A decoder includes a signal amplifier, a demultiplexer and multiple ADCs. The signal amplifier receives a to-be-amplified data signal that originated from an input data signal in a PAM-2M format and that is in a PAM-(2M+1-1) format because of 1+D pulse shaping, and performs amplification and level shifting on the to-be-amplified data signal to generate a to-be-decoded data signal, where M2. The demultiplexer receives the to-be-decoded data signal, and demultiplexes the to-be-decoded data signal into multiple demultiplexed data signals to be respectively received by the ADCs. One of the ADCs is an (M+2)-bit ADC, and converts the corresponding demultiplexed data signal into a first decoded signal containing an (M+1)-bits wide data portion and a one-bit wide error portion. Each of the other one(s) of the ADCs is an (M+1)-bit ADC, and converts the corresponding demultiplexed data signal into a second decoded signal containing an (M+1)-bits wide data portion. |