if we need simple transmitter and receiver,

if we need low bandwidth

Delta sigma modulation achieves "noise shaping" that essentially high-pass filters the quantization noise. This reduces the noise power in the baseband so that oversampling can access more bits of useful signal resolution than would be possible in the presence of the unfiltered noise.

Delta Sigma Delta was created in 1882.

Adaptive delta modulation is used in audio communication systems to avoid the two drawback of delta modulation.

The delta modulation transmits only one bit for one sample. Thus the signaling rate and transmission channel bandwidth is quite small for delta modulation. The transmitter and receiver implementation is very much simple for delta modulation. There is no analog to digital converter involved in delta modulation. The disadvantages of delta modulation are slope overload distortion and granular noise. These are the two drawbacks of delta modulation.