Walsh code

The Walsh code is used to uniquely define individual communication channels. Walsh codes are mathematically orthogonal codes. As such, if two Walsh codes are correlated, the result is intelligible only if these two codes are the same. As a result, a Walsh-encoded signal appears as random noise to a CDMA capable mobile terminal, unless that terminal uses the same code as the one used to encode the incoming signal.

The Walsh code is calculated by the Walsh function.

Example

Denote W(k, n) as Walsh code k in n-length Walsh matrix. It means the k-th row of H(m) Hadamard matrix, where n=m. Here k could be 0,1,...,n-1

W(0,1) = 1

W(0,2) = 1, 1

W(1,2) = 1,-1

W(0,4) = 1, 1, 1, 1

W(1,4) = 1,-1, 1,-1

W(2,4) = 1, 1,-1,-1

W(3,4) = 1,-1,-1, 1

W(0,8) = 1, 1, 1, 1, 1, 1, 1, 1

W(1,8) = 1,-1, 1,-1, 1,-1, 1,-1

W(2,8) = 1, 1,-1,-1, 1, 1,-1,-1

W(3,8) = 1,-1,-1, 1, 1,-1,-1, 1

W(4,8) = 1, 1, 1, 1,-1,-1,-1,-1

W(5,8) = 1,-1, 1,-1,-1, 1,-1, 1

W(6,8) = 1, 1,-1,-1,-1,-1, 1, 1

W(7,8) = 1,-1,-1, 1,-1, 1, 1,-1

It can also be constructed by means of a Walsh tree.

See also

• Joseph Leonard Walsh
• Maximum length sequence

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