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I'm new to signal constellation and trying to understand how M-PAM works. If there is a binary sequence that has on odd number of bits and I want to send a 4-PAM signal, there will be one bit left after encoding a symbol by two bits ($k=2$). For example: the sequence $1001001$ will be encoded as $10\rightarrow3$, $01\rightarrow-1$, $00\rightarrow-3$ and the last bit will be by itself. How do I encode the last bit? What about 16-PAM? Will I need to express the sequence in more bits?

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  • $\begingroup$ start to group bits from lsb and the problem will go. in general, the problems like this are solved with communication protocol $\endgroup$ – V.V.T Sep 11 '20 at 10:00
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This problem is solved in the upper layers of the communication system, not at the PHY.

For example, in the data link layer (DLL), the transmission unit is a frame. Frames are designed to be compatible with the PHY, so that problems like the one you describe don't occur. Also, many DLL protocols allow for fixed-size frames to be padded, or for variable-size frames, which provide some flexibility.

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