CN113641531A - STAR code encoding method and decoding method thereof - Google Patents

Abstract

The invention relates to a coding method and a decoding method of a STAR code. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced. And after the erasure condition of the check column of the STAR code to be decoded is obtained, decoding the STAR code to be decoded according to the erasure condition of the check column and the common factor, and recovering the invalid check column. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

Description

STAR code encoding method and decoding method thereof

Technical Field

The present invention relates to the field of information technology, and in particular, to a STAR code encoding method and a STAR code decoding method.

Background

Binary Maximum Distance Separable (MDS) array codes are widely used in various types of storage systems, such as redundant arrays of inexpensive disks, which have two major advantages: (1) at a given fault tolerance level, storage redundancy is minimized; (2) only an exclusive or operation is involved in encoding and decoding. Specifically, an (n, k, m) binary MDS array code is an array of size m × n, km information bits are encoded to obtain (n-k) m check bits, where nm bits (including km information bits and (n-k) m check bits) are stored in the m × n array. To satisfy the MDS characteristics means that the system can tolerate any r-n-k faults in n columns with minimal storage redundancy. To support storage applications (e.g., databases) with update-intensive workloads, it is desirable to construct binary MDS array codes with less encoding/decoding complexity in terms of the number of exclusive-ors induced in encoding/decoding and with less update complexity in terms of the average number of check bits affected by a single information bit change.

Binary MDS array codes are well studied, for example, EVENODD, X-code, and RDP are common binary MDS array codes and can accommodate any erasure of r 2 columns. In particular, the EVENODD code has a well-designed mathematical structure, which motivates many subsequent researches, such as a STAR code using three parity columns and a generalized EVENODD code using more than two parity columns to extend the structure of the EVENODD code. Currently, an EVENODD + code is proposed, which can achieve the asymptotically optimal update complexity, but only r is 2 parity columns. Another TIP code has r-3 parity columns and achieves optimal update complexity, but has much higher decoding complexity than existing binary MDS array codes (e.g., STAR codes). And the STAR code has r ═ 3 check columns, has three fault-tolerant ability. However, the update complexity of the STAR code is high and the encoding and decoding are not efficient.

Disclosure of Invention

Therefore, it is necessary to provide a STAR code encoding method and a STAR code decoding method, aiming at the defects that the update complexity of the STAR code is high and the encoding and decoding are not efficient enough.

A method of encoding a STAR code, comprising the steps of:

determining the check bit of the second check column and the check bit of the third check column;

determining a common factor;

a common factor is added to the selected check bits of the second check column and the selected check bits of the third check column.

In the above STAR code encoding method, after the check bits of the second check column and the check bits of the third check column are determined, the common factor is determined, and finally the common factor is added to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

In one embodiment, the check bits of the second check column are as follows:

the check bits of the third check column are as follows:

wherein, given an odd number m ≧ k,

defining an (m-1) × (k +3) array code; for j 0, 1, …, k-1, column j is called the information column, storing information bit b_0，j，b_1，j，…，b_m-2，j(ii) a For j ═ k, k +1, k +2, column j is called a parity column, and is used for storing parity bits; subscripts of all blocks need to be subjected to modulo m operation; given an array b of (m-1) x k bits of information_i，jI-0, 1, …, m-2 and j-0, 1, …, k-1, defining a virtual row b for all the j columns_m-1，j＝0。

In one embodiment, the common factor comprises a first common factor b_m-1，k+1With a second common factor b_m-1，k+2；

Wherein the first common factor is of the following formula:

wherein the second common factor is of the formula:

wherein the first common factor is added to the second parity column and the second common factor is added to the third parity column.

In one embodiment, the process of adding a common factor to selected parity bits of a second parity column and selected parity bits of a third parity column comprises the steps of:

adding a common factor to the second check column

Of a check bit and a third check column

And (4) a check bit.

An apparatus for encoding a STAR code, comprising:

the check bit determining module is used for determining the check bit of the second check column and the check bit of the third check column;

a common factor determination module for determining a common factor;

a common factor adding module to add a common factor to the selected parity bits of the second parity column and the selected parity bits of the third parity column.

The above STAR code encoding apparatus determines the check bits of the second check column and the check bits of the third check column, then determines the common factor, and finally adds the common factor to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

A computer storage medium having stored thereon computer instructions which, when executed by a processor, implement the method of encoding STAR code of any of the above embodiments.

The computer storage medium determines the check bits of the second check column and the check bits of the third check column, then determines the common factor, and finally adds the common factor to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method for encoding STAR code of any of the above embodiments when executing the program.

After the check bits of the second check column and the check bits of the third check column are determined, the common factor is determined, and finally the common factor is added to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

A method of decoding a STAR code, comprising the steps of:

acquiring an information column and a check column erasure condition of a STAR code to be decoded;

and decoding the STAR code to be decoded according to the erasure condition of the information column and the check column and the common factor, and recovering the failure information column and the check column.

According to the decoding method of the STAR code, after the information column and the check column of the STAR code to be decoded are obtained to be erased, the STAR code to be decoded is decoded according to the information column and check column erasing condition and the common factor, and the failure information column and the check column are recovered. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

In one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure of the information column and the check column and the common factor comprises the steps of:

when all three columns of check columns are erased, decoding is performed in reverse according to the encoding method of the STAR code as in any of the above embodiments to recover the failed check columns.

In one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure of the information column and the check column and the common factor comprises the steps of:

and when the second check column and the third check column are erased, recovering the failure information column and the check column according to the decoding mode of the EVENODD + code based on the common factor.

In one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure of the information column and the check column and the common factor comprises the steps of:

determining a syndrome bit according to the common factor when the first check column is erased;

determining a start bit according to the syndrome bit;

and recovering the failure information bits according to the initial bits so as to recover the failure information columns and the check columns.

In one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure of the information column and the check column and the common factor comprises the steps of:

determining syndrome bits according to the common factor when no check column is erased;

finding a starting point in the syndrome bit and repairing the second column of erased information;

and recovering the information columns with the first column erased and the information columns with the third column erased according to the decoding mode of the EVENODD + code.

An apparatus for decoding a STAR code, comprising:

the erasure determining module is used for acquiring the erasure condition of the information column and the check column of the STAR code to be decoded;

and the information column and check column recovery module is used for decoding the STAR code to be decoded according to the erasure condition of the information column and the check column and the common factor and recovering the failure information column and the check column.

After the information column and the check column of the STAR code to be decoded are erased, the STAR code to be decoded is decoded according to the information column and the check column erasing condition and the common factor, and the failure information column and the check column are recovered. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

A computer storage medium having stored thereon computer instructions which, when executed by a processor, implement the method of decoding STAR code of any of the above embodiments.

After the information column and the check column of the to-be-decoded STAR code are erased, the to-be-decoded STAR code is decoded according to the information column and the check column erasure and the common factor, and the failure information column and the check column are recovered. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method for decoding STAR code of any of the above embodiments when executing the program.

After the information column and the check column of the STAR code to be decoded are obtained, the computer equipment decodes the STAR code to be decoded according to the information column and the check column erasure and the common factor, and recovers the failure information column and the check column. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

Drawings

FIG. 1 is a flow chart of a STAR code encoding method according to one embodiment;

FIG. 2 is a flow chart of a STAR code encoding method according to another embodiment;

FIG. 3 is a block diagram of an apparatus for encoding STAR codes according to another embodiment;

FIG. 4 is a flow diagram of a STAR code decoding method in accordance with one embodiment;

FIG. 5 is a flow chart of a STAR code decoding method in accordance with another embodiment;

FIG. 6 is a flow chart of a STAR code decoding method in accordance with yet another embodiment;

FIG. 7 is a block diagram of a STAR code decoder according to one embodiment;

FIG. 8 is a schematic diagram of an internal structure of a computer according to an embodiment.

Detailed Description

For better understanding of the objects, technical solutions and effects of the present invention, the present invention will be further explained with reference to the accompanying drawings and examples. Meanwhile, the following described examples are only for explaining the present invention, and are not intended to limit the present invention.

The embodiment of the invention provides a STAR code coding method.

Fig. 1 is a flowchart of a STAR code encoding method according to an embodiment, and as shown in fig. 1, the STAR code encoding method according to an embodiment includes steps S100 to S102:

s100, determining a check bit of a second check column and a check bit of a third check column;

s101, determining a common factor;

s102, adding a common factor to the selected check bit of the second check column and the selected check bit of the third check column.

It should be noted that, in each embodiment of the present embodiment, in order to distinguish the STAR code implemented under the STAR code encoding/decoding method according to each embodiment from the conventional STAR code, the STAR code implemented under the STAR code encoding/decoding method according to each embodiment is collectively referred to as "STAR + code" to facilitate the description of the embodiment.

For a given odd number m ≧ k,

defining an (m-1) × (k +3) array code; for j 0, 1, …, k-1, column j is called the information column, storing information bit b_0，j，b_1，j，…，b_m-2，j(ii) a For j ═ k, k +1, k +2, column j is called a parity column, and is used for storing parity bits; subscripts of all blocks need to be subjected to modulo m operation; given an array b of (m-1) x k bits of information_i，jI-0, 1, …, m-2 and i-0, 1, …, m-2, a virtual row b is defined for all j columns_m-1，j＝0。

Based on the above given, the parity bits in k columns are:

the check bits in the k +1 column and the k +2 column are respectively:

and

wherein, the k column represents the first check column, the k +1 column represents the second check column, and the k +2 column represents the third check column.

After each parity column and parity bit are determined, a common factor is added to the selected parity bit, implementing a STAR + code, unlike a conventional STAR code (where a common factor is added to all parity bits). The selected parity bits are only part of the parity bits.

In one embodiment, the common factor comprises a first common factor b_m-1，k+1With a second common factor b_m-1，k+2；

Wherein the first common factor is of the following formula:

wherein the second common factor is of the formula:

wherein the first common factor is added to the second parity column and the second common factor is added to the third parity column.

In one embodiment, fig. 2 is a flowchart of a STAR code encoding method according to another embodiment, and as shown in fig. 2, a process of adding a common factor to selected parity bits of a second parity column and selected parity bits of a third parity column in step S101 includes step S200:

s200, adding common factors to the second check column

Of a check bit and a third check column

And (4) a check bit.

Based on this, in STAR + (m, k), we will only have two common factors b in columns k +1 and k +2, respectively_m-1，k+1And b_m-1，k+2Is added to

A check bit, and the STAR code combines two common factors b_m-1，k+1And b_m-1，k+2All parity bits added to the second and third parity columns, respectively. This differentiation makes the update complexity of STAR + (m, k) asymptotically optimal. Table 1 below describes an example of STAR + (9, 3) where two factors b are common_8，4And b_8，5To the first two parity bits of column 4 and the last two parity bits of column 5, respectively.

TABLE 1 STAR + (9, 3) TABLE (where common factor b_8，4＝b_7，1+b_6，2，b_8，6＝b_0，1+b_1，2)

To better explain the effects of the embodiments of the present invention, the update complexity of STAR + (m, k) is specifically evaluated below.

If the information bit changes, it is necessary to update one parity bit in the k column and those in the k +1 and k +2 columns

And (4) a check bit. Thus, the update complexity is

If m > k, the update complexity is close to the optimum

Thus, when m is much larger than k, the update complexity is asymptotically optimal, and the update complexity of the STAR code is

If m > k, then strictly greater than STAR + (m, k), Table 2 below gives the update complexity of the STAR code and STAR + (m, k) when k is 7 and m is between 7 and 53. When m > 7, STAR + (m, k) has less update complexity than STAR codes, and this advantage increases as m increases. Since m 49 is not a prime number, the update complexity of the STAR code is not shown in table 2.

Note that the common factor is added to only some of the parity bits in the last two parity columns in STAR + (m, k), while the common factor is added to all of the parity bits in the last two parity columns in STAR code. The encoding/decoding complexity of STAR + (m, k) is low compared to the STAR code.

TABLE 2 STAR + (m, 7) and update complexity Table of STAR codes

In the STAR code encoding method according to any of the above embodiments, after the check bits of the second check column and the check bits of the third check column are determined, the common factor is determined, and finally the common factor is added to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

The embodiment of the invention also provides a STAR code coding device.

Fig. 3 is a block diagram of a STAR code encoding apparatus according to another embodiment, and as shown in fig. 3, the STAR code encoding apparatus according to an embodiment includes a block 100, a block 101, and a block 102:

a check bit determining module 100, configured to determine a check bit of the second check column and a check bit of the third check column;

a common factor determining module 101, configured to determine a common factor;

a common factor adding module 102 for adding a common factor to the selected parity bits of the second parity column and the selected parity bits of the third parity column.

The above STAR code encoding apparatus determines the check bits of the second check column and the check bits of the third check column, then determines the common factor, and finally adds the common factor to the selected check bits of the second check column and the selected check bits of the third check column. Based on this, different from the traditional STAR code, only when two check columns are calculated, common factors are added to partial check bits, so that the coding efficiency is effectively improved, and the updating complexity is reduced.

The embodiment of the invention also provides a decoding method of the STAR code.

Fig. 4 is a flowchart of a STAR code decoding method according to an embodiment, and as shown in fig. 4, the STAR code decoding method includes steps S300 and S301:

s300, acquiring an information column and a check column erasure condition of the STAR code to be decoded;

s301, decoding the STAR code to be decoded according to the erasure condition of the information column and the verification column and the common factor, and recovering the failure information column and the verification column.

The information column and check column erasure condition of each STAR code to be decoded in step S300 includes that the check column is completely erased and partially erased. Therein, the STAR code to be decoded (STAR + code) comprises three check columns. The decoding algorithm of STAR + (m, k) recovers any three columns of erasures, thus also demonstrating its MDS properties. Theorem 1 below illustrates one key property of the decoding algorithm for STAR + (m, k).

Theorem 1: for the

Consider that

According to formula (1) and formula (2), the former formula can be expressed as:

consider b_m-1，k+1And b_m-1，jThe above equation becomes the following equation, with 0, j being defined as 0, 1, …, k-1:

using the same parameters and methods, can also be obtained

Proof theorem 1 is complete.

Therein, two column erasure decoding of STAR + (m, k) can be considered as a special case of three column erasure decoding, so that only the decoding algorithm of three column erasure can be studied. Assuming three columns f, g, h are erased, where 0 ≦ f < g < h ≦ k +2, a decoding algorithm is proposed to reconstruct all erased bits from the remaining k columns. Based on different erase patterns, the reconstruction can be divided into four cases (i) three columns of check column erase, i.e., f k, g k +1, h k + 2; (ii) erasing two check columns, namely f is more than or equal to 0 and less than or equal to k-1, and k is more than or equal to g and less than or equal to h and less than or equal to k + 2; (iii) erasing a column of check columns, namely f is more than or equal to 0 and less than or equal to g and less than or equal to k-1 and k is more than or equal to k and less than or equal to k + 2; (iv) there is no erasure of the check column, i.e., f is more than 0 and less than g and h is more than or equal to k-1.

In one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure of the information column and the check column and the common factor in step S301 includes the steps of:

when all three columns of check columns are erased, decoding is performed in reverse according to the encoding method of the STAR code as in any of the above embodiments to recover the failed check columns.

Applying the STAR code encoding method of any of the above embodiments, the decoding is performed in the same manner as defined in equations (1), (2), and (3) in the STAR code encoding method of any of the embodiments.

For two column parity erase, three modes are included, (i) g-k +1, h-k +2, (ii) g-k, h-k +2, (iii) g-k, h-k + 1. For modes (i) and (ii), the failed information column f can be recovered using the decoding method in the conventional EVENODD + code. The decoding process of g-k, h-k +1 is similar to the decoding method of g-k, h-k + 2. Here, the decoding method in the conventional EVENODD + code is already disclosed, and is not described herein again.

Based on this, in one embodiment, the process of decoding the to-be-decoded STAR code according to the erasure condition of the information column and the check column and the common factor in step S301 includes the steps of:

and when the second check column and the third check column are erased, recovering the failure information column and the check column according to the decoding mode of the EVENODD + code based on the common factor.

Fig. 5 is a flowchart of a STAR code decoding method according to another embodiment when the first check column is erased, and as shown in fig. 5, a process of decoding a STAR code to be decoded according to the information column and check column erasure condition and the common factor in step S301 includes steps S400 to S402:

s400, when the first check column is erased, determining a syndrome bit according to a common factor;

s401, determining a start bit according to the syndrome bit;

s402, recovering the failure information bits according to the initial bits to recover the failure information columns and the check columns.

The decoding algorithm when the first parity column is erased (i.e., h ═ k, 0 ≦ f < g ≦ k-1). The following argument 2 shows how to obtain b_m-1，k+1+b_m-1，k+2。

2 in the introduction.

Calculation of b_m-1，k+1+b_m-1，k+2By passing

Equation (4) is derived from equations (2) and (3); the factor of equation (5)

Is an even number; equation (6) is because { -j, 1-j, …, m-1-j } ═ 0, 1, …, m-1} modm. Based on this, theorem 2 is proved to be completed.

For i ═ 0, 1, …, m-2, by subtracting b from_i，k+1And b_i，k+2All information bits in the k-2 survivor information columns are subtracted to obtain the following 2m-2 syndrome bits

According to lemma 2, (b) can be calculated by adding all bits of equation (7) and equation (8)_-1-f，f+b_-1-g，g)+(b_-1+f，f+b_-1+g，g)。

Considering the case where f > 0, when f > 0, there is an equation (7) when i ═ f-1 (because 0 ≦ f-1 ≦ k-3)

p_f-1，1＝b_-g+f-1，g+(b_-1-f，f+b_-1-g，g) (9)

In equation (7), when i ═ g-1 (since 0. ltoreq. g-1. ltoreq. k-2) has

p_g-1，1＝b_-f+g-1，f+(b_-1-f，f+b_-1-g，g) (10)

Similarly, in equation (8), when i ═ m-f-1 (since m-k + 1. ltoreq. m-f-1. ltoreq. m-2) has

p_m-f-1，1＝b_g-f-1，g+(b_-1+f，f+b_-1+g，g) (11)

In equation (8), when i ═ m-g-1 (since m-k. ltoreq. m-g-1. ltoreq. m-3) has

p_m-g-1，1＝b_f-g-1，f+(b_-1+f，f+b_-1+g，g) (12)

Wherein the bits in equations (9), (10), (11) and (12) are start bits. Starting from the start bit in equation (9), the next information bit can be calculated. First, the bit p is calculated_f-1，1And p_-2g+f-1，2To obtain:

b_-2g+2f-1，f+(b_-1-f，f+b_-1-g，g)+ε(b_-1+f，f+b_-1+g，g)，

where ε ∈ {0, 1 }. Then, b is found in equation (7)_-2g+2f-1，fCan be obtained by adding the above equation to the bits of equation (7) where i-3 f-2 g-1:

η(b_-1-f，f+b_-1-g，g)+ε(b_-1+f，f+b_-1+g，g)+b_-3f-2g-1，g，

where η ∈ {0, 1 }. By repeating the above process

Next, it is possible to obtain:

wherein

Is a non-negative integer. Recall that the term b does not exist in equations (7) and (8), respectively_-1-f，f+b_-1-g，gAnd b_-1+f，f+b_-1+g，g. If:

or

or

or

the above process ends. In the same way, the following can be obtained:

or:

wherein

Is a non-negative integer. By adding the selected bits in equations (7) and (8) until

or

or

or

For the start bit p in equation (11)_-f-1，2It is possible to obtain:

or:

wherein

Is a non-negative integer which is not negative,

or

or

or

for the start bit p in equation (12)_-g-1，2It is possible to obtain:

or

or

or

since there is no b for i-m-1 in equation (7)_-f+i，f+b_-g+i，gIn equation (8), m-1 has no b_f+i，f+b_g+i，g. B is to_-1-f，f+b_-1-g，gAnd m-1 bits in equation (7) are put into the first group, b_-1+f，f+b_-1+g，gAnd the m-1 bits in equation (8) are placed in the second group. Given an integer t, satisfying 0 ≦ t ≦ m-1, one can always find a group containing b in the first group_{(-f+i)mod m，f}＝b_t，fOr b_{(-g+i)mod m，g}＝b_t，gAnd can be found in the second group to contain b_{(f+i)mod m，f}＝b_t，fOr b_{(g+i)mod m，g}＝b_t，gOne bit of (a). For each start bit, recursively selecting one of equations (7) or (8) that can be cancelled until the remaining bits are b_-f-1，f、b_-g-1，g、b_f-1，f、b_g-1，gOne of them. Therefore, all 2(m-1) syndrome bits in equations (7) and (8) calculate one bit using the start bit in equations (9), (10), (11), and (12), and each bit in equations (7) and (8) is used only once when calculating the bit of the start bit in equations (9), (10), (11), and (12). The 2(m-1) bits can be divided into four groups in equations (7) and (8). The bits in each group are used to calculate the bits starting from the start bit. S₁、S₂、S₃And S₄Respectively represent and start bit p_f-1，1、p_g-1，1、p_-f-1，2And p_-g-1，2The relevant groups.

Lemma 3. set group S₁、S₂、S₃And S₄Are respectively | S₁|、|S₂|、|S₃I and I S₄I, have | S₁|＝|S₃I, also | S₂|＝|S₄|。

And (3) proving that: first proving | S₁|＝|S₃L. The sum in equation (13)

Or

End, the sum in equation (14) and

or

And (6) ending. If it is not

Then there is

Otherwise, if

Then there is

On the other hand, if

Then there is

If it is not

Then there is

The number of syndrome bits in equations (13) and (14) is:

and

thus, there are:

for the start bit p_-f-1，2There are bits in equation (17) or equation (18). If the subscript in equation (17) is

Or

The sum in equation (17) ends. Similarly, if the subscript in equation (18) is

Or

The sum in equation (18) ends. If it is not

Is provided with

Furthermore, if

Is provided with

On the other hand, if

Is provided with

If it is not

Is provided with

Thus is provided with

For two start bits p_g-1，1And p_-g-1，2With the same parameters, | S can likewise be proved₂|＝|S₄L. The certification is complete.

According to lemma 3, there is | S₁|＝|S₃I and I S₂|＝|S₄L. Since there are 2(m-1) syndrome bits, and each syndrome bit is in one group, | S is obtained₁|+|S₃|＝|S₂|＝|S₄|＝m-1。

From p_f-1，1Can obtain:

η(b_-1-f，f+b_-1-g，g)+ε(b_-1+f，f+b_-1+g，g)+b_-1-f，f，

if|S₁|＝2f·(2g-2f)^-1mod m， (21)

η(b_-1-f，f+b_-1-g，g)+ε(b_-1+f，f+b_-1+g，g)+b_-1+f，f，

if|S₁|＝2(m-f)·(2g-2f)^-1mod m， (22)

η(b_-1-f，f+b_-1-g，g)+ε(b_-1+f，f+b_-1+g，g)+b_-1+g，g，

if|S₁|＝2(f-2g)·(2g-2f)^-1mod m+1， (23)

and further obtaining:

for p, the same applies_-f-1，1The start bit of (c) can be obtained:

according to lemma 3, there is | S₁|＝|S₃L, together with formula (24) and formula (25), may be derived from p_f-1，1And p_-f-1，2Two different information bits are calculated from the two start bits. Similarly, slave p can also be demonstrated_g-1，1And p_-g-1，2The two start bits calculate two different information bits. Thus, four information bits b are obtained from four start bits_-1+g，g，b_-1+f，f，b_-1-f，fAnd b_-1-g，gAnd further calculates b_-1-f，f+b_-1-g，gAnd b_-1+f，f+b_-1+g，g. Other information bits in the f column and the g column can be calculated according to the conventional STAR code, which is not described herein.

When f is 0, there are two start bits b_g-1，0+b_-1-g，gAnd b_-g-1，0+b_-1+g，gAnd only two bits b need to be calculated by the same method of f > 0_-1-g，gAnd b_-1+g，g。

Consider the example in table 1. If the column f 1, g 2 and l 3 fail. By subtracting the information bit of column 0 from the parity bits of columns 4 and 5, the following bits are obtained:

b_7，2+b_8，4，b_0，1+b_8，4，b_1，1+b_0，2，b_2，1+b_1，2，

b_3，1+b_2，2，b_4，1+b_3，2，b_5，1+b_4，2，b_6，1+b_5，2，

b_1，1+b_2，2，b_2，1+b_3，2，b_3，1+b_4，2，b_4，1+b_5，2，

b_5，1+b_6，2，b_6，1+b_7，2，b_7，1+b_8.5，b_0，2+b_8，5，

by summing all the above bits, b can be obtained_8，4+b_8，5＝b_7，1+b_6，2+b_0，1+b_1，2. When f > 0, there are four start bits b_7，2+b_8，4、b_0，1+b_8，4、b_7，1+b_8，5And b_0，2+b_8，5. From start bit b_7，2+b_8，4Initially, b can be calculated_0，1By:

(b_7，2+b_8，4)+(b_6，1+b_7，2)+(b_6，1+b_5，2)+(b_4，1+b_5，2)+(b_4，1+b_3，2)+(b_2，1+b_3，2)+(b_2，1+b_1，2)+(b_8，4+b_8，5)＝b_0，1

in combination with b_0，1+(b_0，1+b_8，4) Calculation of b_8，4. Once b is completed_8，4Knowing that b can be calculated_8，5. All other information bits can be iteratively decoded to complete the decoding.

Fig. 6 is a flowchart of a STAR code decoding method according to another embodiment when no check column is erased, and as shown in fig. 6, a process of decoding a STAR code to be decoded according to an information column and check column erasure condition and a common factor in step S301 includes steps S500 to S502:

s500, when no check column is erased, determining a syndrome bit according to a common factor;

s501, finding a starting point in the syndrome bit and repairing a second erasure information column;

and S502, recovering the first erasure information column and the third erasure information column according to the decoding mode of the EVENODD + code.

Considering three information columns f, g, and h are erased, where 0 ≦ f < g < h ≦ k-1, it is desirable to recover the information bits in the f, g, and h columns, yet another embodiment of the decoding method for the STAR code is as follows.

The first step is as follows: calculation of b by theorem 1_m-1，k+1And b_m-1，k+2。

The second step is that: by passing from b_m-1，k+1、b_m-1，k+2And subtracting the information bits in the k-3 survivor information columns from the 3(p-1) check bits to calculate the following 3p-1 syndromes:

b_i，f+b_i，g+b_i，h for 0≤i≤p-2，

b_i-f，f+b_i-g，g+b_i-h，h for 0≤i≤p-1，

b_i+f，f+b_i+g，g+b_i+h，h for 0≤i≤p-1.

the third step: find a starting point in g columns and repair g columns.

The fourth step: f columns and h columns are repaired by the decoding algorithm in EVENODD +.

After the four steps are performed, the three erased information columns can be recovered. The method for finding the starting point in the g-column is similar to the conventional recovery method of the RTP code, and is not described herein again.

In the proof of lemma 2, b is calculated by summing all 2(m-1) parity bits in the k +1 and k +2 columns_m-1，k+1+b_m-1，k+2Is a key point in the decoding algorithm. By way of example 2, if an even number of b's are included in column k +1 (column k + 2)_m-1，k+1(b_m-1，k+2) B is always available_m-1，k+1+b_m-1，k+2. This is also b_m-1，k+1Added to the front of k +1 column

Check the bit, and_m-1，k+2added to the k +2 column

One of the reasons for the check bits. However, the number of check bits in the k +1 column (or k +2 columns), respectively, contains b_m-1，k+1(b_m-1，k+2) Should not be less than

Because it is necessary to ensure that all information bits can be recovered for any k-1 column of information plus the (k + 1) th column. In the decoding algorithm for any three information column erasures, b given in theorem 1_m-1，k+1And b_m-1，k+22 is crucial because the decoding algorithm can be reduced to that of conventional RTP.

Note also that in conventional STAR code, the number of columns of information should be prime, with the number of rows equal to the number of columns of information minus 1. However, this constraint is relaxed in STAR + (m, k). When k is m, STAR + (m, k) reduces to a STAR code.

In the STAR code decoding method according to any of the embodiments described above, after the information column and the check column erasure of the STAR code to be decoded are obtained, the STAR code to be decoded is decoded according to the information column and check column erasure and the common factor, and the failure information column and the check column are recovered. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

The embodiment of the invention also provides a STAR code decoding device.

Fig. 7 is a block diagram of a STAR code decoding apparatus according to an embodiment, and as shown in fig. 7, the STAR code decoding apparatus according to an embodiment includes a block 200 and a block 201:

an erasure determining module 200, configured to obtain an information column and a check column erasure condition of a STAR code to be decoded;

and an information column and check column recovery module 201, configured to decode the to-be-decoded STAR code according to the erasure condition of the information column and the check column and the common factor, and recover the failed information column and the check column.

After the information column and the check column of the STAR code to be decoded are erased, the STAR code to be decoded is decoded according to the information column and the check column erasing condition and the common factor, and the failure information column and the check column are recovered. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

Embodiments of the present invention further provide a computer storage medium, on which computer instructions are stored, and when executed by a processor, the instructions implement the STAR code encoding method or the STAR code decoding method of any of the above embodiments.

It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware related to instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, the computer program can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

Alternatively, the integrated unit of the present invention may be stored in a computer-readable storage medium if it is implemented in the form of a software functional module and sold or used as a separate product. Based on such understanding, the technical solutions of the embodiments of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a terminal, or a network device) to execute all or part of the methods of the embodiments of the present invention. And the aforementioned storage medium includes: a removable storage device, a RAM, a ROM, a magnetic or optical disk, or various other media that can store program code.

Corresponding to the computer storage medium, in an embodiment, there is also provided a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the STAR code encoding method or the STAR code decoding method in any of the embodiments.

The computer device may be a terminal, and its internal structure diagram may be as shown in fig. 8. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method of encoding a STAR code or a method of decoding a STAR code. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.

After the information column and the check column of the STAR code to be decoded are obtained, the computer equipment decodes the STAR code to be decoded according to the information column and the check column erasure and the common factor, and recovers the failure information column and the check column. Based on the addition of the common factor of the STAR code to the selected check bit, the decoding efficiency of the STAR code is improved.

The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.

The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (9)

1. A method of encoding a STAR code, comprising the steps of:

determining the check bit of the second check column and the check bit of the third check column;

determining a common factor;

adding the common factor to selected parity bits of the second parity column and selected parity bits of the third parity column.

2. A STAR code encoding method as claimed in claim 1, wherein the check bits of the second check column are as follows:

the check bits of the third check column are as follows:

wherein, given an odd number m ≧ k, gcd (m, l) ═ 1, l ═ 1, 2, …, k-1, define (m-1) × (k +3) array code; for thej is 0, 1, …, k-1, column j is called information column, storing information bit n_0，j，b_1，j，…，b_m-2，j(ii) a For j ═ k, k +1, k +2, column j is called a parity column, and is used for storing parity bits; subscripts of all blocks need to be subjected to modulo m operation; given an array b of (m-1) x k bits of information_i，jI-0, 1, …, m-2 and j-0, 1, …, k-1, defining a virtual row b for all the j columns_m-1，j＝0。

3. STAR code encoding method according to claim 2, characterised in that said common factor comprises a first common factor b_m-1，k+1With a second common factor b_m-1，k+2；

Wherein the first common factor is of the following formula:

wherein the second common factor is of the formula:

wherein a first common factor is added to the second parity column and a second common factor is added to the third parity column.

4. A STAR code encoding method as claimed in claim 2 or 3, wherein said adding said common factor to selected check bits of said second check column and selected check bits of said third check column comprises the steps of:

adding the common factor to the second verify column

Of a check bit and said third check column

And (4) a check bit.

5. A method of decoding a STAR code, comprising the steps of:

acquiring an information column and a check column erasure condition of a STAR code to be decoded;

and decoding the STAR code to be decoded according to the erasure condition of the information column and the check column and the common factor, and recovering the failure information column and the check column.

6. A STAR code decoding method as recited in claim 5, wherein the decoding of the STAR code to be decoded from the information column and check column erasure and the common factor comprises the steps of:

when all three columns of check columns are erased, decoding is performed in reverse according to the STAR code encoding method of any of claims 1 to 5 to recover the failed check columns.

7. A STAR code decoding method as recited in claim 5, wherein the decoding of the STAR code to be decoded from the information column and check column erasure and the common factor comprises the steps of:

and when the second check column and the third check column are erased, recovering the failure information column and the check column according to the decoding mode of the EVENODD + code based on the common factor.

8. A STAR code decoding method as recited in claim 5, wherein the decoding of the STAR code to be decoded from the information column and check column erasure and the common factor comprises the steps of:

determining a syndrome bit according to the common factor when the first check column is erased;

determining a start bit according to the syndrome bit;

and recovering the failure information bits according to each start bit so as to recover the failure information columns and the check columns.

9. A STAR code decoding method as recited in claim 5, wherein the decoding of the STAR code to be decoded from the information column and check column erasure and the common factor comprises the steps of:

determining syndrome bits according to the common factor when no check column is erased;

finding a starting point in the syndrome bit and repairing a second erasure information column;

and recovering the first erasure information column and the third erasure information column according to the decoding mode of the EVENODD + code.

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