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.

Machine-to-Machine (M2M) communications are expected to support extremely harsh requirements on both latency and reliability, which is characterized by the ultra-reliable, low-latency coding (uRLLC) technology in physical layer. In this paper, motivated by the recent development on the finite-blocklength information theory, we propose an ultra-reliable short blocklength analog fountain code (AFC) for M2M communications. First, we use the extrinsic information transfer (EXIT) chart to analyze the AFC compressive sensing belief propagation (CS-BP) decoding algorithm, by tracking the mutual information of AFC CS-BP decoding process, which related to the channel dispersion for the short blocklength AFC. Then, based on the EXIT chart analysis, we propose a Weight-set optimization progressive edge-growth (WO-PEG) encoding algorithm for the short blocklength AFC. Simulation results show that the proposed WO-PEG AFC scheme can effectively improve block error rate (BLER) in the short blocklength regime.