Analog Fountain Codes Research Articles

Improved PEG-Based Construction of Analog Fountain Codes.

This paper proposes an improved progressive edge-growth (PEG) construction of analog fountain codes (AFCs). During edge selection, it simultaneously allocates weight coefficients in descending order. Analysis shows that our proposed construction reduces the probability of large weight coefficients involved in harmful short cycles. Simulation results indicate that it has good block error rate (BLER) in short block length regime.

Partitioned Analog Fountain Codes for Short Packet Communications

Partitioned Analog Fountain Codes for Short Packet Communications

Online Analog Fountain Codes

Analog fountain codes (AFC) are a class of near-capacity rateless codes which have a great potential for meeting the requirements of ultra-reliable low latency communication. In this letter, an online feedback scheme is introduced to enhance error performance and achievable rate of AFC. The retransmission messages are chosen according to Euclidean distance between AFC codewords. Our simulation results show that the proposed online AFC can improve achievable rate up to 0.49 bits/symbols at 25 dB, and reduce block error rate by more than one order of magnitude.

Analysis and Design of Short Analog Fountain Codes for the Multiple Access Channel

In this letter, we design and analyse analog fountain codes (AFC) for the multiple access channel (MAC). First, we present several encoding schemes, including the superposition coding and joint encoding, and decoding schemes, including successive interference cancellation and joint decoding, for multiple access AFC (MA-AFC). We propose different combinations of encoding and decoding schemes for MA-AFC and evaluate their performance in terms of block error rate (BLER) to determine which combination has the best performance. We propose a density evolution (DE) based framework to track the evolution of messages exchanged between check nodes and variable nodes in the iterative joint belief propagation (BP) decoder of MA-AFC. With the proposed DE framework, we formulate optimisation problems to find the optimal AFC code parameters, specifically the weight set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Simulation results show that the AFC code with the optimised parameters outperforms existing AFC code designs in the multiple access scenario.

Rate Compatible Gaussian Modulation

This letter proposes a rate compatible Gaussian modulation (RCGM) for wireless channels. RCGM constructs a high-density non-uniformly spaced Gaussian constellation, and optimizes the mapping schemes by maximizing the Harmonic mean. The information bits are randomly sampled by a sparse matrix whose weights are all powers of 2, then the sampled bits are modulated to the high-density constellation following the mapping scheme. The number of the modulated symbols can be adjusted at a fine granularity according to the channel condition so as to achieve seamless rate adaptation. Both numerical and simulation results show that RCGM outperforms other rate adaptive modulations, such as rate compatible modulation and analog fountain code, in terms of error probability and throughput. RCGM can provide a capacity approaching modulation scheme in a wide range of signal-to-noise ratio even without channel coding.

Short Analog Fountain Code With Quasi-Gray Constellation Mapping Modulation Towards uRLLC

In this paper, a capacity-approaching rateless coded modulation towards ultra-reliable low latency communications (uRLLC) is proposed, including the joint design of short block-length analog fountain code (AFC) and quasi-gray constellation mapping (QGCM) modulation at the transmitter, and a limited feedback mechanism for the receiver. First, based on the nonlinear constellation and quasi-gray mapping, we design a novel rateless coded modulation scheme called AFC-QGCM, and prove it can approach to the Shannon capacity. Further, the theoretical evaluation framework of information density between the achievable rate and signal-to-noise (SNR) of the AFC-QGCM schemes is derived under short block-length. Based on the analysis, we propose a rateless transmission scheme with a limited feedback link over the fading channel without precise channel state information (CSI) at the transmitter, which could utilize the theoretical analysis to determine the optimal coding and modulation parameters during the transmission. Both analysis and simulation results shown that the proposed scheme could approaching to the Polyanskiy-Poor-Verdu (PPV) meta converse benchmark in a wide range SNRs.

Analysis and Design of Analog Fountain Codes for Short Packet Communications

In this paper, we focus on the design and analysis of the Analog Fountain Code (AFC) for short packet communications. We first propose a density evolution (DE) based framework, which tracks the evolution of the probability density function of the messages exchanged between variable and check nodes of AFC in the belief propagation decoder. Using the proposed DE framework, we formulate an optimisation problem to find the optimal AFC code parameters, including the weight-set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Our results show the superiority of our AFC code design compared to existing designs of AFC in the literature and thus the validity of the proposed DE framework in the asymptotically long block length regime. We then focus on selecting the precoder to improve the performance of AFC at short block lengths. Simulation results show that lower precode rates obtain better realised rates over a wide SNR range for short information block lengths. We also discuss the complexity of the AFC decoder and propose a threshold-based decoder to reduce the complexity.

Finite Block-Length Analog Fountain Codes for Ultra-Reliable Low Latency Communications

In this paper, a theoretical framework for the design and evaluation of finite block-length analog fountain codes (AFC) towards ultra-reliable low latency communications (URLLC) is proposed. First, based on the achievable rate analysis and extrinsic information transfer (EXIT) analysis for AFC, we propose a weight adaptive (WA) AFC transmission scheme by introducing a limited feedback link, which can realize the lowest complexity AFC over a wide range SNRs. Further, by combining the conventional EXIT analysis and the dispersion perspective of mutual information, we propose a modified weight selection scheme for short block length WA-AFC (SWA-AFC) scheme. Simulation results show that our SWA-AFC scheme can achieve a superior performance than the existing AFC schemes, and approaching to the Polyansky-Poor-Verdu (PPV) bound.

Novel Design for Short Analog Fountain Codes

Adaptive coding and modulation in current cellular networks relies on a channel quality indicator fed back from the receiver to the transmitter. The process of acquiring channel state information at the transmitter (CSIT) is estimated to take 5–8 ms. For short-packet transmissions in machine-type communications (MTC), the data transmission of small payloads is estimated to take a fraction of a millisecond, i.e., a fraction of the end to end latency. This is especially problematic for ultra-reliable low-latency communications (URLLC) that require an end-to-end latency of 1 ms only. To this end, self-adaptive coding and modulation, aka rateless coding, is much needed to cater for these stringent requirements. In this letter, a new design is proposed for the recently proposed class of rateless codes, dubbed analog fountain codes (AFC), tailored for short-packet transmissions. The numerical results show no error floors down to block error rates of 10−7, thus meeting the ultra-high reliability requirement of URLLC.

A Novel Weight Coefficient PEG Algorithm for Ultra-Reliable Short Length Analog Fountain Codes

The stringent requirements of ultra-reliable and low latency communication (URLLC) services is the most challenging feature of fifth generation systems. The design and optimization of efficient short length codes is essential for URLLC. This letter investigates a novel weight coefficient progressive edge-growth (WCPEG) algorithm to construct ultra-reliable analog fountain codes (AFCs) in the short length regime. Our WCPEG AFC can approach the normal approximation benchmark by eliminating the small girth cycles in the encoding Tanner graph. We first analyze the properties of short length AFC, and then present the comprehensive description and theoretical identification of the WCPEG AFC algorithm. Simulation results demonstrate the superior performance of WCPEG AFC in the short length regime.

Designing Analog Fountain Timing Channels: Undetectability, Robustness, and Model-Adaptation

In existing model-based timing channels, the requirement for the target model to be shared between the sender and the receiver limits the sender’s ability to adapt to changes in the inter-packet delay (IPD) distribution of the application traffic. In this paper, using analog fountain codes (AFCs) with a general model-fitting coding framework, we design timing channel schemes that allow the sender to change the target model without synchronizing with the receiver. We first propose analog fountain timing channels based on symbol transition when the application packet streams have IPD distribution that is shape similar to the distribution of AFC code symbol values. For more general packet streams, we then propose analog fountain timing channels based on symbol split in which the linearly mapped symbols are split using a symbol probability split matrix to mimic the IPD distribution of the application traffic. We use real VoIP and SSH traffic to compare the proposed schemes with model-based timing channels using LT codes and AFC. Experimental results show that both the proposed schemes are model-secure. The robustness of the two schemes is higher than the model-based timing channels using LT codes whereas not as good as those using AFC when the sender and receiver sides are synchronized with respect to the target model. Moreover, when the sender and the receiver are not synchronized with respect to the model, the robustness of the proposed schemes is significantly higher than model-based timing channels.

Probabilistic Rateless Multiple Access for Machine-to-Machine Communication

Future machine to machine (M2M) communications need to support a massive number of devices communicating with each other with little or no human intervention. Random access techniques were originally proposed to enable M2M multiple access, but suffer from severe congestion and access delay in an M2M system with a large number of devices. In this paper, we propose a novel multiple access scheme for M2M communications based on the capacity-approaching analog fountain code to efficiently minimize the access delay and satisfy the delay requirement for each device. This is achieved by allowing M2M devices to transmit at the same time on the same channel in an optimal probabilistic manner based on their individual delay requirements. Simulation results show that the proposed scheme achieves a near optimal rate performance and at the same time guarantees the delay requirements of the devices. We further propose a simple random access strategy and characterized the required overhead. Simulation results show the proposed approach significantly outperforms the existing random access schemes currently used in long term evolution advanced (LTE-A) standard in terms of the access delay.

Binary Compressive Sensing Via Analog Fountain Coding

In this paper, a compressive sensing (CS) approach is proposed for sparse binary signals' compression and reconstruction based on analog fountain codes (AFCs). In the proposed scheme, referred to as the analog fountain compressive sensing (AFCS), each measurement is generated from a linear combination of L randomly selected binary signal elements with real weight coefficients. The weight coefficients are chosen from a finite weight set and L, called measurement degree, is obtained based on a predefined degree distribution function. We propose a simple verification based reconstruction algorithm for the AFCS in the noiseless case. The proposed verification based decoder is analyzed through SUM-OR tree analytical approach and an optimization problem is formulated to find the optimum measurement degree to minimize the number of measurements required for the reconstruction of binary sparse signals. We show that in the AFCS, the number of required measurements is of O(-n log(1-k/n)), where n is the signal length and k is the signal sparsity level. We then consider the signal reconstruction of AFCS in the presence of additive white Gaussian noise (AWGN) and the standard message passing decoder is then used for the signal recovery. Simulation results show that the AFCS can perfectly recover all non-zero elements of the sparse binary signal with a significantly reduced number of measurements, compared to the conventional binary CS and L1-minimization approaches in a wide range of signal to noise ratios (SNRs). Finally, we show a practical application of the AFCS for the sparse event detection in wireless sensor networks (WSNs), where the sensors' readings can be treated as measurements from the CS point of view.

Near-Capacity Adaptive Analog Fountain Codes for Wireless Channels

In this paper, we propose a capacity-approaching analog fountain code (AFC) for wireless channels. In AFC, the number of generated coded symbols is potentially limitless. In contrast to the conventional binary rateless codes, each coded symbol in AFC is a real-valued symbol, generated as a weighted sum of d randomly selected information bits, where d and the weight coefficients are randomly selected from predefined probability mass functions. The coded symbols are then directly transmitted through wireless channels. We analyze the error probability of AFC and design the weight set to minimize the error probability. Simulation results show that AFC achieves the capacity of the Gaussian channel in a wide range of signal to noise ratio (SNR).