CN113783659A - Data processing method, device and medium based on binary erasure channel - Google Patents

Abstract

The invention discloses a data processing method, equipment and medium based on a binary erasure channel, wherein the method comprises the following steps: acquiring an output sequence from an output end of a binary erasure channel, wherein an input sequence corresponding to the input end of the binary erasure channel is a sequence obtained by performing weighted probability arithmetic coding on a target sequence, and the target sequence is a sequence obtained by performing information source processing on an information source sequence; performing weighted probability arithmetic decoding on the output sequence to obtain a decoded sequence; and comparing the decoding sequence with the target sequence, and restoring the information source sequence or carrying out forward error correction on the decoding sequence according to the comparison result. The method provided by the method can realize that the transmission rate approaches the channel capacity of a binary erasure channel, and has data check and error correction capabilities.

Description

Data processing method, device and medium based on binary erasure channel

Technical Field

The present invention relates to the field of information coding technologies, and in particular, to a data processing method, device, and medium based on a binary erasure channel.

Background

Expert scholars have made continuous efforts to construct coding methods that approach the capacity of the channel. In 2009, Arikan professor proposed a coding method based on the channel polarization phenomenon, called Polar Code, which proved to be capable of reaching capacity when the Code length approached infinity. LDPC (Low Density Parity Check Code), Turbo Code can also approach the shannon limit.

The current scheme mostly belongs to coding technology under a BSC (binary symmetric channel) channel, and lacks coding technology applied to a BEC (binary erasure channel) channel, in particular lacks a coding and decoding method which can realize that the transmission rate can approach the channel capacity and has data checking and error correcting capabilities in the BEC (binary erasure channel).

Disclosure of Invention

The present invention is directed to at least solving the problems of the prior art. Therefore, the invention provides a data processing method, a system, equipment and a medium based on a binary erasure channel. The method can realize that the transmission rate approaches to the channel capacity and has data check and error correction capability.

In a first aspect of the present invention, a data processing method based on a binary erasure channel is provided, which is applied to a receiving end, and the data processing method includes:

acquiring an output sequence from an output end of a binary erasure channel, wherein an input sequence corresponding to the input end of the binary erasure channel is a sequence obtained by performing weighted probability arithmetic coding on a target sequence, and the target sequence is a sequence obtained by performing information source processing on an information source sequence;

performing weighted probability arithmetic decoding on the output sequence to obtain a decoded sequence, wherein the weighted probability arithmetic decoding is the inverse process of the weighted probability arithmetic coding;

and comparing the decoding sequence with the target sequence, and restoring the source sequence or carrying out forward error correction on the decoding sequence according to a comparison result.

In a second aspect of the present invention, a data processing method based on a binary erasure channel is provided, which is applied to a sending end, and the data processing method includes:

acquiring an information source sequence;

carrying out information source processing on the information source sequence to obtain a target sequence;

performing weighted probability arithmetic coding on the target sequence to obtain an input sequence;

and transmitting the input sequence to a receiving end through a binary erasure channel so as to trigger the receiving end to carry out weighted probability arithmetic decoding on the output sequence output by the binary erasure channel, trigger the receiving end to compare a decoding result with the target sequence, and trigger the receiving end to restore the information source sequence or carry out forward error correction on the decoding sequence according to the comparison result, wherein the weighted probability arithmetic decoding is the inverse process of the weighted probability arithmetic coding.

In a third aspect of the present invention, there is provided an electronic apparatus comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor when executing the computer program implementing: the data processing method based on the binary erasure channel according to the first aspect of the present invention or the data processing method based on the binary erasure channel according to the second aspect of the present invention.

In a fourth aspect of the present invention, there is provided a computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to perform: the data processing method based on the binary erasure channel according to the first aspect of the present invention or the data processing method based on the binary erasure channel according to the second aspect of the present invention.

In the data processing method based on the binary erasure channel provided in the first aspect of the embodiment of the present application, it is possible to achieve that the transmission rate approaches the channel capacity of the binary erasure channel, and it has the data check and error correction capabilities.

It is to be understood that the advantageous effects of the second aspect to the fourth aspect compared to the related art are the same as the advantageous effects of the first aspect compared to the related art, and reference may be made to the related description of the first aspect, which is not repeated herein.

Drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a block diagram of a data processing system based on a binary erasure channel according to an embodiment of the present invention;

fig. 2 is a schematic flowchart of a data processing method based on a binary erasure channel according to an embodiment of the present invention;

fig. 3 is a schematic diagram of a data processing method based on a binary erasure channel according to an embodiment of the present invention;

fig. 4 is a schematic diagram of a process of encoding a symbol 010 by a weighting model according to an embodiment of the present invention;

fig. 5 is a flowchart illustrating a data processing method based on a binary erasure channel according to another embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

The current scheme mostly belongs to coding technology under a BSC (binary symmetric channel) channel, and lacks coding technology applied to a BEC (binary erasure channel) channel, in particular lacks a coding and decoding method which can realize that the transmission rate can approach the channel capacity and has data checking and error correcting capabilities in the BEC (binary erasure channel).

In order to solve the above-mentioned drawbacks, referring to fig. 1, an embodiment of the present invention provides a data processing system based on a binary erasure channel, where the system includes a sending end and a receiving end, and it should be noted that the present invention does not limit the configuration of the sending end and the receiving end, and the sending end and the receiving end may be any terminals with data processing functions. The transmitting end mainly comprises the processes of executing information source processing, weighting probability arithmetic coding and transmitting a coding result; the receiving end mainly comprises the processes of receiving the output result of the binary erasure channel, carrying out weighted probability arithmetic decoding on the output result, carrying out forward error correction and restoring an information source sequence.

Referring to fig. 2, a data processing method based on a binary erasure channel is provided based on a system embodiment, where the method uses a receiving end as an execution main body, and the method mainly includes the following steps:

step S101, a receiving end obtains an output sequence from an output end of a binary erasure channel, an input sequence corresponding to the input end of the binary erasure channel is a sequence obtained by performing weighted probability arithmetic coding on a target sequence, and the target sequence is a sequence obtained by performing information source processing on an information source sequence.

To facilitate understanding of those skilled in the art, the source sequence in step S101 is first assumed to be X, the target sequence is assumed to be Y, the input sequence is assumed to be V, and the output sequence is assumed to be U.

The following three binary sequences are listed:

firstly, randomly generating a binary source sequence X with a length of n, wherein X is equal to (0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0), and the probability of symbols in the sequence X is equal;

second, performing source processing on the sequence X, and replacing the symbol "1" in the sequence X with "10" to obtain a sequence Y, where Y is (0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0.);

thirdly, another source processing is performed on the sequence X, and if the symbol 1 in the sequence X is replaced by "101" and the symbol 0 is replaced by "01", a sequence Z is obtained, where Z is (0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1). The following process of source processing of the source sequence X is not exhaustive.

Let the length of sequence Y or sequence Z be denoted as l, the purpose of source processing (i.e. sequence conversion) is to make sequence Y and sequence Z satisfy the condition of data check. The conversion of a sequence X sequence into a sequence Z is more computationally intensive than the conversion of a sequence X sequence into a sequence Y. The data verification conditions for sequence Y are:

the number of consecutive symbols 1 in the sequence is at most 1 (1)

The data verification condition of the sequence Z is as follows:

the number of consecutive symbols 0 in the sequence is at most 1 and the number of consecutive symbols 1 is at most 2 (2)

The sequence Z has one more data verification condition than the sequence Y, and different conversion methods enable the sequence to have more data verification conditions. After the information source processing, a large amount of redundant information exists in the sequence Y and the sequence Z, and the sequence Y and the sequence Z can be subjected to lossless compression coding by adopting entropy coding.

In the art, arithmetic coding has poor error tolerance, such as decoding an erroneous binary sequence Y 'or a sequence Z' from a sequence V in which bit errors exist, and when the sequence Y 'does not satisfy the above equation (1), it is inevitable that there is a sequence Y' ≠ Y, or when the sequence Z 'does not satisfy the above equation (2), it is inevitable that there is Z' ≠ Z, and thus data verification can be achieved after encoding and decoding by source processing.

Since there is an obvious Context relationship between the symbols in the sequence Y and the sequence Z, taking the sequence Y as an example, a Context-Adaptive Binary Arithmetic Coding (CABAC) method can be selected to change the sequence Y to (Y)₁，y₂，...，y_l) Code, let R₀＝1，L ₀0, the i (i) th symbol y is 1, 2, 3_iThe binary arithmetic coding operation formula is as follows:

R_i＝R_i-1p(y_i)

L_i＝L_i-1+R_i-1F(y_i-1)

H_i＝L_i+R_i (3)

it should be noted that the above formula (3) includes three formulas, and the formula (3) is common knowledge of those skilled in the art and will not be described in detail herein.

Each symbol X of the sequence X_iE {0, 1}, so y_iWhen equal to 0

Then p (-1) ═ 0 and F (-1) ═ 0(F denotes the cumulative distribution function). Contract y₀When 0, then P (y)_i0) there are two probabilities p (0|0) and p (0| 1); y is_iWhen 1, F (0) is P (y)_i0) and P (y)_i1) there is a probability p (1| 0). When y is_i-11 and y_iProbability P (y) of 0 th symbol when 0_i＝0)＝p(0|1)＝1L is obtained from the above formula (3)_i＝L_i-1，R_i＝R_i-1Then H_i＝H_i-1Then the current symbol 0 is coded in null (or skip), L_lIs the result of the encoding.

The entropy of the sequence X is H (X) -p (0) log₂ p(0)-p(1)log₂p (1) (p (0) ═ p, p (1) ═ 1-p, p is the probability of the symbol 0 and 0 ≦ p ≦ 1), and the information entropy of the sequence Y is h (Y) ═ p (0|0) log₂ p(0|0)-p(1|0)log₂ p(1|0)-p(0|1)log₂p (0|1), h (y) h (x) because p (0|1) is 1 and p (0|0) is p, and p (1|0) is 1-p. Thus L_l＝L_nI.e. sequence Y encodes result L_lEquivalent to sequence X coding result L_n。

Encoding result L of sequence Y_lConversion to a binary sequence of length m, V ═ V₁，v₂，...，v_m) V is transmitted through a DMC (symmetric Discrete Memoryless Channel) Channel, the DMC includes four basic Channel models of BSC, BEC, AWGN (Additive white noise Channel) and rayleigh Channel, and the method mainly relates to the application of a binary erasure Channel (BEC Channel) in the DMC Channel. U ═ U₁，u₂，...，u_m) Is the received binary sequence.

As shown in fig. 3, if U ═ V, sequence U decodes sequence Q, which can restore sequence X; if U ≠ V, since the sequence U decodes the erroneous sequence X 'and the sequence X' has no data check condition, it is impossible to check the error of the sequence U. Similarly, the sequence Z cannot implement data check based on context binary arithmetic coding, and a data check coding method of the sequence Y or Z cannot be constructed based on conditional probability (or markov chain).

When y is_i-1＝1，y_iProbability P (y) of 0 and 0 of i-th symbol_iWhen p (0|1) ═ r (0 < r < 1), U ═ V, then sequence U is decoded to obtain sequence Q ═ Y; since U ≠ V, since the sequence Q must satisfy the above equation (1), it can be effectively determined that U has an error.

P(y_iP (0|1) ═ r can be understood as P (y)_i＝0)＝rp(0|1)＝r，R is called a weight coefficient of probability, and thus the weight coefficients of p (0|0) and p (1|0) are 1. When r < 1 and r → 1, the coding result L of the sequence Y_lApproaching to the sequence X coding result L_nThis conclusion is easily proven based on information entropy.

Order to

Is defined as a weighted probability. The simplest weighted probability is that the weight coefficients of all symbol probabilities are the same real number r, let y_iE.a ═ {0, 1.·, s }, the weighted cumulative distribution function is defined as:

if y_i∈{0，1}，y_iWhen F (y) is 0_i-1，r)＝rF(y_i-1)＝rp(-1)＝0；y_iWhen 1 is F (y)_i-1，r)＝rF(y_i-1) ═ rp (0). Let R₀＝1，L ₀0, the i (i) th symbol y is 1, 2, 3_iThe arithmetic expression of weighted probability arithmetic coding of (1) includes:

R_i＝R_i-1rp(y_i)

L_i＝L_i-1+R_i-1rF(y_i-1)

H_i＝L_i+R_i (5)

note that the above formula (5) includes three formulas.

The transmission rate of the DMC channel in fig. 3 is I (V; U) ═ H (V) -H (V | U). The BEC (epsilon) channel is one of the DMC channels, where epsilon represents the erasure probability of an erasure symbol. The BEC (epsilon) channel transmits symbols v epsilon {0, 1}, receives symbols

For erasure symbols, which are in the BEC (epsilon) channel, the probability of erasure is epsilon. Then p (u-0 | v-0) ═ p (u-1 | v ═ 1) ═ 1-epsilon,

the transmission rate R of the BEC (epsilon) channel can be obtained_BECH (v) -epsilon, channel capacity C_BECComprises the following steps:

C_BEC＝1-ε (6)

before introducing weighted probability arithmetic coding of a target sequence Y to obtain an input sequence V, the logic principle of weighted probability arithmetic coding is introduced:

defining 1, setting a discrete random variable y, y ∈ a { (0, 1.·, k }, P { y ═ a } ═ P (a) (a ∈ a), and weighting a probability quality function as

p (a) is a probability mass function, 0 ≦ p (a ≦ 1), r is a weight coefficient, and:

F(a)＝∑_y≤a p(y) (7)

if F (a, r) satisfies F (a, r) ═ rf (a), F (a, r) is referred to as a weighted cumulative distribution function, and is simply referred to as a weighted distribution function. It is apparent that the weighted probability sum of all symbols is

There are three basic cases for the weight coefficient r: r is more than 0 and less than 1; r is 1; r > 1 and in this case the lossless coding must have a maximum value r_max. Let r > 1, a ═ {0, 1}, the probabilities of symbol 0 and symbol 1 in sequence Y be p (0) ═ p, and p (1) ═ 1-p, respectively. Encoding y according to equation (5) above_i+1＝0，y _i+21 and y_i+3The process of 0 is shown in fig. 4.

According to FIG. 4, L_i+3＝L_i+R_ir²p²，R_i+3＝R_ir³p²(1-p)，H_i+3＝L_i+R_ir²p²+R_ir³p²(1-p). Due to y _i+10, F (-1) 0, so L_i+1＝L_i，R_i+1＝R_irp，H_i+1＝L_i+R_iAnd rp. Let H_i+3≤H_i+1The following can be obtained:

let equation ar²+ br + c ═ 0, where a ═ p (1-p), b ═ p, c ═ 1, and r > 0. The positive real number satisfying the equation is

Simplifying:

binary sequences of all 0's or all 1's are not considered and no error correction is needed, so 0 < p < 1. In decoding, the symbol y is assigned according to the above equation (5)_i+1Corresponding interval when y_i+1When 0 is defined as the interval [ L_i，L_i+R_irp) when y_i+1When 1 is the interval [ L_i+R_irp，L_i+R_ir). Then, when L is_i+3＜L_i+R_i rp time y _i+10; when L is_i+3≥L_i+R_i rp time y _i+11. Since 1-p > 0, 4(1-p)²＞0，4p²-8p+4＞0，p²-4p+4＞4p-3p²，(2-p)²＞4p-3p²，

Can obtain the product

Namely, it is

Suppose L_i+3＝L_i+R_ir²p²≥L_i+R_irp, can be obtained

R is more than 0 and less than or equal to r_maxAnd is

If this is not true, L can be obtained_i+3＝L_i+R_ir²p²＜L_i+R_irp, then y_i+1＝0。

Due to y_i+1Not equal to 0, so L_i+1＝L_i，R_i+1＝R_iAnd rp. When L is_i+3＜L_i+1+R_i+1rp time y_i+2When L is 0_i+3≥L_i+1+R_{i+ 1} rp time y _i+21. Due to L_i+1+R_i+1rp＝L_i+R_ir²p²Therefore L is_i+3＝L_i+1+R_i+1rp, then y_i+2＝1。

Due to y _i+21, so L_i+2＝L_i+1+R_i+1rF(0)＝L_i+R_ir²p²，R_i+2＝R_i+1r(1-p)＝R_ir²p (1-p). When L is_i+3＜L_i+2+R_i+2rp time y_i+3When L is 0_i+3≥L_i+2+R_i+2 rp time y _i+31. Due to L_i+2+R_i+2rp＝L_i+R_ir²p²+R_ir³p²(1-p) and R_ir³p²(1-p) > 0, so that L_i+3＝L_i+R_ir²p²＜L_i+2+R_i+2rp, then y_i+3＝0。

Theory 1, order

p is the probability of the symbol 0 in the sequence Y when

Time weighted probability arithmetic coding losslessly decodes sequence Y by V.

And (3) proving that: suppose L_i(i ≧ 1, i ∈ Z) losslessly decodable y₁，y₂，...，y_iSince the sequence Y satisfies the above formula (1), it is verified in two cases.

In the first case: y is_i1, no y is present_i+1When y is equal to 1_i+1L is obtained by encoding 0 according to the above formula (5)_i+1＝L_i，R_i+1＝R_irp because of L_i+1＝L_iTherefore L is_i+1Lossless coding y₁，y₂，...，y_i. Due to R_irp＞0，L_i+1＜L_i+R_irp, so decoded to y_i+1＝0。

In the second case: y is_iL is obtained by coding according to the above formula (5) as 0_i＝L_i-1，R_i＝R_i-1rp，L_i-1Lossless coding y₁，y₂，...，y_i. When y is_i+1L is obtained by encoding 0 according to the above formula (5)_i+1＝L_i，R_i+1＝R_irp because of L_i+1＝L_iTherefore L is_i+1Lossless coding y₁，y₂，...，y_i. Due to L_i+1＜L_i+R_irp, so decoded to y_i+1＝0。

When y is_i+1L is obtained by encoding 1 according to the above formula (5)_i+1＝L_i+R_ir²p²，R_i+1＝R_i-1r²p (1-p). Since rp < 1, L_i+1＜L_i+R_irp, decoding to y _i0. Due to y_iIs equal to 0, and L_i+1+R_i+1rp＝L_i+R_ir²p²What is, what isWith L_i+1＝L_i+1+R_i+1rp, decoding to y _i+11. When y is_i＝0，y_i+1When 1, if y can be proved_i-1Can be correctly decoded, then L can be obtained by the induction method_i+1Lossless coding y₁，y₂，...，y_i，y_i+1。

When y is_i-1＝0，y_i＝0，y_i+1L is obtained by 1-hour coding_i＝L_i-1＝L_i-2，L_i+1＝L_i-2+R_i-2r³p³. Since rp < 1, L_i+1＜L_i-2+R_i-2rp, decoding to y _i-10. When y is_i-1＝1，y_i＝0，y_i+1L is obtained by 1-hour coding_i-1＝L_i-2+R_{i- 2}rp，L_i＝L_i-1，L_i+1＝L_i+R_irp＝L_i-2+R_i-2rp+R_i-1r³p²(1-p). Obviously, L_i+1＞L_i-2+R_i-2rp, decoding to y _i-11. I.e. y_i-1Can be correctly decoded.

Let t +2( t 1, 2, 3..) symbols from the i +1 th position in the sequence Y be 0, 1,. 1, 0, where the consecutive number of symbols 1 is t. According to the above formula (5):

from H_i+t+2≤H_i+1The following can be obtained:

when in use

The method comprises the following steps:

theory 2, when the number of consecutive symbols 1 in the sequence Y is at most t

And is

Time weighted probability arithmetic coding losslessly decodes sequence Y by V.

And (3) proving that: let d be the number of consecutive symbols 1 in the sequence Y, d is greater than or equal to 0 and less than or equal to t. When d is 0, L can be obtained according to the above formula (5)_i+t+2＝L_i+t+1＝L_i+t＝…＝L_iDue to the fact

So y_i+1＝y_i+2＝…＝y _i+t+20. When d is more than or equal to 1 and less than or equal to t,

according to the above formula (5), a

When decoding, because

So L_i+d+2Can accurately decode y _i+10. Due to y_i+1Is equal to 0, so

Due to the fact that

Therefore, it is not only easy to use

L_i+d+2Can accurately decode y _i+21. When d is greater than or equal to 2

L_i+d+2Can accurately decode y _i+d+11. Due to L_i+d+2＝L_i+d+1And is

So L_i+d+2Can accurately decode y _i+d+20. When d is t +1

So y _i+11, decoding error; when d is t +1+ c (c is more than or equal to 1)

So y _i+11, decoding error. The lossless decoding sequence Y of V can be obtained when d is more than or equal to 0 and less than or equal to t. When in use

And is

Then V can be decoded without loss when d is more than or equal to 0 and less than or equal to t according to the proving steps.

In some embodiments, weighted probability arithmetic coding of the target sequence Y to obtain the input sequence V comprises the steps of:

in the encoding process, the source sequence X can be processed into Y and the sequence Y by the source for weighted probability arithmetic coding and merging, and according to fig. 3, the encoding step of the sequence X with the length of n by the sending end is as follows:

(1) initialization parameter, R₀←1，L₀Oid ← 0, p ← 0, i ← 1. Wherein R is₀Representing a coding variable R_iInitial value of, L₀Representing a coded variable L_iP represents the probability of the symbol 0 in the target sequence Y, and i represents a variable.

(2) The number of symbols 0 in the statistical sequence X is denoted c.

(3)

Where p represents the probability of symbol 0 in sequence Y and n represents the sequence length of source sequence X.

(4)

r_maxRepresents the maximum value of the weight coefficient of the weighted probability arithmetic coding.

(5) Obtaining the ith symbol X in the sequence X_i. It is noted that the process of source processing for the sequence X has been merged into the encoding step here.

(6) If x_iWhen R is equal to 0, then R_i←R_i-1r_maxp。

(7) If x_iWhen 1, then R_i←R_i-1r_max ²p (1-p) and L_i←L_i-1+R_i-1r_maxp。

(8)i←i+1。

(9) If i is less than or equal to n, repeating the steps (5) to (9).

(10) L is converted into a binary sequence V of length m. It should be noted that L here represents the sequence output after the last symbol in the sequence X is encoded.

(11) And sending the sequences V, c and n to a receiving end.

The receiving end will receive the output sequence U from the output of the binary erasure channel.

And S102, the receiving end carries out weighted probability arithmetic decoding on the output sequence to obtain a decoded sequence, wherein the weighted probability arithmetic decoding is the inverse process of weighted probability arithmetic coding.

In some embodiments, weighted probability arithmetic coding of the output sequence U (in which case the output sequence U is not necessarily identical to the input sequence V, and verification is required) to obtain the decoded sequence Q comprises the steps of:

the receiving end receives the sequences U, c and n and converts U into a real number U. According to FIG. 3, let q_iIs the ith symbol in sequence Q, l ═ 2 n-c. The decoding step at the receiving end is as follows:

(1) initialization parameter, R₀←1，L₀Section number of keys, section number, section. Where s represents the last decoded symbol.

(2)

(3)

(4)H←L_i-1+R_i-1r_maxp。

(5) And when u is larger than or equal to H and s is equal to 1, Q ← null, and the decoding is finished.

(6) When L is not less than H and s is 0, q_i←1，s←1，R_i←R_i-1r_max(1-p)，L_i←L_i-1+R_i-1r_maxp。

(7) When L < H and s ═ 1, s ← 0, R_i←R_i-1r_maxp。

(8) When L < H and s is 0, q_i←0，s←0，R_i←R_i-1r_maxp。

(9)i←i+1。

(10) If i is less than or equal to l, repeating the steps (4) to (10).

(11) Returning to the sequence Q.

Since the sequence Y satisfies the above formula (1), Q is satisfied when u.gtoreq.H in the above step (5)_iIf "11" is decoded because s is 1, U ≠ V, and the data is erroneous. The receiving end obtains a binary sequence Q (Q) through weighted probability arithmetic decoding₁，q₂，...，q_l) When the sequence Q satisfies the above formula (1), there is a probability P_errSo that Q ≠ Y, then P_errThe average decoding error probability is the average decoding error probability of the method, which will be analyzed later. When Q does not satisfy the above formula (1), Q ≠ Y is inevitable, and the embodiment of the method constructs a forward error correction method based on the binary erasure channel model in step S103.

Step S103, the receiving end compares the decoding sequence with the target sequence, and restores the information source sequence or carries out forward error correction on the decoding sequence according to the comparison result.

In some embodiments, step S103 specifically includes: comparing whether the decoding sequence Q is consistent with the target sequence Y or not, and when the decoding sequence Q is consistent with the target sequence Y, restoring an information source sequence X according to the decoding sequence Q; and when the decoding sequence Q is inconsistent with the target sequence Y, carrying out forward error correction on the decoding sequence Q until the decoding sequence Q is consistent with the target sequence Y. Because the content sent to the channel by the sending end does not contain the target sequence Y, the standard that the receiving end judges whether the decoding sequence Q is consistent with the target sequence Y is to judge whether the decoding sequence Q meets the above formula (1).

In some embodiments, the forward error correction process for BEC (epsilon) is as follows:

let e erasure symbols exist in the sequence U

Taking values as {0, 1}, and sequentially marking the e erasure symbols as

Let i be 1, 2^eTo obtain Table 1.

TABLE 1

As shown in Table 1, the ith mode assigns e erasures in the sequence USymbols, e.g. when i is 1

When i is 2

And substituting the sequence U into the weighted probability arithmetic decoding, and carrying out a decoding process again, wherein if Q is not equal to null, the forward error correction decoding is finished. The method comprises the following steps:

(1) initialization parameter, i ← 1.

(2) The e erasure symbols in the sequence U are assigned in the ith way of table 1.

(3) And substituting U into the weighted probability arithmetic coding.

(4) If i is less than or equal to 2^eAnd Q ≠ null, decoding is completed, and then the process is finished.

(5) If i < 2^eAnd Q ═ null, i ← i +1, and steps (2) to (5) are repeated.

Because 2^eAll possibilities are covered, so 2^eAt least one of the possibilities exists such that the sequence Q satisfies the above formula (1).

Information entropy, coding rate and decoding error probability and simulation experiment results of the above method embodiments are given below;

firstly, weighting probability model information entropy, coding rate and average decoding error probability;

(1) weighted probability model information entropy.

Let binary discrete memoryless information source sequence Y ═ Y₁，y₂，...，y_l)(y_iE.g., a is {0, 1}), when r is 1,

defined by shannon information entropy, the entropy of Y is:

H(X)＝-p(0)log₂ p(0)-p(1)log₂ p(1) (12)

when r ≠ 1, the definition has a probability

Random variable y of_iThe self information quantity is as follows:

I(y_i)＝-log₂ p(y_i) (13)

set of { y_iIn a } (i ═ 1, 2., l, a ∈ a), there is c_aA symbol a. The total information content of the source sequence Y when r is known is:

-c₀ log₂ p(0)-c₁ log₂ p (1)

the average amount of information per symbol is then:

definition 2, let H (Y, r) be:

after r is determined according to definition 2, the length of V after arithmetic coding by weighted probability is nH (Y, r) (bit/symbol). The weighted probability arithmetic lossless coding minimum limit is then:

and (3) proving that: according to theory 1, r_maxIs the maximum value of weighted probability arithmetic lossless coding, and r_maxIs greater than 1. When r > r_maxV cannot reduce the sequence Y, so H (Y, r)_max) Is a weighted probability arithmetic lossless coding minimum limit.

(2) Coding rate;

the amount of information carried by each bit in sequence Y is on average H (Y, r)_max) (bit/symbol) and the total information amount is lH (Y, r)_max) (bit). The total information amount of the source sequence X is nh (X) (bit), and the coding rate of weighted probability arithmetic coding can be obtained:

let the probability of symbol 0 in the binary source sequence X with length n be q (q is more than or equal to 0 and less than or equal to 1). According to the above formula (12), nh (x) ═ qn log₂ q-(1-q)n log₂(1-q). The length of sequence Y is l ═ 2-q) n, then

Theory 3 when

The weighted probability arithmetic coding rate R is 1.

And (3) proving that:

time nh (x) ═ n (bit). According to theory 2

Then

From the above formula (16):

probability mass function of symbol 0 and symbol 1 in sequence Y

And is

Theory 4 when

The weighted probability arithmetic coding rate can reach 1.

And (3) proving that: according to the above formula (17),

since q is 0. ltoreq. q.ltoreq.1, 4(1-q)²Not less than 0, then 4-8q +4q²Is more than or equal to 0. Due to 4-8q +4q²＝(3-2q)²- (5-4q) ≥ 0, so

Due to the fact that

Can obtain the product

Then

Because of the fact that

And 2-2q is more than or equal to 0,

therefore, it is not only easy to use

I.e. l tablets (Y, r)_max) -nH (X) is not less than 0

The weighted probability arithmetic coding rate can reach 1.

(3) Average decoding error probability;

let event E represent a set of sequences Q satisfying the above formula (1), and event E has f (l) sequences Y. When l is 1, E is (0, 1), f (l is 1) is 2, and the complementary event is

When l is 2, E is (00, 01, 10), f (l is 2) is 3,

when l is 3, E is (000, 001, 010, 100, 101), f (l is 3) is 5,

when l is more than or equal to 3:

f(l)＝f(l-1)+f(l-2) (18)

the probability of an available event E is:

let f (l) sequences Q in event E obey a uniform distribution, then:

thus, the probability of Q ∈ E and Q ≠ Y is:

p (Q ≠ Y | Q ∈ E) is the average decoding error probability, thus P_err＝P(Q≠Y|Q∈E)。

Theory 5, lim_l→∞P_err＝lim_l→∞(Q≠Y|Q∈E)＝0。

And (3) proving that: l → infinity is P (Y ≠ Q) → 1, and P (Y ≠ Q | Y ∈ E) → P (E) is obtained. According to FiboThat order is that F (0) is 0, F (1) is 1, and when l is greater than or equal to 2, l belongs to N^*And F (l) ═ F (l-1) + F (l-2). So that l ≧ 1, l ∈ N^*When F (l) ═ F (l) + F (l + 1). Derived from the fibonacci number polynomials:

the following can be obtained:

due to the fact that

So l → ∞ time P (E) → 0, i.e. lim_l→∞P(Q≠Y|Q∈E)＝0。

Let event F denote the set of sequences Q satisfying the above formula (2), and there are g (l) sequences Q for event F. When l is 1, F is (0, 1), g (l is 1) is 2, and the complementary event is

When l is 2, F is (01, 10, 11), g (l is 2) is 3,

when l is 3, F is (010, 101, 011, 110), F (l is 3) is 4,

when l is more than or equal to 4:

g(l)＝g(l-2)+g(l-3) (22)

obtaining:

f (l) and g (l) are both monotonicIncreasing and g (l) ≦ f (l), i.e.

According to theory 5, → ∞ time

P_errGiven as P (Q ≠ Z | Q ∈ F), lim can be obtained_l→∞ P _err0. P can be calculated from the above equations (21) and (23)_errAs in table 2.

l(bit)	P(Q≠Y|Q∈E)	P(Q≠Z|Q∈F)
			20	0.016890526	0.000443459
64	1.50584*10-6	5.9561*10-12
			112	5.75104*10-11	1.53974*10-20
256	3.20367*10-24	2.66011*10-46

TABLE 2

V, c and n are known to the receiving end according to the weighted probability arithmetic coding described above. Theory 4, lH (Y, r)_max) M is the bit length of sequence V, the probability of symbol 0 in sequence Y

And is

So H (Y, r)_max) As is known, then:

when l is substituted into the above equations (21) and (23), P (Q ≠ Y | Q ∈ E) and P (Q ≠ Z | Q ∈ F) can be obtained, and when the value of l is determined, P (Q ≠ Y | Q ∈ E) and P (Q ≠ Z | Q ∈ F) are determined, and the value of n cannot be determined.

Secondly, the channel capacity can be reached;

according to fig. 3, the sequence Y is encoded with weighted probability arithmetic into a binary sequence V, and the transmission rate I (V; U) of the DMC channel is H (V) -H (V | U), so R_BEC＝H(V)-ε。

According to theory 3, since the coding rate R is 1, the coding rate R is not equal to 1

Then

Since the symbol probabilities in sequence X are equal, h (X) is 1, and m is n. Sequence V can losslessly code sequence Y according to theoretical 2, and replacing "10" with "1" in sequence Y can losslessly restore sequence X, so sequence V can losslessly restore sequence X. H (0) H (V) 1, assuming H (V) 1, then mH (V) nH (X), not conforming to the theory of undistorted source coding, only mH (V) nH (X) time can be decoded without loss, so H (V) 1, i.e. VThe symbol probabilities are equal. Thus, the

When R is_BEC＝1-ε＝C_BEC。

According to theories 4 and 2, because R.ltoreq.1, lH (Y, R)_max) m.gtoreq.nH (X), i.e., m.gtoreq.n. When m > n, redundant information is present in the sequence V. At this time, the sequence V is subjected to lossless coding to obtain a sequence V ', and then the sequence V ' is transmitted through a DMC channel, wherein U ' is a received binary sequence. The receiving end firstly decodes U 'into U, then decodes the U into a sequence Q, if Q does not satisfy the above formula (1), Q is not equal to Y, and the receiving end can carry out forward error correction decoding on U' according to the method. Since V ' can losslessly code X, H (V ') ═ H (X) ═ 1, i.e., symbol probabilities in V ' are equal. Then R is the transmission rate I (V '; U') -H (V '| U') of the DMC channel_BSC＝1-H(ξ)＝C_BSC，R_BEC＝1-ε＝C_BEC。

Through the analysis, the data processing method based on the binary erasure channel provided by the invention is different from the coding methods such as BCH, Hamming Code, RS, CRC, LDPC, Turbo, Polar Code and the like, and a direct comparison method is difficult to find from the coding methods. Experiments prove that the coding rate can reach 1, when the code length approaches infinity, the transmission rate can reach the channel capacity by the method, the code rate is 1/2, and the method shows good performance in simulation experiments under Binary Input Additive White Noise (BIAWGN) channels.

Referring to fig. 5, an embodiment of the present invention provides a data processing method based on a binary erasure channel, where an execution main body of the method is a sending end, and the method mainly includes the following steps:

step S201, the transmitting end obtains the information source sequence.

And S202, the transmitting end performs information source processing on the information source sequence to obtain a target sequence.

And S203, the sending end carries out weighted probability arithmetic coding on the target sequence to obtain an input sequence.

Step S204, the sending end transmits the input sequence to the receiving end through the binary erasure channel to trigger the receiving end to carry out weighted probability arithmetic decoding on the output sequence output by the binary erasure channel, trigger the receiving end to compare the decoding result with the target sequence, and trigger the receiving end to restore the information source sequence or carry out forward error correction on the decoding sequence according to the comparison result, wherein the weighted probability arithmetic decoding is the inverse process of weighted probability arithmetic coding.

It should be noted that the method embodiment and the above method embodiment are based on the same inventive concept, and the execution main body of the method embodiment is a receiving end, and the execution main body of the method embodiment is a transmitting end, so that the related contents of the above embodiments are also applicable to this embodiment, and are not described again here.

An embodiment of the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor.

The processor and memory may be connected by a bus or other means.

The memory, which is a non-transitory computer readable storage medium, may be used to store non-transitory software programs as well as non-transitory computer executable programs. Further, the memory may include high speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory located remotely from the processor, and these remote memories may be connected to the processor through a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.

It should be noted that the electronic device in this embodiment may be applied to, for example, a transmitting end or a receiving end in the embodiment shown in fig. 1, the device in this embodiment can form a part of a system architecture in the embodiment shown in fig. 1, and these embodiments all belong to the same inventive concept, so these embodiments have the same implementation principle and technical effect, and are not described in detail here.

The non-transitory software programs and instructions required to implement the binary erasure channel based data processing method of the above described embodiment are stored in a memory and, when executed by a processor, perform the above described embodiment method, e.g. performing the above described method steps S101 to S103 in fig. 2 and S201 to S204 in fig. 5.

The above described terminal embodiments are merely illustrative, wherein the units illustrated as separate components may or may not be physically separate, i.e. may be located in one place, or may also be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment.

Furthermore, an embodiment of the present invention provides a computer-readable storage medium, which stores computer-executable instructions, which are executed by a processor or a controller, for example, by a processor in the terminal embodiment, and can make the processor execute the binary erasure channel-based data processing method in the above-described embodiment, for example, execute the above-described method steps S101 to S103 in fig. 2 and method steps S201 to S204 in fig. 5.

One of ordinary skill in the art will appreciate that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (10)

1. A data processing method based on a binary erasure channel is applied to a receiving end, and the data processing method comprises the following steps:

acquiring an output sequence from an output end of a binary erasure channel, wherein an input sequence corresponding to the input end of the binary erasure channel is a sequence obtained by performing weighted probability arithmetic coding on a target sequence, and the target sequence is a sequence obtained by performing information source processing on an information source sequence;

performing weighted probability arithmetic decoding on the output sequence to obtain a decoded sequence, wherein the weighted probability arithmetic decoding is the inverse process of the weighted probability arithmetic coding;

and comparing the decoding sequence with the target sequence, and restoring the source sequence or carrying out forward error correction on the decoding sequence according to a comparison result.

2. The binary erasure channel-based data processing method of claim 1, wherein the comparing the decoded sequence with the target sequence, and recovering the source sequence or performing forward error correction on the decoded sequence according to the comparison result comprises:

when the decoding sequence is consistent with the target sequence, restoring the source sequence according to the decoding sequence; and when the decoded sequence is inconsistent with the target sequence, carrying out forward error correction on the decoded sequence until the decoded sequence is consistent with the target sequence.

3. The binary erasure channel-based data processing method of claim 2, wherein said forward error correcting said decoded sequence comprises:

assigning values to erasure symbols in the output sequence, and performing the weighted probability arithmetic decoding on the output sequence assigned with the erasure symbols.

4. The binary erasure channel-based data processing method of claim 3, wherein said assigning erasure symbols in said output sequence comprises:

obtaining 2 of the erasure symbol^eArranging, wherein e represents the number of erasure symbols in the output sequence;

and selecting one arrangement mode from the 2e arrangement modes to assign values to the erasure symbols in the output sequence.

5. The binary erasure channel-based data processing method of claim 1, wherein the source sequence is subjected to source processing, comprising:

each symbol 1 in the source sequence is followed by a symbol 0.

6. The binary erasure channel-based data processing method of claim 5, wherein said comparing said decoded sequence with said target sequence comprises:

when two continuous symbols 1 appear in the coding sequence, the coding sequence is not consistent with the target sequence; when two consecutive symbols 1 do not appear in the decoded sequence, the decoded sequence is identical to the target sequence.

7. The binary erasure channel-based data processing method of claim 6, wherein the target sequence is weighted probability arithmetic coded, comprising:

making the source sequence X;

for the ith bit symbol X in X_iAnd encoding until the encoding is finished by the last X-bit symbol, wherein the encoding comprises the following steps:

when x is_iWhen R is equal to 0, then R_i＝R_i-1r_maxp; when x is_iWhen 1, then R_i＝R_i-1r_max ²p (1-p) and L_i＝L_i-1+R_i-1r_maxp, wherein r is_maxWeight coefficients representing the weighted probability arithmetic coding, the

Said p represents the probability of the symbol 0 in said target sequence, said

The n represents the sequence length of the X, the c represents the number of symbols 0 in the source sequence, and the R represents_iAnd said L_iA coding variable representing the weighted probability arithmetic coding.

8. A data processing method based on a binary erasure channel is applied to a transmitting end, and the data processing method comprises the following steps:

acquiring an information source sequence;

carrying out information source processing on the information source sequence to obtain a target sequence;

performing weighted probability arithmetic coding on the target sequence to obtain an input sequence;

and transmitting the input sequence to a receiving end through a binary erasure channel so as to trigger the receiving end to carry out weighted probability arithmetic decoding on the output sequence output by the binary erasure channel, trigger the receiving end to compare a decoding result with the target sequence, and trigger the receiving end to restore the information source sequence or carry out forward error correction on the decoding sequence according to the comparison result, wherein the weighted probability arithmetic decoding is the inverse process of the weighted probability arithmetic coding.

9. An electronic device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor when executing the computer program implements:

the binary erasure channel-based data processing method of any one of claims 1 through 7 or the binary erasure channel-based data processing method of claim 8.

10. A computer-readable storage medium having stored thereon computer-executable instructions for performing:

the binary erasure channel-based data processing method of any one of claims 1 through 7 or the binary erasure channel-based data processing method of claim 8.

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