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Low Complexity Implementation Of LDPC Decoder using MIN-Sum Algorithm

Geo Niju Shanth, S. Chamandi Priya

Published Jul 12, 2013• 0 citations
OpenAlex

Abstract

This paper presents a resource efficient LDPC decoder architecture. The algorithm used for decoding LDPC is the min-sum algorithm. The decoder reduces the inter-connect complexity by restricting the extrinsic message length to 2 bits and also simplifies the check node operation. The algorithm is simulated and the results show that the performance is better than that of other algorithms. This algorithm can be incorporated into partially parallel hardware architecture to get significant savings in hardware resources when implemented in FPGA.

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This paper presents a resource efficient LDPC decoder architecture. The algorithm used for decoding LDPC is the min-sum algorithm. The decoder reduces the inter-connect complexity by restricting the extrinsic message length to 2 bits and also simplifies the check node operation. The algorithm is simulated and the results show that the performance is better than that of other algorithms. This algorithm can be incorporated into partially parallel hardware architecture to get significant savings in hardware resources when implemented in FPGA.
This thesis is focused on the design and implementation of binary low-density parity-check (LDPC) code decoders for high-speed modern communication systems. The basic of LDPC codes and the performance and bottlenecks, in terms of complexity and hardware efficiency, of the main soft-decision and hard-decision decoding algorithms (such as Min-Sum, Optimized 2-bit Min-Sum and Reliability-based iterative Majority-Logic) are analyzed. The complexity and performance of those algorithms are improved to allow efficient hardware architectures.\n\nA new decoding algorithm called One-Minimum Min-Sum is proposed. It reduces considerably the complexity of the check node update equations of the Min-Sum algorithm. The second minimum is estimated from the first minimum value by a means of a linear approximation that allows a dynamic adjustment. The Optimized 2-bit Min-Sum algorithm is modified to initialize it with the complete LLR values and to introduce the extrinsic information in the messages sent from the variable nodes. Its variable node equation is reformulated to reduce its complexity. Both algorithms were tested for the (2048,1723) RS-based LDPC code and (16129,15372) LDPC code using an FPGA-based hardware emulator. They exhibit BER performance very close to Min-Sum algorithm and do not introduce early error-floor. \n\nIn order to show the hardware advantages of the proposed algorithms, hardware decoders were implemented in a 90 nm CMOS process and FPGA devices based on two types of architectures: full-parallel and partial-parallel one with horizontal layered schedule. The results show that the decoders are more area-time efficient than other published decoders and that the low-complexity of the Modified Optimized 2-bit Min-Sum allows the implementation of 10 Gbps decoders in current FPGA devices. \n\nFinally, a new hard-decision decoding algorithm, the Historical-Extrinsic Reliability-Based Iterative Decoder, is presented. This algorithm introduces the new idea of considering hard-decision votes as soft-decision to compute the extrinsic information of previous iterations. It is suitable for high-rate codes and improves the BER performance of the previous RBI-MLGD algorithms, with similar complexity.
This paper has presented various min-sum related LDPC decoding algorithms and their typical hardware architectures of check node update in the scenario of parallel implementation. The m-to-2m decoder has been introduced to generate more efficient new hardware implementations of check node update, which can obviously reduce the number of multiplication operations for normalized min-sum algorithm for high rate LDPC codes. Simulations have claimed the performance of normalized min-sum is nearly the same as that of Log-BP, namely the optimal algorithm. In general, this paper has proved that normalized min-sum is good choices as LDPC decoding methods.
The objective of this work is to propose a modified Min-Sum decoding Low Density Parity Check (LDPC) algorithm and perform the hardware implementation analysis of Min-Sum, optimized Min-Sum and modified Min-Sum decoders. The Min-Sum algorithm mainly uses the process of finding the minimum and addition. Hence the number of multiplications is drastically reduced which helps in reducing the complexity of implementation. Adding an optimisation factor to the decoder increases the accuracy and reduces the number of iterations required to compute the decoded message. Hence the process of optimisation reduces the overall decoding time required. Modified Min-Sum algorithm is proposed to further improve the performance by decreasing the number of stages in the decoding process which reduces the complexity in Field Programmable Gate Array (FPGA) implementation.
In this paper, the partial-min algorithms are proposed for updating the check node messages in decoding low-density parity-check (LDPC) codes. The proposed methods can achieve a good performance-versus-complexity tradeoff by reducing both the check node processor complexity and the decoder memory requirements. Float-point and fixed-point simulation results show that a near optimum performance can be maintained. The architecture of a check node processor implementing the partial-min algorithms is also presented. The hardware expense especially the memory requirement is analyzed and compared with normal decoding architectures
We present a memory efficient serial low density parity check (LDPC) decoder that implements a modified sum product algorithm (SPA). The modification is similar to the approximate min constraint presented by C. Jones et al. (see IEEE Conf. Military Commun., MILCOM 2003, p.157-162, 2003) but differs in hardware implementation to suit a serial architecture. Our main contribution is the proposed architecture that exploits the min constraint to reduce the storage of extrinsic messages which forms the bulk of the hardware. The least reliable bit to check input along with the check sum are the only quantities stored in the decoder. Extrinsic message memory reduction increases with the rate of the code and up to 68% saving is achieved for a rate 9/10 code. Simulation results show that the proposed changes do not degrade the bit error rate performance.
In this paper, we propose an efficient message passing architecture for permutation matrices based LDPC code decoders. Min-sum algorithm is reformulated to facilitate significant reduction of routing complexity and memory usage. For a (2048, 1723) (6, 32) LDPC code with 4-bit quantization, 54% outgoing wires per variable node unit and 90% outgoing wires per check node unit can be saved. To further reduce hardware complexity, an optimized nonuniform quantization scheme using only 3 bits to represent each message has been investigated. The simulation result shows that it has only 0.25dB performance loss from the floating-point SPA