• If the encoding regular, the sea codes are HM, HM-1 ... H2H1, the code law of the sea codes is: (1) Calibration distribution: in the Hamer of the M-bit, each checkpin is distributed in position The position of 2 ^ (i-1) is 2 ^ (i-1), that is, the position of the caliber is 1, 2, 4, 8, ..., the rest is the data bit; the data bits are arranged in the original order relationship. If the effective information code is ... D5D4D3D2D1, the compiled sea code is ... D5P4D4D3D2P3D1P2P1. (2) Calibration relationship: Verification relationship The HI of the sea codes must have multiple calibration bit checks, and the relationship is the sum of the bit number of the calibration bit is the bit number of the check digit. If D1 (3) is to be checked by P2 (2) and P1 (bit number 1), D2 (5) is to be by P3 (bit number 4) and P1 two calibration bit check, D3 (6) to be verified by the P2 and P3 two check digits, D4 (7) should be verified by the three check digits of P1, P2, P3 , ... The purpose of this arrangement is to hope that the result of the verification correctly reflects the bit number of the misplaced. (3) When the code distance of the legal code is increased, the code distance of all codes is as uniform as possible to ensure balancing all the verification capabilities.
Top Reply to: One_add_one () I want to sleep :) () Reputation: 100 2002-06-04 18: 38: 52Z score: 0? Hamming distance
In an code set collection, the number of bit between the corresponding bit of code elements between any two codewords is defined as the Hamming distance between the two codewords. That is, D (x, y) = σx [i] ⊕Y [i], here i = 0, 1, .. n-1, x, y is N bit encoding, ⊕ indicates that videolis, for example, (00 ) The distance from (01) is 1, (110) and (101) of 2. In a code group collection, the minimum of the Hamming distance between any two codes is called the minimum Hamming Distance of this code group. The larger the minimum Hamming distance, the more anti-interference ability.
Below we use D to represent the minimum Hamming distance of the code group. 1. When the code group is used to detect an error, the error detects E-bit bit is detected, and D> = E 1 is provided with a code word a and b, which is D., if A has an error, then A change Codewords are formed with a spherical surface of the e-shaped radius of the E-plane radius. In order to accurately distinguish these codewords are neither a nor B, then the points on the spherical surface turned into a spherical surface should be at least one distance (if b is on the spherical surface or in the spherical, it cannot distinguish it B is not an error code of A. That is, the minimum distance D> = E 1 between A and B.
2. If the code group is used to correct the error, set the error correctable T bit, then D> = 2T 1 is provided with code words A and B, if a has t possible, and the B has also there. The A code becomes a codeword on the spherical surface of the radius of A, and the B code becomes a codeword on the spherical surface of the radius of B. In order to distinguish a codeword in the end of the T wrong, it is a misfinal code belonging to A or a B error, A, B should not intersect two spheres of the ball, that is, the distance between the ball A, B It should be greater than 2T, so D> = 2T 1.
3. If the code group is used to correct T misal, detect E, then D> = E T 1, here E> T
This case in which this error error correction method is combined is similar to the above two cases. When the codeword occurs, the system works according to the error correction method. When the codeword appears more than T mishan, when it is wrong, the system works according to the error mode; when the E is an error, B appears to correct the fault, but also to discover a fault, then Taking a ball with A as a ball, e as a radius, the ball in B is the ball, T is the radius of the radius, so the distance between A and B should be greater than or equal to E T 1, ie D> = E T 1. Hamming code
The Hanming code is a linear packet code. Linear packet coding refers to the sequence segment of the information sequence into length K, and the supervisory code of the R bit is attached later, and the supervisory code and the information code constitute a linear relationship, that is, they can contact the linear equations. . The anti-interference code thus constructed is referred to as a linear packet code.
The code length is N, the information bit length is k, the supervisory bit length is R = N-K. If you need to correct an error, every bit may be wrong because the length of N is required, there is a total of n types, and there is no mistake, so we must use the length of the supervisor to indicate N 1. Case. The supervisory code for the length is a total of 2 ^ R. Therefore, 2 ^ r> = n 1, ie r> = log (n 1)
We use an example to illustrate the Chinese codes. Suppose k = 4, you need to correct one error, then 2 ^ R> = N 1 = k r 1 = 4 R 1 solution R> = 3. We take R = 3, then the code length is 3 4 = 7. Use A6, A5, ... A0 to represent these seven yards. Use S1, S2, S3 to represent the correction subsequent in the three ties. We make the following provisions (this rule is arbitrary):
S1 S2 S3 misthlights 0 0 1 A0 0 1 0 A1 1 0 0 A2 0 1 1 A3 1 0 1 A4 1 1 0 A5 1 1 1 A6 0 0 0 0 0 无 错 按 按 按 按 按 表 表, only one The miscode position is 1 to 1 when A2, A4, A5 or A6, otherwise S1 is 0. This means A2, A4, A5, A6 four symbols constitute an even check relationship: S1 = a6⊕a5⊕a4⊕a2 (1) Tonghe, you can get: S2 = a6⊕a5⊕a3⊕a1 ( 2) When the signal (3) is transmitted, the value of the information bits A6, A5, A4, and A3 depend on the input signal, and is random. Supervise the A2, A1, and A0 should be determined according to the value of the information bits, that is, the value of the supervisory position should make S1, S2, S3 in the above formula (1) (2) (3), which means There is no error in the initial case. which is
A6⊕a5⊕a4 ⊕A2 = 0 A6⊕A5⊕A3 ⊕A1 = 0 A6⊕A4 ⊕A3⊕a0 = 0 is moved by the above formula, obtained:
A2 = A6⊕A5⊕A4 A1 = A6⊕A5⊕A3 A0 = A6⊕A4 ⊕A3 Known information bits, the values of the three supervisors of A2, A1, and A0 can be calculated according to the above formula.
After the receiving end is subjected to each code group, the S1, S2, S3 is calculated according to (1) to (3), and then check the table to know the error code.
For example, if the received codeword is 0000011, it is calculated according to (1) to (3): S1 = 0, S2 = 1, S3 = 1 The table can have an error code in the A3 bit. The minimum Hamming distance of this coding method is D = 3, so this encoding can correct a misal code or detect two misfinalizes.
