In this paper, performance of orthogonal frequency division multiplexing (OFDM) with index modulation (IM) based schemes is evaluated. We consider the well known OFDM-IM, where partial subcarriers are activated and the corresponding indices convey extra information, and its variant multiple-mode OFDM-IM (MM-OFDM-IM) which provides better spectral efficiency (SE) and uncoded bit error rate (BER) by activating all subcarriers and using distinguishable constellations. Although uncoded performance has been extensively discussed for these techniques, performance with channel codes involved lacks of evaluation and discussion. Therefore, we present both uncoded and coded BER performance with new radio (NR) low density parity check (LDPC) code in this paper, where LDPC codes with different code rates are employed. Simulation results show that OFDM-IM based scheme with LDPC code outperforms the conventional OFDM with LDPC code only within a limited code rate range, although its uncoded performance offers large gains at high SNR.

In this paper, we focus on the finite-length performance of spinal codes with a sliding window decoder over binary erasure channel. An expression of the error probability of spinal codes is derived. Particularly, we also derive an expression of the error probability of spinal codes with some known tail bits, which can improve the error-control performance. Moreover, easier-to-compute upper and lower bounds on the error probability are also provided. Simulation results show that the error-control performance can be improved by introducing known tail bits and the performance becomes better with the increase of the maximum window length. Finally, the derived bounds can well evaluate the error performance of spinal codes.

In this paper, we propose a rateless two-way spinal code. There exist two encoding processes in the proposed code, i.e., the forward encoding process and the backward encoding process. Rather than the original spinal code, where each message segment only has relationship with the coded symbols corresponding to itself and the later message segments, the information of each message segment of the proposed code is conveyed by the coded symbols corresponding to all the message segments. Based on this two-way coding strategy, we propose an iterative decoding algorithm. Different transmission schemes, including the symmetric transmission and the asymmetric transmission, are also discussed in this paper. Our analysis illustrates that the asymmetric transmission can be treated as a tradeoff between the performance and the decoding complexity. Simulation results show that the proposed code outperforms not only the original spinal code but also some strong channel codes, such as polar codes and raptor codes.

In this paper, we propose and analyze an unequal error protection (UEP) rateless spinal code, which can provide UEP and unequal recovery time properties. The proposed UEP spinal codes achieve UEP by the permutation of different priority levels and the setup of different segment sizes for different priority levels. In addition, an unequal length transmission scheme to improve the transmission rate is proposed, where the number of transmitted symbols in each pass varies. Moreover, we analyze the finite-length performance of the proposed UEP spinal code, which enables us to provide the upper bound of average error probability for each priority level under maximum likelihood decoding. Based on this finite-length result, we discuss the design of UEP spinal code, which is flexible and efficient. Furthermore, the asymptotic performance analysis shows that the proposed UEP spinal code with a practical decoder can achieve the capacities of both binary symmetric channel and additive white Gaussian noise channel. Simulation results verify our analysis.

In this paper, we propose a rateless superposition spinal coding scheme for the half-duplex relay channel, which is an optimal realization of the information theoretic coding scheme for decode-and-forward (DF) relaying. The proposed coding scheme has a simple coding structure and can be implemented flexibly. More importantly, the encoders and decoders can maintain unchanged for varying channel conditions. We also contribute to the optimization of the proposed coding scheme, which can provide an excellent rate performance. Since only two parameters are considered in the optimization, the optimization can be realized with low complexity. Furthermore, we prove that the proposed coding scheme can achieve the theoretic limit of half-duplex DF relaying. Simulation results show that the average transmission rates of the proposed coding scheme are very close to the theoretic limits for both Gaussian relay channel and fading relay channel.