorithm (GA) based LDPC code search algorithm with hardware considerations. Regular quasi-cyclic LDPC codes are used due to its friendliness to hardware implementation. Our hardware architecture design schedules pipeline LDPC decoding operation to boost the hardware utilization efficiency (HUE) of LDPC decoder. A LDPC decoder with a block size of 12288 is implemented in FPGA to validate our code and architecture design.