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International Conference on Signal Processing Systems (ICSPS)

Improved BP-OSD cascade decoding algorithm using limited likelihood information

Qiao Guo-lei, Zijian Dong

Published Jul 1, 2010• 1 citation
Publisher

Abstract

In this work, we use restricted likelihood information of belief propagation (BP) algorithm to improve the accuracy of sorting in order statistic decoding (OSD) for low-density parity-check (LDPC) codes. The reliability information delivered from the last BP iteration to OSD algorithm is inaccurate because that the propagation information may be enlarged for the existence of girths, thence limitation on iterative information can been applied to improve the OSD decoding performance. Simulation results show that the proposed method is effective.

DOI
10.1109/icsps.2010.5555229

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In this work, we use restricted likelihood information of belief propagation (BP) algorithm to improve the accuracy of sorting in order statistic decoding (OSD) for low-density parity-check (LDPC) codes. The reliability information delivered from the last BP iteration to OSD algorithm is inaccurate because that the propagation information may be enlarged for the existence of girths, thence limitation on iterative information can been applied to improve the OSD decoding performance. Simulation results show that the proposed method is effective.
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.
In this work, we present an improvement on low complexity serial concatenation of belief propagation (BP) - order statistic decoding (OSD) algorithm for low-density parity-check (LDPC) codes. We introduce a more reliable method to reconstruct ordered information sequence in terms of the accumulated log-likelihood ratio (LLR) transitions of variable nodes. We give a general expression for both the existing BP-OSD algorithm and our proposed new method according to a structure similar to an infinite impulse response (IIR) filter. This improved algorithm achieves noticeable performance gains with only modest increase in computation complexity.
This article deals with Ordered Statistics Decoding (OSD) applied to the soft outputs of the Belief Propagation (BP) algorithm. We first model the weighted sum of the a posteriori LLRs across BP decoding iterations into a neuron. The neuron is then trained with the focal loss to compute for each BP decoding failure a set of accumulated Log Likelihood Ratios (LLRs) suited for OSD post-processing. Then, we propose a recursive selection procedure of LLRs sets, for multiple OSD post-processing. This selection is carried out from the sets of a posteriori LLRs calculated at each BP iteration, and from the accumulated LLRs optimized for the OSD, based on their joint probabilities of failure with OSD post-processing. An OSD is then applied to each set of LLRs belonging to the selection. In addition, we propose to reduce the OSD post-processing decoding complexity without significantly degrading its performance. Our results show that this new decoding method provides an effective way to bridge the gap to maximum likelihood decoding for short and long Low Density Parity Check (LDPC) codes.
For high rate LDPC codes with light column weight and few redundant checks in their parity check matrix, the belief propagation (BP) decodings yield good error performance at the cost of high complexity. Aiming at seeking a effective decoder with good performance versus complexity tradeoff for this kind of LDPC codes, we present a new decoding framework which cascades a bit flipping (BF) variant with the ordered statistic decoding (OSD). During the iterative decoding of BF variant, the flipping value for each codeword bit is summed. The summation for each bit will be utilized as the reliability input for the OSD postprocessing, if no valid codeword is found after the maximum number of iterations for the BF variant is reached. With respect to the BP, simulation results show that the proposed BF-OSD achieves comparable performance with much less complexity.
In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high b/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.