Dynamic iteration stopping algorithm for non-binary LDPC-coded high-order PRCPM in the Rayleigh fading channel

Abstract

This paper mainly studies the association between non-binary low-density parity-check codes and high-order partial response continuous phase modulation, which prevents information loss in the mutual conversion of bit and symbol probabilities. Although the iterative detection and decoding technique applied in this system can obtain good performance/complexity tradeoff, the iterative process still encounters the problems of positive feedback and relatively large decoding delay, similar to other iterative coded modulation systems. The inhibitory effects of different extrinsic information exchange methods on positive feedback under different signal-to-noise ratio (SNR) conditions are investigated in this work to address this issue. Two dynamic iterative stopping algorithms, namely, cross entropy and hard decision aided combined with weighted extrinsic information exchange for cases with medium and high SNRs, are then proposed. Extrinsic information exchange between the demodulator and the decoder is conducted in the two algorithms through weighted processing. Iterative detection is subsequently performed based on two stopping criteria of dynamic iterative decoding. Theoretic analysis and simulation results for the Rayleigh fading channel show that the combination of weighted extrinsic information exchange and the two dynamic iterative stopping algorithms effectively resists positive feedback and improves the convergence of iterative detection and bit error rate performance. Such a combination also reduces the average iteration number to improve the real-time performance of iterative detection and decoding.

The effects of the cross-entropy stopping criterion and quadrature amplitude modulation on iterative turbo decoding performance

“…Meanwhile, the frame size (N) was set to either 1000, 5000, or 10,000 for each data transmission. The turbo code generator (in octal) and code rate values were (7,5), (17,15), (37,21), and (1/2, 1/3). The codes were simulated under the AWGN channel, and the maximum iteration number max () I was set to 8.…”

“…Also, the BER performances of the CESC and FISC are the same for the threshold values of 0.01, 0.001, and 0.0001. (17,15), the threshold values of 0.01, 0.001, and 0.0001 can terminate early at 2.9, 3, and 3 AIN, respectively, representing reductions of around 65%, 65%, and 63.75% compared to FISC. The BER performances of the CESC and FISC were the same at thresholds of 0.01, 0.001, and 0.0001.…”

“…The AIN and BER performances of the CESC at different threshold values for different turbo code generators are depicted in Figure 5. The graphs for g = (7,5), (17,15) and (37,21) show that the AIN for threshold values of 0.01, 0.001 and 0.0001 started to reduce at 2 dB. At 4 dB Eb/No, the threshold values of 0.01, 0.001, and 0.0001 can terminate early at 3 AIN, representing savings of around 62.5% from a FISC.…”

“…The average number of bits required to identify an event selected from the set is determined by the cross-entropy between two probability distributions A and B, over the same underlying set of events, according to information theory. This is especially true when the set's coding method is optimised for an estimated probability distribution A rather than the genuine distribution B. Cross-entropy is used in many applications, such as for determining stopping criteria in iterative decoding scenarios [13]- [15], defining loss functions in machine learning [21], [22], and optimising classification models [23].…”

“…Fowdur et al [14], [24] proposed the cross-entropy stopping criterion (CESC) to calculate improvements in mutual information to cease turbo decoder iterations. Most of the research on iterative turbo decoding stopping criteria have utilised the binary phase-shift keying (BPSK) modulation technique [6], [7], [11], [15], which is the simplest form of phase-shift keying. High-speed networks such as long-term evolution (LTE) networks and those based on fifth-generation (5G) technology require high modulation (For example, eight phase-shift keyings (8PSK), 16 phase-shift keyings (16PSK), 16-QAM, 32-QAM, and 64-QAM) to transfer data at a sufficient speed [14], [16], [25].…”