This paper proposes a burst-mode digital signal processing architecture for digital coherent time-division-multiplexed passive optical network (PON) upstream transmission, wherein two key advances are introduced to shorten the preamble length of burst signals required to complete adaptive equalization, as performed by a constant modulus algorithm: tap coefficients of a finite impulse response (FIR) filter are pre-calculated in the optical network unit (ONU) discovery process, and the feed-forward state of polarization compensation is employed before adaptive equalization. The bit error rate performance attained by the proposal is experimentally evaluated; successful burst-mode coherent detection with a high sensitivity of -44.7 dBm is demonstrated for 20 Gbit/s single polarization-quadrature phase shift keying burst signals transmitted over a 40 km single mode fiber, even with the use of a short preamble of 1.3 mu s, which meets the optical power specifications required for a 512-way split system. The proposal utilizes register request signals whose preamble is longer than those used in current PON systems to optimize the tap coefficients of the FIR filter, which may disrupt smooth ONU registration in high-splitting-ratio systems. To evaluate this impact, numerical calculations based on the Monte Carlo method are conducted, and the results show that the time required to complete the registration of 512 ONUs is just 40 s or so.