Analysis and Design of Analog Fountain Codes for Short Packet Communications

TL;DR

This paper introduces a density evolution framework for designing and optimizing Analog Fountain Codes tailored for short packet communications, demonstrating improved performance and reduced decoding complexity.

Contribution

It presents a novel density evolution framework for AFC design, optimizing code parameters for short packets, and proposes a low-complexity threshold-based decoder.

Findings

A new DE-based optimization method improves AFC performance.

Lower precode rates enhance realized rates at short block lengths.

Proposed threshold decoder reduces decoding complexity.

Abstract

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.