Methods and apparatus for transmission and reception with polar codes
A polar coding and coding technology, applied in the field of communication, can solve the problem of low coding complexity
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Embodiment 1
[0140] Example 1: Constructing a transformation map by permutation:
[0141] Input: natural number m, N=2 m , the permutation π of the set {0,1,...,N-1};
[0142] output: transform map
[0143] Step 1: Construct corresponding to M π The polynomial f of row 0, row 1 up to row (m-1) 0 ,f 1 ,..., f m-1 ;
[0144] Step 2: Construct the transformation map by
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[0146] Here is an example to illustrate the principle:
[0147] Let m=3, N=8, permutation π is a quasi-cyclic shift on 4.
[0148] The replacement plan is:
[0149] Construct the matrix M according to the permutation π π :
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[0151] Step 1: M π The first row of g 6 ,M π The second line of g 5 ,M π The third row of g 3 +g 7 ;
[0152] Then, f 0 =x 0 , f 1 =x 1 , f 2 =x 2 +1.
[0153] Step 2: Construct the transformation map
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[0162] The transformation matrix Tu can be derived a...
Embodiment 2
[0165] Example 2: Constructing a permutation through a transformation map
[0166] Input: natural number m, N=2 m , the transformation map
[0167] Output: permutation π.
[0168] Step 1: Construct the matrix
[0169] Step 2: For each i ∈ {0,1,...,N-1}, choose the number j i such that the ith column of M is equal to the jth i List;
[0170] Step 3: Construct the permutation by
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[0172] Here is an example to illustrate the principle:
[0173] Let m=3, N=8, and construct the transformation map by
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[0182] Step 1: According to permutation construct matrix
[0183] The first row of g 6 +g 7 , The second line of g 5 +g 6 , The third row of g 3 +g 5 :
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[0185] Step 2: Find the number j i , making the ith column of M equal to the jth i column, i.e. j 0 =5,j 1 = 2,j 2 = 3,j 3 = 4,j 4 = 1,j 5 =6,j 6 =7,j 7 = 0;
[0186] St...
Embodiment 3
[0188] Example 3: Designing Polar Codes with Transform Mapping
[0189] Input: natural number m, transformation map
[0190] Output: set I of polar code C, permutation π.
[0191] Step 1: Utilize Transform Mapping Construct permutation π;
[0192] Step 2: Calculate the degree d=min{s|π s =id, s is a natural number};
[0193] Step 3: Define a "Relationship Set" makes:
[0194] m j Appear in middle}.
[0195] in including its elements will be subject to u i A set of indexes affected;
[0196] Step 4: , allocate the collection
[0197] Step 5: For s from 2 to d, such that and construct the collection by
[0198] Step 6: when assigning
[0199] Step 7: Construct I as some set O i the union of .
[0200] A polar code can be constructed with an information set I, based on which permutations are applied 0, 1, up to d-1 times on the coded bits to soft merge up to d different replicas.
[0201] The following are instructions for using the given tr...
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