Low-density parity-check (LDPC) codes have been adapted for the fifth and ensuing sixth-generation wireless systems to enhance the throughput and meet low-latency communication applications. In this paper, we investigate the performance of a cell-free (CF) massive multiple-input multiple-output (mMIMO) system wherein the subset of access points serve the users in a user-centric manner. We consider the uplink data transmission scenario wherein LDPC codes are used to encode the source signal transmitted by a user. We incorporate the M-ary quadrature amplitude modulation scheme and present the analytical framework to derive the closed-form expressions for the bounds on pairwise error probability (PEP) for the considered system. Monte Carlo simulations confirm the correctness of the derived bounds. Interestingly, results show that the simulated PEP approaches close to lower bound in a high signal-to-interference plus noise ratio (SINR) regime with an increasing modulation index. Further, in a dense network with more active users than the serving antennas at AP, simulated PEP is nearer to the upper bounds in a high SINR regime.