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In this work, we discuss time-shift coding and GRAND ZigZag decoding for uncoordinated multiple access channels (MACs). Time-shift coding relies on the delay difference of the received packets to prevent fully overlapped collisions. Users transmit with different time-shifts in designated time slots until the receiver successfully decodes all messages. At the receiver side, ZigZag decoding is employed to separate packets with linear complexity in noiseless scenarios. For cases with noise, a guessing random additive noise decoding (GRAND)-based algorithm is utilized to identify the most probable noise vector in conjunction with ZigZag decoding. Simulation results demonstrate that time-shift coding significantly reduces collision probabilities, thereby enhancing system throughput in noiseless scenarios. In the context of Gaussian MAC, the GRAND ZigZag decoding method outperforms successive interference cancellation (SIC)-based schemes in high signal-to-noise ratio (SNR) regimes.