I am implementing a LED driver for a LCD that has the particular arrangement of the backlight LEDs shown in the picture bellow, 4 parallel LEDs. It seems quite inconvenient not to have them in a series string as the typical voltage needed over the string is now only 3V, bellow what a typical boost constant current LED driver implementation can achieve with standard 3.3V input voltage. Is there an common appropriate way to do this that enables PWM dimming ?
Treat the whole backlight as a single LED, and go with the manufacturer specs of voltage and current. The fact that it happens to be implemented with four LEDs inside is irrelevant, and there is nothing you can do about it anyway.
If you want to adjust the brightness via PWM, then drive it in pulses. The simplest way is to arrange for the maximum current when the switch is on. The duty cycle then becomes the fraction of maximum brightness.
Keep in mind that humans perceive light intensity logarithmically, not linearly. Therefore, brightness levels of 1, 1/2, 1/4, 1/8, etc, will appear to be about equal steps.