CN110113056B - Word-oriented coding and decoding method with forward erasure correcting function - Google Patents
Word-oriented coding and decoding method with forward erasure correcting function Download PDFInfo
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- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1148—Structural properties of the code parity-check or generator matrix
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Abstract
The invention belongs to the technical field of communication, in particular to a word-oriented coding and decoding method with a forward erasure correcting function, which generates a system code coding matrix according to coding characteristics; generating a decoding table; finishing data coding according to a system code coding matrix, and expanding each group of original information groups containing n words into coding information groups containing 2n words; and (3) completing decoding according to the decoding table, and restoring the coding information group formed by the 2n words into an original information group, namely, in the 2n words in the coding information group, any word not exceeding n words is lost, and correctly recovering the original information group. The invention has flexible coding and good erasure correcting effect.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a word-oriented coding and decoding method with a forward erasure correcting function.
Background
When data is transmitted on a one-way communication channel depending on a communication protocol, such as satellite communication, deep wells, deep sea, and the like, random loss of information words often occurs due to a channel quality problem. According to the corresponding communication protocol: (1) one can ensure that the received data must be correct; (2) one can know the position of the specific word loss, but cannot determine the specific content of the word loss;
at this time, how to perform erasure coding on the original data so that the coded data has a certain anti-missing capability is one of important ways to improve the reliability of unidirectional communication.
The current common approach is to use error correction coding or RS codes to solve the word loss problem.
Error correction coding can be used to correct data transmission errors, but it should be noted that the "transmission errors" that can be solved by error correction coding can be data loss or data content errors, and theoretically, conventional error correction coding is not a technology tailored to solve the word loss problem in the present application. Therefore, the error correction effect is not ideal for the specific error type of "data loss".
RS codes are a kind of effective erasure codes, and are also the most widely used erasure codes at present. But the defects are that 1. the coding and decoding method is complex, needs deeper mathematical knowledge background, and the principle is not easy to be mastered by engineering personnel; in the encoding process of the RS code, once the bit length of a symbol is determined, the code length can only take a fixed value, and cannot be changed as required, resulting in limited encoding flexibility.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a word-oriented coding and decoding method with a forward erasure correction function, which has flexible coding and good erasure correction effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a character-oriented coding and decoding method with a forward erasure correcting function, which comprises the following steps:
generating a system code coding matrix according to the coding characteristics;
generating a decoding table;
finishing data coding according to a system code coding matrix, and expanding each group of original information groups containing n words into coding information groups containing 2n words;
and (3) completing decoding according to the decoding table, and restoring the coding information group formed by the 2n words into an original information group, namely, in the 2n words in the coding information group, any word not exceeding n words is lost, and correctly recovering the original information group.
Preferably, the generating a systematic code encoding matrix according to the encoding characteristics includes:
inputting the number of words contained in each group of coded information as n, and inputting each word length as m-bit;
finding the irreducible polynomial f (x) of degree m with coefficients taken from the binary finite field GF (2), and then according to algebraic theory, the remaining class ring of the modulus f (x) is denoted as GF (2) [ x ]]/<f(x)>Forming a finite field GF (2)m)；
In the finite field GF (2)m) Up looking for 2n mutually different elements a1,a2,…,an,b1,b2,…,bn；
In the finite field GF (2)m) Up looking for any non-0 element c0When 1 is less than or equal to i and j is less than or equal to n, the definition is
Define matrix B ═ (B)i,j)n×2nHere, the
The matrix B acts as a coding matrix.
Preferably, the generating a decoding table comprises:
traverse messages from 0 to 2mn-1, for each traversed value (m)1,m2,…,mn) Calculating a 2 n-dimensional vector
Will be (m) th of table T1,…,mn) With the index value corresponding to the entry position alpha, i.e.
T[(m1,m2,…,mn)]＝α；
And after the traversal of the message value is completed, T is used as a decoding table.
Preferably, the completing data encoding according to the system code encoding matrix includes:
the inputs are: (1) encoding a matrix B; (2) original information group Message (m) composed of n words to be encoded1,m2,…,mn)；
The output is: after encoding, an Encoded information group Encoded _ M ═ of (e) consisting of 2n words1,e2,…,e2n)；
The calculation formula for the transformation from the original set of information to the encoded set of information is: encoded _ M is Message × B; i is more than or equal to 1 and less than or equal to 2n, all have
Encoded _ M is transmitted as a coded data group into the channel.
Preferably, the finishing the decoding according to the decoding table comprises:
the inputs are: received data set Encoded _ M '(e)'1,e′2,…,e′2n)；
The output is: original data Message;
for i is more than or equal to 1 and less than or equal to 2n, checking e 'in sequence'iIf it is lost, let θiIf not, let θiThe offset vector θ is generated by 1 ═ θ1,θ2,…,θ2n)；
And for i not less than 1 and not more than 2n, judging: if thetaiWhen d is equal to 0, order di0; if thetaiWhen the value is 1, order di＝e′iThereby generating a query vector D ═ (D)1,d2,…,d2n)；
And (3) judging: if theta1＝θ2＝…＝θn1, then directly returns Message ═ e'1,e′2,…,e′n) And the process is ended; otherwise, executing the following steps;
in the decoding table T, traversing the entries, and extracting the currently traversed entries
T[k]＝(α1,α2,…,α2n)；
Construct vector TEMP ═ TEMP (TEMP)1,temp2,…,temp2n) Here, the
Judgment of D&Whether TEMP is an all 0 vector, operation here "&"denotes a bitwise AND operation; if yes, take out T [ k ]]＝(α1,α2,…,α2n) And outputs a decoded value Message ═ (α)1,α2,…,αn) And ending decoding; otherwise, the next time of extracting the currently traversed entry is carried out.
Compared with the prior art, the invention has the following advantages:
the invention provides a word-oriented coding and decoding method with a forward erasure correcting function, which is essentially a special error correction code specially used for solving the data loss, and can correctly restore the original message on the premise of losing 50 percent of blocks of single group of data at most. Meanwhile, the coding matrix of the invention is fast to generate, the coding and decoding algorithm is easy to realize, the code length is limited by the limited domain scale of the code element, and the invention has good environmental adaptability.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a word-oriented coding and decoding method with forward erasure correction function according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order that those skilled in the art will better understand the disclosure, the invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Example one
Referring to fig. 1, fig. 1 is a flowchart illustrating a word-oriented encoding and decoding method with forward erasure correction function according to an embodiment of the present invention, where the method includes:
step 1, generating a system code coding matrix according to coding characteristics;
step 2, generating a decoding table;
step 3, completing data coding according to the system code coding matrix, assuming that each group of information to be coded consists of n words, each word is m-bit in length, and expanding each group of original information groups containing the n words into coding information groups of 2n words;
and 4, finishing decoding according to the decoding table, and restoring the coding information group formed by the 2n words into an original information group, namely, in the 2n words in the coding information group, any word not exceeding n words is lost, and the original information group can be correctly recovered.
Preferably, the generating a systematic code encoding matrix according to the encoding characteristics includes:
step S101, inputting the number of words contained in each group of coded information as n, and inputting each word length as m-bit;
step S102, find the irreducible polynomial f (x) of m times with coefficient from binary finite field GF (2), then according to algebraic theory, model f (x) residual ring, and record as GF (2) [ x ]]/<f(x)>Forming a finite field GF (2)m)；
Step S103, in the finite field GF (2)m) Up looking for 2n mutually different elements a1,a2,…,an,b1,b2,…,bn；
Step S104, in the finite field GF (2)m) Up looking for any non-0 element c0When 1 is less than or equal to i and j is less than or equal to n, the definition is
In step S105, the matrix B ═ (B) is definedi,j)n×2nHere, the
The matrix B acts as a coding matrix.
Preferably, the generating a decoding table includes: with the encoding matrix B of step 1 as input, a decoding table T is generated by sequentially executing the following steps.
Step S201, traverse the message from 0 to 2mn-1, for each traversal toValue of (m)1,m2,…,mn) Calculating a 2 n-dimensional vector
Step S202, the (m) th table T1,…,mn) With the index value corresponding to the entry position alpha, i.e.
T[(m1,m2,…,mn)]＝α；
Step S203, after the traversal of the message value is completed, T is used as a decoding table.
Preferably, the completing data encoding according to the systematic code encoding matrix includes:
the inputs are: (1) the coding matrix B generated in the step 1; (2) original information group Message (m) composed of n words to be encoded1,m2,…,mn)；
The output is: after encoding, an Encoded information group Encoded _ M ═ of (e) consisting of 2n words1,e2,…,e2n)；
Step S301, calculating Encoded _ M as Message × B; i is more than or equal to 1 and less than or equal to 2n, all have
In step S302, Encoded _ M is transmitted as a coded data group in a channel.
Preferably, the finishing the decoding according to the decoding table comprises:
the inputs are: received data set Encoded _ M '(e)'1,e′2,…,e′2n)；
The output is: original data Message;
step S401, for i being more than or equal to 1 and less than or equal to 2n, sequentially checking e'iIf it is lost, let θiIf not, let θiThe offset vector θ is generated by 1 ═ θ1,θ2,…,θ2n)；
Step S402, for 1 ≤ i ≤2n, judging: if thetaiWhen d is equal to 0, order di0; if thetaiWhen the value is 1, order di＝e′iThereby generating a query vector D ═ (D)1,d2,…,d2n)；
Step S403, determining: if theta1＝θ2＝…＝θn1, then directly returns Message ═ e'1,e′2,…,e′n) And the process is ended; otherwise, executing the following steps;
step S404, traversing the entries in the decoding table T, and extracting the currently traversed entries
T[k]＝(α1,α2,…,α2n)；
In step S405, the construction vector TEMP ═ is (TEMP)1,temp2,…,temp2n) Here, the
Step S406, judging D&Whether TEMP is an all 0 vector, operation here "&"denotes a bitwise AND operation; if yes, take out T [ k ]]＝(α1,α2,…,α2n) And outputs a decoded value Message ═ (α)1,α2,…,αn) And ending decoding; otherwise, the process returns to step S404 for the next extraction.
The invention provides a word-oriented coding and decoding method with a forward erasure correcting function, which is a special error correction coding specially used for solving data loss, can correctly restore original information on the premise that at most 50% of character blocks are lost for single group of data, and has good erasure correcting effect; the invention also provides an efficient design scheme of the system code coding matrix, the size of the coding matrix can be flexibly selected according to different coding parameters, the coding matrix is generated quickly, a coding and decoding algorithm is easy to realize, the mathematical basic requirement on users and programmers is not high, the code length is slightly restricted by the limited domain scale of the code element, and the system code coding matrix has good environmental adaptability.
The following is a specific example to facilitate a better understanding of the invention.
Example two
Step 1, generating a system code coding matrix according to coding characteristics;
step S101, inputting the number of words contained in each group of coded information to be 4, and inputting each word length to be 4-bit;
step S102, constructing a finite field GF (2)4)＝GF(2)[x]/<x4+x+1>；
Step S103, in the finite field GF (2)4) Up to find 8 mutually different elements
a1＝1,a2＝2,a3＝3,a4＝4,b1＝5,b2＝6,b3＝7,b4＝8；
Step S104, in the finite field GF (2)4) Up-looking for non-0 element c0When 1 ≦ i, j ≦ 4, defined as 2
In step S105, the matrix B ═ (B) is definedi,j)4×8Here, the
Namely, it is
The matrix B acts as a coding matrix.
Step 2, taking the coding matrix B of the step 1 as input, and sequentially executing the following steps to generate a decoding table T;
step S201, traverse the message from 0 to 216-1, for each traversed value (m)1,m2,m3,m4) Calculating an 8-dimensional vector
Step S202, the (m) th table T1,m2,m3,m4) With the index value corresponding to the entry position alpha, i.e.
T[(m1,m2,m3,m4)]＝α；
Step S203, after the traversal of the message value is completed, T is used as a decoding table.
In the above generated T value table, for example, we want to calculate T [1]]Then input 1 may be expressed as (m)1,m2,m3,m4) When it is (0,0,0,1), it is calculated according to step S201
α＝[(1×b4,1),(1×b4,2),…,(1×b4,8)]＝(0,0,0,1,2,1,15,7)，
From step S202, it can be seen that the value of T [1] is (0,0,0,1,2,1,15, 7).
Step 3, finishing the data coding process;
the inputs are: (1) the coding matrix B generated in the step 1; (2) original information set Message (m) composed of 4 words to be encoded1,m2,m3,m4)；
The output is: coded information group consisting of 8 words after coding
Encoded_M＝(e1,e2,e3,e4,e5,e6,e7,e8)；
Step S301, calculating Encoded _ M as Message × B; i is more than or equal to 1 and less than or equal to 8, all of which have
In step S302, Encoded _ M is transmitted as a coded data group in a channel.
Assuming that in step 3, the data to be Encoded is Message (0,0,0,1), after step 3 is executed, the Encoded data is Encoded _ M Message × B (0,0,0,1,2,1,15, 7).
Step 4, finishing the decoding process based on the decoding table T given in the step 2;
the inputs are: received data set Encoded _ M '(e)'1,e′2,e′3,e′4,e′5,e′6,e′7,e′8)；
The output is: original data Message;
we assume that due to channel reasons, the Encoded data received at the receiving side is Encoded _ M' (?, 0,1,?, 1,15,?), where? indicates that there is a loss of signal at this location.
Step S401, for i being more than or equal to 1 and less than or equal to 8, sequentially checking e'iIf it is lost, let θiIf not, let θiThe offset vector θ is generated by 1 ═ θ1,θ2,…,θ8)；
The receiver constructs a misalignment vector θ as (0,0,1,1,0,1,1,0) according to step S401;
step S402, for i not less than 1 and not more than 8, judging: if thetaiWhen d is equal to 0, order di0; if thetaiWhen the value is 1, order di＝e′iThereby generating a query vector D ═ (D)1,d2,…,d8)；
The receiver generates a query vector D as (0,0,0,1,0,1,15,0) according to step S402;
step S403, determining: if theta1＝θ2＝…＝θ41, then directly returns Message ═ e'1,e′2,…,e′8) And the process is ended; otherwise, executing the following steps;
the receiver executes step S403, determines that the termination condition is not met, and executes step S404;
step S404, traversing the entries in the decoding table T, and extracting the currently traversed entries
T[k]＝(α1,α2,…,α8)；
The receiver executes step S404 until extraction T [1] become (0,0,0,1,2,1,15, 7);
in step S405, the construction vector TEMP ═ is (TEMP)1,temp2,…,temp8) Here, the
The receiver executes step S405, and a TEMP ═ is constructed (0,0,0,1,0,1,15, 0);
step S406, judging whether the D & TEMP is a full 0 vector, wherein the operation "&" represents bitwise AND operation;
if so, then from T [ k ]]Taking out the component (. alpha.)1,α2,α3,α4) And outputting as a decoding value, and ending the decoding;
otherwise, the process returns to step S404 for the next extraction.
The receiver performs step S406 to calculate and determine that D & TEMP is 0, so that component (0,0,0,1) is taken out from T [1] and output as a decoded value, and the decoding of the step data is completed.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (3)
1. A word-oriented encoding and decoding method with forward erasure correction, comprising the steps of:
generating a system code coding matrix according to the coding characteristics, specifically:
inputting the number of words contained in each group of coded information as n, and inputting each word length as m-bit;
finding the irreducible polynomial f (x) of degree m with coefficients taken from the binary finite field GF (2), and then according to algebraic theory, the remaining class ring of the modulus f (x) is denoted as GF (2) [ x ]]/<f(x)>Forming a finite field GF (2)m)；
In the finite field GF (2)m) Up looking for 2n mutually different elements a1,a2,…,an,b1,b2,…,bn；
In the finite field GF (2)m) Up looking for any non-0 element c0When 1 is less than or equal to i and j is less than or equal to n, the definition is
Define matrix B ═ (B)i,j)n×2nHere, the
The matrix B is used as a coding matrix;
generating a decoding table, specifically:
traverse messages from 0 to 2mn-1, for each traversed value (m)1,m2,…,mn) Calculating a 2 n-dimensional vector
Will be (m) th of table T1,…,mn) With the index value corresponding to the entry position alpha, i.e.
T[(m1,m2,…,mn)]＝α；
After the traversal of the message value is completed, T is used as a decoding table;
finishing data coding according to a system code coding matrix, and expanding each group of original information groups containing n words into coding information groups containing 2n words;
and (3) completing decoding according to the decoding table, and restoring the coding information group formed by the 2n words into an original information group, namely, in the 2n words in the coding information group, any word not exceeding n words is lost, and correctly recovering the original information group.
2. The word-oriented coding/decoding method with forward erasure correction function as claimed in claim 1, wherein said performing data coding according to the systematic code coding matrix comprises:
the inputs are: (1) encoding a matrix B; (2) original information group Message (m) composed of n words to be encoded1,m2,…,mn)；
The output is: after encoding, an Encoded information group Encoded _ M ═ of (e) consisting of 2n words1,e2,…,e2n)；
The calculation formula for the transformation from the original set of information to the encoded set of information is: encoded _ M is Message × B; i is more than or equal to 1 and less than or equal to 2n, all have
Encoded _ M is transmitted as a coded data group into the channel.
3. The word-oriented coding/decoding method with forward erasure correction function as claimed in claim 2, wherein said decoding according to the decoding table comprises:
the inputs are: received data set Encoded _ M '(e)'1,e′2,…,e′2n)；
The output is: original data Message;
for i is more than or equal to 1 and less than or equal to 2n, checking e 'in sequence'iIf it is lost, let θiIf not, let θiThe offset vector θ is generated by 1 ═ θ1,θ2,…,θ2n)；
And for i not less than 1 and not more than 2n, judging: if thetaiWhen d is equal to 0, order di0; if thetaiWhen the value is 1, order di＝e′iThereby generating a query vector D ═ (D)1,d2,…,d2n)；
And (3) judging: if theta1＝θ2＝…＝θn1, then directly returns Message ═ e'1,e′2,…,e′n) And the process is ended; otherwise, executing the following steps;
in the decoding table T, traversing the entries, and extracting the currently traversed entries
T[k]＝(α1,α2,…,α2n)；
Construct vector TEMP ═ TEMP (TEMP)1,temp2,…,temp2n) Here, the
Judgment of D&Whether TEMP is an all 0 vector, operation here "&"denotes a bitwise AND operation; if yes, take out T [ k ]]＝(α1,α2,…,α2n) And outputs a decoded value Message ═ (α)1,α2,…,αn) And ending decoding; otherwise, the next time of extracting the currently traversed entry is carried out.
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