A novel background calibration technique for Time-Interleaved Analog-to-Digital Converters (TI-ADCs) is presented in this paper. This technique is applicable to equalized digital communication receivers. As shown by Tsai et al. [1] and Luna et al. [2], in a digital receiver it is possible to treat the TI-ADC errors as part of the communication channel and take advantage of the adaptive equalizer to compensate them. Therefore calibration becomes an integral part of the channel equalization. No special purpose analog or digital calibration blocks or algorithms are required. However, there is a large class of receivers where the equalization technique cannot be directly applied because other signal processing blocks are located between the TI-ADC and the equalizer. The technique presented here generalizes earlier works to this class of receivers. The error backpropagation algorithm, traditionally used in machine learning, is applied to the error computed at the receiver slicer and used to adapt an auxiliary equalizer adjacent to the TI-ADC, called the Compensation Equalizer (CE). Simulations using a dual polarization optical coherent receiver model demonstrate accurate and robust mismatch compensation across different application scenarios. Several Quadrature Amplitude Modulation (QAM) schemes are tested in simulations and experimentally. Measurements on an emulation platform which includes an 8 bit, 4 GS/s TI-ADC prototype chip fabricated in 130nm CMOS technology, show an almost ideal mitigation of the impact of the mismatches on the receiver performance when 64-QAM and 256-QAM schemes are tested. An absolute improvement in the TI-ADC performance of $\sim$15 dB in both SNDR and SFDR is measured.