A fast correlator transform (FCT) algorithm and methods and systems for implementing
same, correlate an encoded data word (X0-XM-1) with encoding
coefficients (C0-CM-1), wherein each of (X0-XM-1)
is represented by one or more bits and each said coefficient is represented by
one or more bits, wherein each coefficient has k possible states, and wherein M
is greater than 1. In accordance with the invention, X0 is multiplied
by each state (C0(0) through C0(k-1)) of the coefficient
C0, thereby generating results X0C0(0) through
X0C0(k-1). This is repeating for data bits (X1-XM-1)
and corresponding coefficients (C1-CM-1), respectively. The
results are grouped into N groups. Members of each of the N groups are added to
one another, thereby generating a first layer of correlation results. The first
layer of results is grouped and the members of each group are summed with one another
to generate a second layer of results. This process is repeated as necessary until
a final layer of results is generated. The final layer of results includes a separate
correlation output for each possible state of the complete set of coefficients
(C0-CM-1). The final layer of results is compared to identify
a most likely code encoded on said data word. In an embodiment, the summations
are pruned to exclude summations that would result in invalid combinations of the
encoding coefficients (C0-CM-1). In an embodiment, substantially
the same hardware is utilized for processing in-phase and quadrature phase components
of the data word (X0-XM-1). In an embodiment, the coefficients
(C0-CM-1) represent real numbers. In an alternative embodiment,
the coefficients (C0-CM-1) represent complex numbers. In
an embodiment, the coefficients (C0-CM-1) are represented
with a single bit. Alternatively, the coefficients (C0-CM-1)
are represented with multiple bits (e.g., magnitude). In an embodiment, the coefficients
(C0-CM-1) represent a cyclic code keying ("CCK") code set
substantially in accordance with IEEE 802.11 WLAN standard.