  We demonstrate balanced-detection dual-comb spectroscopy (DCS) using two
free-running mechanical sharing dual-comb fiber lasers assisted by an
all-computational digital phase correction algorithm. The mutual coherence
between the combs allows us perform mode-resolved spectroscopy of gaseous
hydrogen cyanide by digitally compensating residual timing and offset frequency
fluctuations of the dual-comb signal. Setting the repetition rate difference
between the combs to 500 Hz (1.5 kHz) yields more than 2000 resolved radio
frequency comb lines after phase correction in a 3-dB bandwidth centered at
1560 nm of wavelength. Through coadding the corrected interferograms (IGMs), we
obtain a single time-domain trace with a SNR of 6378 (13960) and 12.64 (13.77)
bits of dynamic range in 1 second of averaging. The spectral SNR of the coadded
trace reaches 529 (585), corresponding to a figure of merit of SNR of
1.3$\times$10$^6$ (1.4$\times$10$^6$). The measured absorption spectrum of
hydrogen cyanide agrees well with the HITRAN database.
