Shock-cell noise is a particular noise that appears in imperfectly expanded jets. Under these expansion conditions a series of expansions and compressions appear following a shock-cell type structure. The interaction between the vortices developed at the lip of the nozzle and the shock-cells generates what is known as shock-cell noise. This noise has the particularity to be propagated upstream with a higher intensity. This publication will focus on the shock-cell noise generated by an axisymmetric under-expanded 10 to the power of 6 Reynolds single jet. The LES computations are carried out using the elsA code developed by ONERA and extended by CERFACS with high-order compact schemes. They are validated against experimental results. The LES simulation is initialized with a RANS solution where the nozzle exit conditions are imposed. Even though no inflow forcing is applied, good agreement is obtained in terms of flow structures and broadband shock-cell noise that is propagated to the farfield by means of the Ffowcs-Williams & Hawkings analogy.