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In this paper, a new method for decoding Low Density Parity Check (LDPC) codes, based on Multi-Layer Perceptron (MLP) neural networks is proposed. Due to the fact that in neural networks all procedures are processed in parallel, this method can be considered as a viable alternative to Message Passing Algorithm (MPA), with high computational complexity. Our proposed algorithm runs with soft criterion and concurrently does not use probabilistic quantities to decide what the estimated codeword is. Although the neural decoder performance is close to the error performance of Sum Product Algorithm (SPA), it is comparatively less complex. Therefore, the proposed decoder emerges as a new infrastructure for decoding LDPC codes.
Min-Sum decoding is widely used for decoding LDPC codes in many modern digital video broadcasting decoding due to its relative low complexity and robustness against quantization error. However, the suboptimal performance of the Min-Sum affects the integrated performance of wireless receivers. In this paper, we present the idea of adapting the scaling factor of the Min-Sum decoder with iterations through a simple approximation. For the ease of implementation the scaling factor can be changed in a staircase fashion. The stair step is designed to optimize the decoder performance and the required storage for its different values. The variable scaling factor proposed algorithm produces a non-trivial improvement of the performance of the Min-Sum decoding as verified by simulation results.
In this paper, we propose a novel low complexity scaling strategy of min-sum decoding algorithm for irregular LDPC codes. In the proposed method, we generalize our previously proposed simplified Variable Scaled Min-Sum (SVS-min-sum) by replacing the sub-optimal starting value and heuristic update for the scaling factor sequence by optimized values. Density evolution and Nelder-Mead optimization are used offline, prior to the decoding, to obtain the optimal starting point and per iteration updating step size for the scaling factor sequence of the proposed scaling strategy. The optimization of these parameters proves to be of noticeable positive impact on the decoding performance. We used different DVB-T2 LDPC codes in our simulation. Simulation results show the superior performance (in both WER and latency) of the proposed algorithm to other Min-Sum based algorithms. In addition to that, generalized SVS-min-sum algorithm has very close performance to LLR-SPA with much lower complexity.
This paper summarizes the design of a programmable processor with transport triggered architecture (TTA) for decoding LDPC and turbo codes. The processor architecture is designed in such a manner that it can be programmed for LDPC or turbo decoding for the purpose of internetworking and roaming between different networks. The standard trellis based maximum a posteriori (MAP) algorithm is used for turbo decoding. Unlike most other implementations, a supercode based sum-product algorithm is used for the check node message computation for LDPC decoding. This approach ensures the highest hardware utilization of the processor architecture for the two different algorithms. Up to our knowledge, this is the first attempt to design a TTA processor for the LDPC decoder. The processor is programmed with a high level language to meet the time-to-market requirement. The optimization techniques and the usage of the function units for both algorithms are explained in detail. The processor achieves 22.64 Mbps throughput for turbo decoding with a single iteration and 10.12 Mbps throughput for LDPC decoding with five iterations for a clock frequency of 200 MHz.
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without resorting on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity, but the optimal fraction is strictly smaller than one. We then consider techniques to further reduce the gap to capacity by means of random puncturing, and the inclusion of a certain fraction of generalized variable nodes in the graph.
In this paper, the application of non-binary low-density parity-check (NBLDPC) codes to MIMO systems which employ hundreds of antennas at both the transmitter and the receiver has been proposed. Together with the well-known low-complexity MMSE detection, the moderate length NBLDPC codes can operate closer to the MIMO capacity, e.g., capacity-gap about 3.5 dB (the best known gap is more than 7 dB). To further reduce the complexity of MMSE detection, a novel soft output detection that can provide an excellent coded performance in low SNR region with 99% complexity reduction is also proposed. The asymptotic performance is analysed by using the Monte Carlo density evolution. It is found that the NBLDPC codes can operate within 1.6 dB from the MIMO capacity. Furthermore, the merit of using the NBLDPC codes in large MIMO systems with the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems is also pointed out.