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In this paper, we model Density Evolution (DE) using Recurrent NeuralNetworks (RNNs) with the aim of designing capacity-approaching IrregularLow-Density Parity-Check (LDPC) codes for binary erasure channels. Inparticular, we present a method for determining the coefficients of the degreedistributions, characterizing the structure of an LDPC code. We refer to ourRNN architecture as Neural Density Evolution (NDE) and determine the weights ofthe RNN that correspond to optimal designs by minimizing a loss function thatenforces the properties of asymptotically optimal design, as well as thedesired structural characteristics of the code. This renders the LDPC designprocess highly configurable, as constraints can be added to meet applications'requirements by means of modifying the loss function. In order to train theRNN, we generate data corresponding to the expected channel noise. We analyzethe complexity and optimality of NDE theoretically, and compare it withtraditional design methods that employ differential evolution. Simulationsillustrate that NDE improves upon differential evolution both in terms ofasymptotic performance and complexity. Although we focus on asymptoticsettings, we evaluate designs found by NDE for finite codeword lengths andobserve that performance remains satisfactory across a variety of channels.

Design of Capacity-Approaching Low-Density Parity-Check Codes using Recurrent Neural Networks