In this paper, we propose an improved iterative demapping/decoding method for short length low-density paritycheck (LDPC) coded bit-interleaved coded modulations (BICM). For short length LDPC, there exist cycles in the bipartite graph, thereby leading to the high correlation among the extrinsic information of bits out from BP decoder. Based on the Gaussian assumption of the extrinsic log-likelihood ratios (LLRs)delivered by BP decoder, we multiply the extrinsic output of the decoder by a scaling factor and then pass it as a priori information to the demodulator for the next iteration. In this way, we can decrease the correlation of coded bits within the symbol and thus reduce the error propagation. Simulation results show that the proposed method can achieve noticeable performance gains for short length LDPC coded BICM-ID with a minor computation complexity increase.
In this paper, we propose an improved iterative demapping/decoding method for short length low-density paritycheck (LDPC) coded bit-interleaved coded modulations (BICM). For short length LDPC, there exist cycles in the bipartite graph, thereby leading to the high correlation among the extrinsic information of bits out from BP decoder. Based on the Gaussian assumption of the extrinsic log-likelihood ratios (LLRs)delivered by BP decoder, we multiply the extrinsic output of the decoder by a scaling factor and then pass it as a priori information to the demodulator for the next iteration. In this way, we can decrease the correlation of coded bits within the symbol and thus reduce the error propagation. Simulation results show that the proposed method can achieve noticeable performance gains for short length LDPC coded BICM-ID with a minor computation complexity increase.
The LDPC coded bit-interleaved coded modulation iterative decoding(BICM-ID)system was modeled by a normal factor graph.From the angle of the message update rule,uniformly reweighted belief propagation algorithm(URW-BP)and belief propagation algorithm(BP)are unified and interpreted as message passing algorithm by variation method.Combining the local nature of BP with the improved performance of URW-BP in graphs with cycles,the uniformly reweighted iterative decoding algorithm(URID)was derived and the impact of edge appearance probabilities(EAP)on its performance discussed. Simulation results for AWGN and Rayleigh fading channel and different modulation illustrate the performance improvement of URID compared with other iterative decoding algorithms such as BP and DifferenceMap BP(DMBP)algorithm.
It is well known that extremely long low-density parity-check (LDPC) codes perform exceptionally well for error correction applications, short-length codes are preferable in practical applications. However, short-length LDPC codes suffer from performance degradation owing to graph-based impairments such as short cycles, trapping sets and stopping sets and so on in the bipartite graph of the LDPC matrix. In particular, performance degradation at moderate to high Eb/N0 is caused by the oscillations in bit node a posteriori probabilities induced by short cycles and trapping sets in bipartite graphs. In this study, a computationally efficient algorithm is proposed to improve the performance of short-length LDPC codes at moderate to high Eb/N0. This algorithm makes use of the information generated by the belief propagation (BP) algorithm in previous iterations before a decoding failure occurs. Using this information, a reliability-based estimation is performed on each bit node to supplement the BP algorithm. The proposed algorithm gives an appreciable coding gain as compared with BP decoding for LDPC codes of a code rate equal to or less than 1/2 rate coding. The coding gains are modest to significant in the case of optimised (for bipartite graph conditioning) regular LDPC codes, whereas the coding gains are huge in the case of unoptimised codes. Hence, this algorithm is useful for relaxing some stringent constraints on the graphical structure of the LDPC code and for developing hardware-friendly designs.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
Low-Density Parity-Check (LDPC) codes are one of the most popular codes used in nowadays’ communication due to their high coding efficiency at low decoding complexity. With these characteristics, LDPC codes are suitable for high-speed information transmission systems. The widely used decoding algorithm for LDPC codes is Belief Propagation (BP) decoding with which the performance of LDPC codes can approach the Shannon limit. With the development of 5G, a lot of attention is given to the so-called ultra-reliable low latency communication scenario which needs the short code to transmit. However, short codes will not have a very good performance with BP decoding. To solve this problem, investigations have been done such as multiple-bases BP decoding. Although this decoding method has a better performance than BP decoding, it will cause a high complexity in the hardware implementation. Besides, an investigation on the stochastic decoding for shortcodes was proposed in 2003. This decoding method is hardware friendly, but its performance can only approach BP decoding. Inspired by multiple-bases BP decoding and stochastic decoding, binary stochastic decoding with parallel decoders is proposed in this thesis firstly. It represents stochastic sequences with multiple parallel Tanner graphs and uses hard-decision decoding in the iterative part because of the binary input bits. However, this decoding method has a severe performance loss compared to BP decoding. To avoid this problem, the enhancement method is used to make the binary sequences be non-binary sequences that can form more powerful parallel decoders. Then the non-binary symbols of these new sequences are transformed to their corresponding log-likelihood ratio which enables the iterative part to use BP decoding. In addition, combining with the ML decision of list decoding, the decision part of our stochastic decoder can fully utilize the output to increase the efficiency of the decoding method. After ensuring the performance of our non-binary stochastic decoding to be better than BP decoding, the complexity of the decoder is reduced to save the computational resources. Finally, with constant adjustments, the bit width of each non-binary symbol is determined to be 15, and the sequence length is reduced to 20 which can let the non-binary stochastic decoding has an acceptable complexity while keeping good performance.
A great deal of experiment indicate that, during the decoding course of message passing for LDPC codes, a phenomenon of oscillating always exists in some variable messages named extrinsic log-likelihood rate (ex-LLR). It could arose bit error. This paper tells of why the magnitudes of a posterior LLRs and ex-LLRs of some bits would oscillated, and thus two improved algorithms are proposed, which could improve the decoding performance being deteriorated by ex-LLR oscillation. The computer simulation shows that, for short and middle length LDPC codes, the proposed algorithms could lower the error floor without increasing the complexity, so these two algorithms could achieve better BER and BLER than the conventional LLR-BP decoding algorithm.
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.