The HT-SIG field of 802.11n PLCP preamble contains a 8-bit CRC for the receiver to validate the sanity of the header. Here is how to calculate it.

HT-SIG CRC calculation

HT-SIG contains 48 bits and spans in 2 OFDM symbols (BPSK modulated, 1/2 rate). This diagram from the 802.11-2012 standard describes the logic to calculate the CRC for the first 34 bits of the field.

Here is a Python version of the implementation.

def calc_crc(bits):
    c = [1] * 8

    for b in bits:
        next_c = [0] * 8
        next_c[0] = b ^ c[7]
        next_c[1] = b ^ c[7] ^ c[0]
        next_c[2] = b ^ c[7] ^ c[1]
        next_c[3] = c[2]
        next_c[4] = c[3]
        next_c[5] = c[4]
        next_c[6] = c[5]
        next_c[7] = c[6]
        c = next_c

    return [1-b for b in c[::-1]]

c is the 8-bit shift register. For each incoming bits, we calculate the next value of each bit in the register and store them in next_c.

Finally, we perform two operations: reverse and two's complement. Note that c[7] is the first output bit.

The standard also provides a test case.

>>> s = '1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0'
>>> bits = [int(b) for b in s.split()]
>>> calc_crc(bits)
[1, 0, 1, 0, 1, 0, 0, 0]

Translating the logic into HDLs such as Verilog is quite straightforward.

module ht_sig_crc (
    input clock,
    input enable,
    input reset,

    input bit,
    input input_strobe,

    output [7:0] crc
);

reg [7:0] C;
genvar i;

generate
for (i = 0; i < 8; i=i+1) begin: reverse
    assign crc[i] = ~C[7-i];
end
endgenerate


always @(posedge clock) begin
    if (reset) begin
        C <= 8'hff;
    end else if (enable) begin
        if (input_strobe) begin
            C[0] <= bit ^ C[7];
            C[1] <= bit ^ C[7] ^ C[0];
            C[2] <= bit ^ C[7] ^ C[1];
            C[7:3] <= C[6:2];
        end
    end
end

endmodule

Here we use the generate block to do the bit-reverse and negation.