ADS117L11: Unipolar input mode and negative inputs

Tool/software:

Hello, I am using the ADS117L11 in a unipolar differential input mode as described in section 8.3.1 of the data sheet.

I have AVDD1 = 5V and AVSS = GND. A front end INA851 does my unipolar to differential conversion with the ADC VCM output setting the common mode.

So I have expecting that the ADC would convert (AINP - AINN) into a signed 16-bit value with -Vref < AINP - AINN < Vref.

Then reading section 8.5.7.1, table 8-15 seems to imply that only the 0 to Vref input range is accepted in the unipolar input range ("If the input is configured for unipolar mode, the conversion data are coded in straight-binary format to represent only positive signals over the 0 to Vref").

I do not get it. What is the point of having a differential input (shitted in common mode) if AINP - AINN MUST be positive ? What am I missing here ?

How should I configured the ADS17L11 to fully benefit from a differential signal witth common mode ? 

Thanks

Pascal