Sentence examples for minimal parity from inspiring English sources

Then we let ω increase from 1 to 13, combine the binary minimal parity matrices for the minimal polynomials mI(1)(x)…mI x), in order to form H ω by Equation 52, and calculate the LCs of H ω × C r = 0(1 ≤ ω ≤ q) by Equation 48.

where λ ω (1 ≤ ω ≤ q) denotes the index of L m λ ω x in L. Step 3: Let ω increase from 1 to q, combine the binary minimal parity matrices for the minimal polynomials m λ 1 x … m λ ω x, in order to form H ω as follows: H ω = H b min ( m λ 1 x ) H b min ( m λ 2 x ) ⋮ H b min ( m λ ω x ), 1 ≤ ω ≤ q (52).

The code length and synchronization positions are estimated by checking the minimal parity-check matrices.

According to these coefficients of m λ (x), we can obtain the minimal polynomial-based binary, minimal parity-check matrix Hbmin(m λ (x)) with the following steps.

Therefore, we can simply obtain the minimal parity-check matrices of the shortened codes by deleting the first l s columns of Hbmin(m λ (x)).

According to Equation 45, we can calculate the k th syndrome for a given minimal parity-check matrix of Hbmin(m λ (x)).

G = I | Q, (24)   3) The minimal parity-check matrix can be obtained as follows: H b min m λ x = Q T | I (25)  .

H4 is obtained by combining the minimal parity-check matrices Hbmin(m4 x)), Hbmin(m1 x)), Hbmin(m2 x)) and Hbmin(m3 x)).

These minimal polynomials have the minimal parity-check matrices with low rows, so the adaptive processing can only reduce the influence for low number of unreliable decision bits.

The details of the additional steps are listed below: Step 6: List the binary minimal parity-check matrices over GF(2 m ) which have low rows: Hbmin mL 1 x)), Hbmin mL 2 x)),…, Hbmin mL η(x)), here η represents the number of binary minimal parity-check matrices with low rows.

Therefore, the number of rows of the binary minimal parity-check matrices Hbmin(m1 x)), Hbmin(m2 x)) and Hbmin(m3 x)) corresponding to m1 x), m2 x) and m3 x) are also 6, 3, and 1, respectively.