The AMC1203 is basically the modulator section of a normal Delta-Sigma converter. The output from this device is a serial data stream which would need to be put through a digital filter. You can achieve 16-bit resolution by using a sinc3 filter with a decimation ratio of 256. The filter portion could be built using an FPGA or with an off the shelf chip like the AMC1210. There are details on the VHDL available for FPGA implementation off the 'Reference Design' link from the ADS1202 product folder:
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