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Wireless Engineering and Technology

Estimation of Two-Dimensional Correction Factors for Min-Sum Decoding of Regular LDPC Code

Ahmed Abdulkadhim Hamad

Published Jan 1, 2013• 2 citations
Publisher

Abstract

In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.

DOI
10.4236/wet.2013.44027

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In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity.
Two-dimensional (2-D) correction schemes are proposed to improve the performance of conventional min-sum (MS) decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization is presented to obtain the optimal 2-D factors. Both density evolution analysis and simulation show that the proposed method provides a comparable performance as belief propagation (BP) decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of BP decoding. With respect to conventional MS and 1-D normalized MS decodings, the 2-D normalized MS offers a better performance. The 2-D offset MS decoding exhibits a similar behavior.
A two-dimensional post normalization scheme is proposed to improve the performance of conventional min-sum (MS) and normalized MS decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization algorithm is presented to obtain the optimal two-dimensional normalization factors. Both density evolution analysis and specific code simulation show that the proposed method provides a comparable performance as belief propagation decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of belief propagation decoding in the high SNR region. With respect to standard MS and one-dimensional normalized MS decodings, the two-dimensional normalized MS offers a considerably better performance.
Among various decoding algorithms of low-density parity-check (LDPC) codes, the minsum (MS) algorithm and its modified algorithms are widely adopted because of their computational simplicity compared to the sum-product (SP) algorithm with slight loss of decoding performance.In the MS algorithm, the magnitude of the output message from a check node (CN) processing unit is decided by either the smallest or the next smallest input message which are denoted as min1 and min2, respectively.It has been shown that multiplying a scaling factor to the output of CN message will improve the decoding performance.Further, Zhong et al. have shown that multiplying different scaling factors (called a 2-dimensional scaling) to min1 and min2 much increases the performance of the LDPC decoder.In this paper, the simplified 2-dimensional scaled (S2DS) MS algorithm is proposed.In the proposed algorithm, we figure out a pair of the most efficient scaling factors which multiplications can be replaced with combinations of addition and shift operations.Furthermore, one scaling operation is approximated by the difference between min1 and min2.The simulation results show that S2DS achieves the error correcting performance which is close to or outperforms the SP algorithm regardless of coding rates, and its computational complexity is the lowest comparing to modified versions of MS algorithms.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that 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.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that 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.
Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that 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.