Online fountain codes (OFC) have attracted much attention for their good intermediate performance, which is important for receivers with low-complexity requirement. However, low-complexity receivers generally have limited buffer size to store coded symbols that have not been fully decoded yet, as well as limited power budget for feedback transmissions. In this paper, we propose improved transmission schemes for online fountain codes to reduce the buffer occupancy and feedback transmissions. Firstly, we analyze the relationship between buffer occupancy and overhead as well as the relationship between recovery rate and overhead for online fountain codes. Motivated by the analysis, we propose the weighted online fountain codes (WOFC) which can adapt to various buffer sizes by adjusting the weight to control the probability that a coded symbol can be fully processed immediately, and analyze its performance. Then we further propose weighted online fountain codes with low feedback (WOFC-LF), which utilize the proposed analysis to estimate the recovery rate, and reduce feedback transmissions. Simulation results verify the effectiveness of the analysis for both OFC and WOFC, and demonstrate the superior performance of WOFC-LF with limited buffer size and feedback transmissions.

For the benefit of improved intermediate performance, recently online fountain codes attract much research attention. However, there is a trade-off between the intermediate performance and the full recovery overhead for online fountain codes, which prevents them to be improved simultaneously. We analyze this trade-off, and propose to improve both of these two performance. We first propose a method called Online Fountain Codes without Build-up phase (OFCNB) where the degree-1 coded symbols are transmitted at first and the build-up phase is removed to improve the intermediate performance. Then we analyze the performance of OFCNB theoretically. Motivated by the analysis results, we propose Systematic Online Fountain Codes (SOFC) to further reduce the full recovery overhead. Theoretical analysis shows that SOFC has better intermediate performance, and it also requires lower full recovery overhead when the channel erasure rate is lower than a constant. Simulation results verify the analysis and demonstrate the superior performance of OFCNB and SOFC in comparison to other online fountain codes.

Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel to enable efficient and reliable transmission of coded symbols. In this paper, we propose using deep learning approaches to decode fixed-length and variable-length CS codes. Traditional encoding and decoding of fixed-length CS codes rely on look-up tables (LUTs), which is prone to errors that occur during transmission. We introduce fixed-length constrained sequence decoding based on multiple layer perception (MLP) networks and convolutional neural networks (CNNs), and demonstrate that we are able to achieve low bit error rates that are close to maximum a posteriori probability (MAP) decoding as well as improve the system throughput. Further, implementation of capacity-achieving fixed-length codes, where the complexity is prohibitively high with LUT decoding, becomes practical with deep learning-based decoding. We then consider CNN-aided decoding of variable-length CS codes. Different from conventional decoding where the received sequence is processed bit-by-bit, we propose using CNNs to perform one-shot batch-processing of variable-length CS codes such that an entire batch is decoded at once, which improves the system throughput. Moreover, since the CNNs can exploit global information with batch-processing instead of only making use of local information as in conventional bit-by-bit processing, the error rates can be reduced. We present simulation results that show excellent performance with both fixed-length and variable-length CS codes that are used in the frontiers of wireless communication systems.

The use of constrained sequence (CS) codes is important for the robust operation of transmission and data storage systems. While most analysis and development of CS codes have focused on fixed-length codes, recent research has demonstrated the advantages of variable-length CS codes. In our design of capacity-approaching variable-length CS codes, the construction of minimal sets is critical. In this paper, we propose an approach to construct minimal sets for a variety of constraints based on the finite-state machine (FSM) description of CSs. We develop three criteria to select the optimal state of the FSM that enables the design of a single-state encoder that results in the highest maximum possible code rate, and we apply these criteria to several constraints to illustrate the advantages that can be achieved. We then introduce FSM partitions and propose a recursive construction algorithm to establish the minimal set of the specified state. Finally, we present the construction of single-state capacity-approaching variable-length CS codes to show the improved efficiency and reduced implementation complexity that can be achieved compared with CS codes currently in use.

Ultra-reliable forward error correction (FEC) codes approaching the Shannon limit have played an important role in increasing spectral efficiency of wireless communications. In addition to the error correction performance, both low-power and low-latency decoding are demanded for the fifth generation (5G) wireless applications. In this paper, we introduce turbo product codes (TPC) consisting of multiple polar codes to enable highly parallel decoding for high- throughput and low-latency FEC. With turbo iterative decoding, the proposed polar-TPC can outperform the conventional BCH-based TPC by 0.5 dB, and can approach the performance of the corresponding long polar code within 0.2 dB with a capability of 256- times faster decoding. In addition, we apply irregular polar codes, whose polarization units are pruned, to further reduce the computational complexity by 50% and decoding latency by 80% without sacrificing performance. We analyze the impact of list size, turbo iteration count, and fading channels to demonstrate the potential of the polar-TPC for 5G wireless systems.

The online property of fountain codes enables the encoder to efficiently find the optimal encoding strategy that minimizes the encoding overhead based on the instantaneous decoding state. Therefore, the receiver is able to optimally recover data from losses that differ significantly from the initial expectation. In this paper, we propose a framework to analyze the relationship between overhead and the number of recovered source symbols for online fountain codes based on random graph theory. Motivated by the analysis, we propose improved online fountain codes (IOFCs) by introducing a designated selection of source symbols. Theoretical analysis shows that IOFC has lower overhead compared with the conventional online fountain codes. We verify the proposed analysis via simulation results and demonstrate the tradeoff between full recovery and intermediate performance in comparison to other online fountain codes.

Recent advancements in polar coding have achieved practical performance competitive with other capacity-achieving codes such as low-density parity-check codes. In this paper, we propose a new family called irregular polar codes, where polarlization units are irregularly inactivated to achieve additional degrees of freedom for code design. We first discuss the code construction for irregular polar-coded modulation by taking non-uniform bit-reliability into consideration. We then apply the proposed polar codes to wireless massive multiple-input multiple- output (MIMO) communication channels. Simulation results show that the irregular polar codes can significantly reduce encoding/decoding complexity up to 50% while also yielding a marginal improvement in error rate performance.

We propose using variable-length constrained sequence codes to mitigate inter-cell interference (ICI) in all-bit-line flash memory with multi-page programming for single-level cell, multi-level cell, and triple-level cell flash memory structures. We outline constraints that mitigate ICI in these systems based on an observation of the Gray mapping of data symbols, and we derive the capacity of each constraint. Based on a finite state machine representation of each constraint, we construct variable-length constrained sequence codes with code rates very close to capacity to mitigate ICI in these flash memories. We then exploit the inherent error control capability of the proposed constrained sequence codes to alleviate error propagation. Finally, we integrate these codes with error control codes and present simulation results that demonstrate the enhanced bit error rate performance that can be achieved.

The authors propose a low complexity list successive cancellation (LCLSC) decoding algorithm, where the advantages of the successive cancellation (SC) decoding and the list successive cancellation (LSC) decoding are both considered. In the proposed decoding, SC decoding instead of LSC decoding is implemented when all information bits from bad subchannels are received reliably. While the reliability of each information bit is estimated by its likelihood ratio (LR), the bit channel quality is measured via its Bhattacharyya parameter. To achieve this goal, the authors introduce two thresholds: LR threshold and Bhattacharyya parameter threshold. Also, the methods to determine them are both elaborated. The numerical results suggest that the complexity of LCLSC decoding is much lower than LSC decoding and can be close to that of SC decoding, while the error performance is almost equal to that of LSC decoding. Especially, when the code rate is in low region, the advantage of our decoding is more obvious.