The \GX\ electromagnetic barrel calorimeter (\BC) is composed of a lead and scintillating fibre matrix. It will primarily detect photons in the 0.06-3.5~GeV energy range using 3840 silicon photo multipliers (\SiPMs) in a 2.2~T surrounding magnetic field and ca. 20$^\circ$ thermal equibrium volume. In order to monitor the {\em relative} gain of the \SiPMs, a monitoring system based on pulsed \LEDs\ is proposed herein. A blue-green \LED\, mounted on a miniature PC board, will be attached to each \SiPM\ light guide and its light will be transported via a short Kuraray ScSF-78MJ fibre to the light guide, at an angle that aims most of the light to the far/opposing \SiPM. The system can be designed so that each \LED\ can simultaneously ``flash'' both near and far \SiPMs\ within a gain factor of two. The \LED\ boards will be powered and pulsed by a controller board, located outside the \BC's volume. These \LEDs\ have a light variation of 0.5\%/$^\circ$C and the system is projected to degrade by 7\%/year in pulsed DC mode.
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