This paper analyzes the performance of Alamouti coded short-packet non-orthogonal multiple access (NOMA) systems with hybrid multicast-unicast transmission over Nakagami-mfading, where only the statistical channel state information is available at the transmitter, and the multicast and unicast signals are intended for all users and a particular user, respectively. Due to practical limitations, channel estimation errors (CEEs), residual hardware impairments (RHIs), and imperfect successive interference cancellation (SIC) are considered. We first derive approximate closed-form expressions for the average block error rate (BLER) and the corresponding asymptotic expressions at all users. Using such expressions, we analyze the diversity performance including conventional diversity order and finite signal-to-noise ratio (SNR) diversity order. After this, we quantify the relationship among the blocklength of information transmission, power allocation, and pilot sequence length under users’ reliability constraints. Finally, numerical and simulation results show that CEEs, RHIs, and imperfect SIC greatly affect the transmission blocklength. Moreover, RHIs lead to the error floor at high SNRs and finite-SNR diversity order is an effective performance metric at low or medium SNRs. They also show that there exist optimal values for the power allocation coefficients, blocklength of information transmission, and pilot sequence length that minimize the transmission blocklength in the considered hybrid multicast-unicast system. They further show that the NOMA scheme is superior to the orthogonal multiple access counterpart by achieving low-latency transmission.

As a state of the art coding technology, fountain codes are promising to drive the outage probability to zero in non-orthogonal multiple access (NOMA) system suffering from severely fading channels. In this paper, we study cross-layer design for a downlink fountain-coded NOMA system with a base station and two users. In order to achieve successful decoding for both users over block Rayleigh fading channels, an optimization problem, taking optimal allocation of redundancy between packet-level fountain coding and physical-layer channel coding into account, is formulated. The sum of the overall code rates is maximized subjected to a minimum physical-layer code rate constraint of the weak user for the single-input single-output scenario. Numerical analysis shows that it is vital to rapidly increase the overall code rate for the weaker user to maximize the sum of the overall code rates and very little redundancy is required for packet-level fountain coding at the weak user, when the total transmit power is large and the channel gain difference between two users becomes small.

Expanding window fountain (EWF) codes use a windowing technique to achieve unequal error protection (UEP) and unequal recovery time. UEP affords significant performance improvement of the more important bits (MIB), but at the cost of performance deterioration of the less important bits (LIB), resulting in poor intermediate performance of the EWF coding. In this study, the authors propose the utilisation of intermediate feedback in EWF coding to terminate the encoding of the MIB after their recovery, with the purpose of enhancing the intermediate performance of EWF codes over binary input additive white Gaussian noise (BIAWGN) channels. The effectiveness of the proposed coding scheme is analysed and evaluated by using extrinsic information transfer functions to investigate the theoretical performance and obtain the closed‐form formula of the bit error rate (BER) of the LIB after the intermediate feedback. The results of the theoretical analysis and simulation of the scheme using additive white Gaussian noises with different signal‐to‐noise ratios reveal an improvement in the BER performance of the LIB compared to the case of conventional EWF coding, and also show that the scheme significantly enhances the intermediate performance of the EWF codes and improves the transmission efficiency.

In this paper we consider scalable video multicasting over erasure networks with heterogeneous video quality requirements. With random linear network coding (RLNC) applied at the intermediate nodes the information received by the destinations is determined by the associated channel rank distributions based on which we obtain the optimal achievable code rate at the source node. We show that although a concatenation of priority encoded transmission (PET) with RLNC achieves the optimal code rate it incurs prohibitive high coding complexity. On the other hand batched sparse (BATS) code has been recently proposed for unicast networks which has low coding complexity with near-optimal overhead. However the existing BATS code design cannot be applied for multicast networks with heterogeneous channel rank distributions at different destinations. To this end we propose a novel expanding window BATS (EW-BATS) code where the input symbols are grouped into overlapped windows according to their importance levels. The more important symbols are encoded with lower rate and hence they can be decoded by more destinations while the less important symbols are encoded with higher rate and are only decoded by the destinations with high throughput for video quality enhancement. Based on asymptotical performance analysis we formulate the linear optimization problems to jointly optimize the degree distributions for each window and the window selection probabilities. Simulation results show that the proposed EW-BATS code satisfies the decoding requirements with much lower transmission overhead compared with separate BATS code where the degree distributions are separately optimized for each destination.

New Raptor codes, based on low rate low-density parity-check (LDPC) codes, are proposed for short message length over various channels. The proposed Raptor codes are obtained by pre-coding the information bits by low rate LDPC codes and utilizing a low constant average degree distribution with high intermediate symbol recovery rate (ISRR). Simulation results demonstrate that the proposed Raptor codes outperform conventional Raptor codes for small message length.

In this paper, we investigate feedback in EWF codes. The considered type of feedback is an acknowledgment, which is a single bit per source block to inform the most important bits have been decoded completely. Moreover, we propose a practical prediction model to calculate the average overheads of successful decoding for different importance classes of the source block. Asymptotic analysis and simulation results demonstrate that, compared with standard EWF codes, the proposed EWF codes with feedback can obtain a lower average overhead of successful decoding in lower prioritized data, and the proposed prediction model is effective.

Novel precoded Expanding Window Fountain (EWF) codes, based on low rate low-density parity-check (LDPC) codes, are investigated for finite message length over binary erasure channels (BECs). The proposed codes are obtained by utilizing low rate LDPC codes as precodes and degree distributions with high intermediate symbol recovery rate for EWF codes. Simulation results show that, compared with conventional precoded EWF codes, our proposed codes have better performance in the scenarios of small and moderate message lengths over the BEC.

In this study, the authors propose an improved design of expanding window fountain (EWF) codes over the binary input additive white Gaussian noise channels. The encoding process is modified to get almost regular variable‐node degree distributions. Compared with the conventional EWF codes, their proposed scheme can lower the error floor. Furthermore, they combine the EWF encoding process with unequal power allocation to improve unequal error protection (UEP) performance, and construct pre‐coded EWF codes by concatenating their proposed EWF codes with high‐rate low‐density parity‐check codes. Both asymptotic analysis and simulation results show that, compared with the conventional scheme, their proposed scheme can get better UEP performance and design flexibility.

In this paper, we propose an efficient scheme to construct fountain codes that can provide unequal error protection (UEP) property. To reduce the coding complexity and improve the performance of previous duplicate UEP schemes in the literature, we implement different rate low-density parity-check codes instead of the duplication process and replace the high-complexity classical robust soliton distribution by low constant average degree distributions with high intermediate symbol recovery rates. Asymptotic analysis of both the duplicate scheme and our scheme is obtained by deriving unequal density evolution formulas over the binary erasure channel. Compared to previous UEP schemes, our scheme has lower complexity. Experimental results show that our scheme can obtain better decoding performance, especially for smaller input information length. Comparison of peak signal-noise ratio performance for the scalable video coding shows that, for moderate input information length, our scheme can provide a better basic video quality at lower overhead, but needs larger overhead to achieve a high video quality.

In this paper, we propose an efficient scheme to construct LT codes that can provide unequal error protection (UEP) property. We implement low rate LDPC codes instead of the duplication and utilize a low constant average degree distribution with high intermediate symbol recovery rates (ISRR) to improve the performance of more important bits (MIB). Asymptotic analysis of the proposed scheme is obtained by deriving unequal density evolution (DE) formulas over the binary erasure channel (BEC). Utilizing LDPC codes and the degree distribution with high ISRR in the proposed scheme, the UEP property is flexible and efficient. Compared with previous duplicate UEP-LT codes, mathematical analysis and simulation results demonstrate that the proposed UEP-LT codes have better performance.

To improve the throughput performance without feedback channel, a partial cooperation scheme based on fountain codes is proposed in this paper. Compared with the incremental relaying where the signal is retransmitted in fixed or selective relay and fed back to the source from the destination, the proposed scheme only requires the partner to offer partial encoded packets in collaborative phase. Simulation results show that throughput performance of the proposed scheme outperforms that of incremental relaying, which has ever been considered as the optimal scheme in three-terminal cooperative communications system with the partial cooperation parameter around 0.1 in our simulation. In particular, the proposed scheme allows for an easy extension to multiple partners.

In many communication systems, it is necessary to use unequal error protection (UEP) techniques. The design issues of UEP fountain codes over the binary erasure channel (BEC) have been extensively studied in recent years. In this paper, we investigate the performance of two main classes of UEP fountain codes (i.e., UEP-LT codes and Expanding Window Fountain (EWF) codes) over the binary input additive white Gaussian noise (BIAWGN) channel. We derive analysis formulas of the UEP fountain codes under belief propagation (BP) decoding by using the "semi-Gaussian" approximation technique, and compare our results with the results proved over the BEC.