Within the framework of the French 600MWe Advanced Sodium Technological Reactor for Industrial Demonstration project (ASTRID), a Gas Power Conversion System (PCS) based on a Brayton cycle is studied. This innovative option has never been implemented in any Sodium Fast Reactor and is mainly justified by safety and acceptance considerations in inherently eliminating the sodium-water and sodium-water-air reaction risk existing in Steam Generators with a Rankine cycle.The present work describes the progress in the design of the ASTRID innovative compact Sodium Gas Heat Exchanger (SGHE) and highlights the industrial challenges this technology raises.This paper presents the details of the design of the SGHE which allows a high thermal compactness. The main studies supporting the development are described whether on the external pressure vessel or on the compact internal heat exchanger modules.At last, the qualification process is presented through a number of qualification phases at different scales.