Encoding method and encoder for (n,n(n-1),n-1) permutation group code in communication modulation system

Patent metadata

Field	Value
Publication number	US-11038738-B2
Application number	US-201916727944-A
Country	US
Kind code	B2
Filing date	Dec 27, 2019
Priority date	Mar 6, 2019
Publication date	Jun 15, 2021
Grant date	Jun 15, 2021

Abstract

The present disclosure provides an encoding method and an encoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system, in which 2 k k-length binary information sequences are mapped to 2 k n-length permutation codeword signal points in a n-dimensional modulation constellation Γ n . The constellation Γ n with the coset characteristics is formed by selecting 2 k n-length permutation codewords from n(n−1) permutation codewords of a code set P n,x i of the (n, n(n−1), n−1) permutation group code based on coset partition. The constellation Γ n is a coset code in which 2 k 1 cosets are included and each coset includes 2 k 2 permutation codewords, where k=k 1 +k 2 , and 2 k ≤n(n−1). The present disclosure utilizes the coset characteristics to realize one-to-one correspondence mapping of the binary information sequence set to the permutation code constellation, so that the time complexity of executing the encoder is at most the linear complexity of the code length n.

First claim

What is claimed is:

1. An encoding method for a (n, n(n−1), n−1) permutation group code in a communication modulation system, wherein the encoding method maps a k-length binary information sequence to a n-length permutation codeword in a signal constellation Γ n formed by the (n, n(n−1), n−1) permutation group code based on coset partition, wherein n is a code length, the encoding method comprising the following steps of:
constructing the (n, n(n−1), n−1) permutation group code, wherein when n is a prime number, the (n, n(n−1), n−1) permutation group code contains n(n−1) permutation codewords, each of the n(n−1) permutation codewords contains n code elements, a minimum Hamming distance between any two of the n(n−1) permutation codewords is n−1, and a code set P n,x i of the (n, n(n−1), n−1) permutation group code is obtained by following expressions:

P

n
,

x
i

=

C
n

⁢

L

n
,

x
i

=

{

c
i

∘

l
j

❘

c
i

∈

C
n

,

l
j

∈

L

n
,

x
i

,

i
∈

Z
n

,

j
∈

Z

n
-
1

}

(
1
)

=

{

(

t
rn

)

n
-
1

⁢

L

n
,

x
i

}

=

{

(

t

l
⁢

⁢
1

)

n
-
1

⁢

L

n
,

x
i

}

(
2
)

wherein the code set P n,x i is obtained by an operator “∘” composition operation of a special cyclic subgroup C n with a cardinality of |C n |=n and a largest single fixed point subgroup L n,x i with a cardinality of |L n,x i |=n−1, c i represents an element in C n , l j represents an element in L n,x i , Z n represents a positive integer finite domain expressed by Z n ={1,2, . . . , n}, Z n-1 represents a positive integer finite domain expressed by Z n-1 ={1,2, . . . n−1}, and the code set P n,x i has a cardinality of |P n,x i |=n(n−1);
the largest single fixed point subgroup L n,x i is obtained by an expression (3):
L n,x i ={a ( l 1,x i −x i )+ x i |a∈Z n-1 ,x i ∈Z n ,l 1,x 1 =[1 . . . n ]}  (3)

wherein when n is a prime number, the largest single fix

Assignees

• Univ Huazhong Science Tech

Inventors

• Peng Li
• Chen si jia
• Shi Ying Long
• Gao ya yu
• Dai Bin
• Zhang Lin
• Liang Kun
• Zhou Bo
• Qin Zhen

Classifications

• H04L27/106 Primary

  M-ary FSK · CPC title

• H04L27/36 Primary

  Modulator circuits; Transmitter circuits · CPC title

• H04L27/12

  Modulator circuits; Transmitter circuits · CPC title

• H04L27/3416

  in which the information is carried by both the individual signal points and the subset to which the individual points belong, e.g. using coset coding, lattice coding, or related schemes · CPC title

• H03M7/6011

  Encoder aspects · CPC title