Encoding and Decoding Methods and Devices, and System

Patent metadata

Field	Value
Publication number	US-2024007131-A1
Application number	US-202318469087-A
Country	US
Kind code	A1
Filing date	Sep 18, 2023
Priority date	Mar 18, 2021
Publication date	Jan 4, 2024
Grant date	—

Abstract

An encoding method includes: obtaining a generator matrix for encoding, where the generator matrix is determined based on a target parity-check matrix of a Hamming code for encoding, the target parity-check matrix is based on a target function for decoding, the target function is used to determine a not-all-zero row vector extended based on the target parity-check matrix, and the target function is one of a predetermined function set; encoding information bits using the generator matrix to obtain an encoded data stream; and sending the encoded data stream.

First claim

What is claimed is:

1 . A method comprising:
obtaining a generator matrix for encoding, wherein the generator matrix is based on a target parity-check matrix of a Hamming code for encoding, wherein the target parity-check matrix is based on a target function for decoding, and wherein the target function is one of a predetermined function set; encoding information bits using the generator matrix to obtain an encoded data stream; and sending the encoded data stream.

2 . The method of claim 1 , wherein a target function h(s 0,i ,s 1,i ,s 2,i ) determines a not-all-zero row vector based on at least some elements of first three elements s 0,i , s 1,i , and s 2,i of column vectors corresponding to the not-all-zero row vector, wherein the predetermined function set comprises one or more of the following: h(s 0,i ,s 1,i ,s 2,i )=s 1,i ∧s 2,i , h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 1,i , h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 2,i , h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 1,i ∧ s 2,i , h(s 0,i ,s 1,i ,s 2,i )= s 0,i ∧s 1,i ∧s 2,i , h(s 0,i ,s 1,i ,s 2,i )=(s 0,i ∧ s 2,i )∨ (s 1,i ∧ s 2,i ), h(s 0,i ,s 1,i ,s 2,i )=(s 0,i ∧ s 1,i )∨( s 1,i ∧s 2,i ), h(s 0,i ,s 1,i ,s 2,i )=( s 0,i ∧s 1,i )∨( s 0,i ∧s 2,i ), h(s 0,i ,s 1,i ,s 2,i )= (s 1,i ∧ s 2,i )∨(s 0,i ∧s 1,i ), or h(s 0,i ,s 1,i ,s 2,i )= (s 1,i ∧ s 2,i )∨(s 0,i ∧s 2,i ).

3 . The method of claim 2 , wherein a code length of the Hamming code is 180, wherein a length of the information bits is 170, wherein all elements in a ninth row of the target parity-check matrix are 1, wherein the target function h(s 0,i ,s 1,i ,s 2,i ) determines an element s 8,i of a column vector corresponding to the not-all-zero row vector as s 8,i =h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 1,i , wherein i is an integer greater than or equal to 0 and less than 180, wherein i=2 7 s 7,i +2 6 s 6,i +2 5 s 5,i +2 4 s 4,i +2 3 s 3,i +2 2 s 2,i +2s 1,i +s 0,i , and wherein s 8,i , s 7,i , s 6,i , s 5,i , s 4,i , s 3,i , s 2,i , s 1,i , and, s 0,i are respectively elements of column vectors corresponding to a row vector of the target parity-check matrix.

4 . The method of claim 2 , wherein a code length of the Hamming code is 128, wherein a length of the information bits is 119, wherein all elements s 8,i in an eighth row of the target parity-check matrix are 1, wherein the target function h(s 0,i ,s 1,i ,s 2,i ) determines an element s 7,i of a column vector corresponding to the not-all-zero row vector as one of s 7,i =h(s 0,i ,s 1,i ,s 2,i )=s 0,1 ∧s 1,i , s 7,i =h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 2,i , or s 7,i =h(s 0,i ,s 1,i ,s 2,i )=s 1,i ∧s 2,i , and wherein i is an integer greater than or equal to 0 and less than 128, wherein i=2 66 s 6,i +2 5 s 5,i +2 4 s 4,i +2 3 s 3,i +2 2 s 2,i +2s 1,i +s 0,i , and wherein s 7,i , s 6,i , s 5,i , s 4,i , s 3,i , s 2,i , s 1,i , and s 0,i are respectively elements of column vectors corresponding to a row vector of the target parity-check matrix.

5 . The method of claim 2 , wherein a code length of the Hamming code is 64, wherein a length of the information bits is 56, wherein all elements s 7,i in a seventh row of the target parity-check matrix are 1, wherein the target function h(s 0,i ,s 1,i ,s 2,i ) determines an element s 6,i of a column vector corresponding to the not-all-zero row vector as one of s 6,i =h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 1,i , s 6,i =h(s 0,i ,s 1,i ,s 2,i )=s 0,i ∧s 2,i , and s 6,i =h(s 0,i ,s 1,i ,s 2,i )=s 1,i ∧s 2,i , wherein i is an integer greater than or equal to 0 and less than 64, wherein i=2 5 s 5,i +2 4 s 4,i +2 3 s 3,i +2 2 s 2,i +2s 1,i +s 0,i , and wherein s 6,i , s 5,i , s 4,i , s 2,i , s 2,i , s 1,i , and s 0,i are respectively elements of column vectors corresponding to a row vector of the target parity-check matrix.

6 . The method of claim 1 , wherein the generator matrix is based on a system check matrix, and wherein the system check matrix is obtained by transforming the target parity-check matrix.

7 . The method of claim 1 , wherein the predetermined function set comprises a plurality of candidate functions for determining a not-all-zero row vector extended based on the target parity-check matrix.

8 . The method of claim 7 , further comprising:
determining a plurality of candidate parity-check matrices based on the plurality of candidate functions; selecting a non-singular matrix from the plurality of candidate parity-check matrices to obtain a first candidate parity-check matrix set; transforming the first candidate parity-check matrix set into a second candidate parity-check matrix set in a systematic form; determining a third parameter associated with each candidate parity-check matrix in the second candidate parity-check matrix set, wherein the third parameter indicates encoding complexity of the Hamming code; selecting a first group of candidate parity-check matrices from the first candidate parity-check matrix set based on the third parameter; and determining the target parity-check matrix from the first group of candidate parity-check matrices.

9 . The method of claim 8 , further comprising:
determining a fourth parameter associated with each candidate parity-check matrix in the first group of candidate parity-check matrices, wherein the fourth parameter indicates a quantity of minimum code weights of the Hamming code corresponding to each candidate parity-check matrix in the first group of candidate parity-check matrices; selecting a second group of candidate parity-check matrices from the first group of candidate parity-check matrices based on the fourth parameter; and determining the target parity-check matrix from the second group of candidate parity-check matrices.

10 . The method of claim 7 , further comprising:
determining a plurality of candidate parity-check matrices based on the plurality of candidate functions; selecting a non-singular matrix from the plurality of candidate parity-check matrices to obtain a first candidate parity-check matrix set; transforming the first candidate parity-check matrix set into a second candidate parity-check matrix set in a systematic form; determining a fourth parameter associated with each candidate parity-check matrix in the second candidate parity-check matrix set, wherein the fourth parameter indicates a quantity of minimum code weights of the Hamming code corresponding to each candidate parity-check matrix in the second candidate parity-check matrix set; selecting a first group of candidate parity-check matrices from the first candidate parity-check matrix set based on the fourth parameter; and determining the target parity-check matrix from the first group of candidate parity-check matrices.

11 . The method of claim 10 , further comprising:
determining a third parameter associated with each candidate parity-check matrix in the first group of candidate parity-check matrices, wherein the third parameter indicates encoding complexity of the Hamming code; selecting a second group of candidate parity-check matrices from the first group of candidate parity-check matrices, wherein the second group of candidate parity-check matrices has the third parameter below a predetermined threshold; and determining the target parity-check matrix from the second group of candidate parity-check matrices.

12 . The method of claim 8 , further comprising for each candidate parity-check matrix in the first candidate parity-check matrix set:
moving at least some linearly independent column vectors from right to left to a rightmost of a corresponding candidate parity-check matrix; and performing elementary row transformation, so that a right part of the corresponding candidate parity-check matrix is an ide

Assignees

• Huawei Tech Co Ltd

Inventors

• Huang Kechao
• Leung Wai Kong Raymond
• Ma Huixiao
• Yang Xiaoling

Classifications

• H03M13/1174 Primary

  Parity-check or generator matrices built from sub-matrices representing known block codes such as, e.g. Hamming codes, e.g. generalized LDPC codes · CPC title

• H03M13/1168

  wherein the sub-matrices have column and row weights greater than one, e.g. multi-diagonal sub-matrices · CPC title

• H03M13/1111

  Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms · CPC title

• H03M13/11 Primary

  using multiple parity bits · CPC title

• H03M13/19 Primary

  Single error correction without using particular properties of the cyclic codes, e.g. Hamming codes, extended or generalised Hamming codes · CPC title