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This work studies the equalization methods for the reduced zero‐padding version of the orthogonal time frequency space modulation. Here, the focus is on applications in low data rate scenarios such as the Internet of Things, and the case where the number of subcarriers and time slots are small will be considered. First, the system equation is established to model the inter‐subcarrier and inter‐slot interference phenomena. Based on the system model, three sphere‐decoding based equalization methods are proposed. The first method is to directly apply the sphere‐decoding algorithm on the full‐scale system model; for the second method, the transmitter needs to perform the triangular precoding; and for the third method, the transmitter needs to perform the diagonal precoding. Simulation results show that the proposed sphere‐decoding based methods achieve better bit error rate performance than the state‐of‐the‐art methods like message passing, unitary approximate message passing, and variational approximate message passing, especially when the channel has severe inter‐slot interference. [ABSTRACT FROM AUTHOR]

The successive cancellation flip (SC Flip) decoding algorithm was recently suggested for decoding polar codes, which could improve the performance of the frame error rate (FER). The performance of the SC Flip (SCF) decoding algorithm is strong, and its computational complexity tends to be the same as that of the SC decoder at medium to high signal‐to‐noise ratios (SNRs). However, the decoding latency of the SCF decoding algorithm is large. In this paper, a new method for detecting whether or not the flipped bit is correct is proposed. The proposed method makes a decision according to the changing log likelihood ratio (LLR) value caused by the flipped bit to ensure that the decoding process can be terminated in advance and the decoding latency is reduced. The simulation results show that the proposed Latency‐Reduced SCF decoding algorithm can decrease computational complexity and decoding latency, while also achieving similar decoding performance compared to its counterpart. [ABSTRACT FROM AUTHOR]

In this study, the authors propose a new two-stage decoding scheme for low-density parity-check codes to lower the error-floor, which consists of the conventional belief propagation (BP) decoding algorithm as the first-stage decoding and the redecodings with manipulated log-likelihood ratios (LLRs) of variable nodes as the second-stage decoding. In the first-stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes are determined, which can be partly included in the small trapping sets. In the second-stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re-decoding trials. Each re-decoding trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion. The parallel unreliable path search algorithm is also proposed for practical application of the proposed algorithm. Numerical results show that the proposed early stopping criteria and the proposed decoding algorithms for the second-stage decoding can correct most of the unsuccessfully decoded codewords by the first-stage decoding in the error-floor region. [ABSTRACT FROM AUTHOR]

A new decoding strategy of belief propagation (BP) for low-density parity-check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node-wise residual belief propagation (NW RBP) or informed variable-to-check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non-concatenated single decoder. In addition, as the signal-to-noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub-decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub-decoder flooding. [ABSTRACT FROM AUTHOR]

The distribution of information bits and frozen bits on the decoder graph can be exploited to simplify the successive-cancellation (SC) decoding of polar codes. In this study, the authors establish a general simplified SC decoding framework for polar codes with arbitrary block-length, which is independent of any specific or explicit generator matrices and considerably reduces decoding complexity while retaining the same error performance. Then, based on the fact that the complexity reduction depends on the distribution of information bits, a so-called m-radius reselection scheme is proposed to construct multiple feasible information sets which are different from the original one defined by Arıkan. In this way, flexible tradeoffs between performance and complexity could be achieved. [ABSTRACT FROM AUTHOR]