Monte Carlo simulations are provided in Section 6. We give the decoding algorithms for adaptive Hamming product codes in Section 5.
#Maxqda ungroup subcodes code
The adaptive message coding scheme and construction of Hamming product code are proposed in Section 4. Section 3 presents the discrete density evolution analysis on unreliable LDPC decoders. In Section 2, the system models are introduced. Both theoretical analysis and Monte Carlo simulations demonstrate that the proposed adaptive message coding scheme outperforms the TMR scheme in decoding both thresholds and residual errors for various storage error levels. We also discuss low complexity iterative decoding algorithms for the Hamming product code.
Moreover, we introduce a construction of Hamming product code for the adaptive coding, which has a multistage coding structure and outstanding error-correcting capability. Then, two LSBs are adaptively employed for sign bits protection based on the magnitude level of message package. The structure of message package permits more efficient block coding schemes for the sign bits other than simple TMR method. First, we put the messages into packages by taking advantage of the parallel message architecture of the quasi-cyclic (QC) LDPC decoders. By analyzing the convergence process of LDPC decoding as well as referring to the results in, it shows that when the magnitude of message is small, the precision bits, that is, the least significant bits (LSBs), are nonnegligible for decoding performance, while when the message has a large magnitude value, the sign bit becomes even more critical for the residual errors.īased on the aforementioned observations, we propose an adaptive embedded coding scheme for the unreliable messages to achieve a robust LDPC decoder. However, since two quantization bits are occupied for protecting the sign bit, the TMR scheme is not always beneficial for various storage error levels due to the loss of quantization precision. To protect the sign bit inside each quantized message, the traditional method is the static triple modular redundancy (TMR) scheme as applied in. It indicates that the sign bits of the messages play the most important role in the decoding performance of LDPC codes, which means setting protection on sign bits is efficient enough. We develop a discrete density evolution analysis for LDPC decoders with faulty messages. In general, the existing works treated each finite-precision message as an integer, while this paper discusses the various impacts of different bits of the finite-precision message. It showed that quantizing messages with more bits was not always beneficial for LDPC decoders with hardware errors. Finite-precision message for the min-sum decoding of LDPC was studied in. Besides these bit flipping decoding algorithms, the belief propagation (BP) decoding of LDPC on noisy hardware was studied in, where infinite-precision message with additive Gaussian noise was considered. Extended studies on faulty Gallager B decoders were then developed in. Varshney considered the thresholds and residual errors of LDPC codes with the faulty Gallager A decoding in the earlier stage. There are studies on the effects of unreliable hardware on LDPC decoders. Thus, it is important to consider the robustness of LDPC decoders utilizing unreliable memories. Such unreliable storage will severely degrade the performance of LDPC codes. However, the radiation environment will give rise to fault problems for memories when LDPC decoders are used in the spacecraft.
The outstanding performance of LDPC is based on the soft-decoding algorithms which consume a large number of memories. Low-Density Parity-Check (LDPC) codes are widely used in space communications due to their capacity-approaching capabilities. Theoretic analysis indicates that the proposed scheme outperforms traditional triple modular redundancy (TMR) scheme in decoding both threshold and residual errors, while Monte Carlo simulations show that the performance loss is less than 0.2 dB when the storage error probability varies from to.
Thirdly, we give a construction of Hamming product code for the adaptive coding and present low complexity decoding algorithms. Secondly, we analyze the effects of quantization precision loss for static sign bit protection and propose an embedded dynamic coding scheme by adaptively employing the least significant bits (LSBs) to protect the sign bits. Firstly, we develop a discrete density evolution analysis for faulty LDPC decoders, which indicates that protecting the sign bits of messages is effective enough for finite-precision LDPC decoders. This paper discusses the impacts of message errors on LDPC decoders and schemes improving the robustness. Unreliable message storage severely degrades the performance of LDPC decoders.