Long Code

The long code is a period 2⁴²-1 LFSR sequence that is used for spreading the reverse link. There is only one long code sequence. Different stations are distinguished not by the sequence itself but by its relative phase. The fact that the long code is added to each of the two (I and Q) short code sequences ensures that cross correlations between the signals from distinct stations are always small.

The long code LFSR tap polynomial is:

The different phases of the long code are generated by use of one of the well-known properties of LFSR sequences. Any modulo-2 sum of different phases of a LFSR sequence gives a third phase of that same sequence. A corollary of this property is the fact that all internal nodes of any LFSR generator also run through the same sequence as the generator output, but with different phases.

This addition property of LFSR sequences is exploited in the long code generation process for the reverse link spreading. A 42-bit number, the Long Code Mask, is used to select particular bits of the 42-bit long code generator register. The selected nodes are summed, modulo 2. The resultant of the sum, that is, the modulo-2 inner product of the generator state with the mask, is the generator output corresponding to that mask.

 

Figure 1. Long Code Mask logic.

 

It can be shown that each distinct mask results in a distinct phase. The Long Code Mask thus serves as a reverse link address.

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