CN105680883A - Polarization code and multi-bit even parity check code cascaded error correction coding method - Google Patents

Abstract

The invention discloses a polarization code and multi-bit even parity check code cascaded error correction coding method. The method comprises the steps: a transmitting end encoder utilizes a multi-bit even parity check code as an outer code, and utilizes a polarization code as an inner code; a receiving end decoder decodes by utilizing a modified successive cancellation list (SCL) decoding algorithm. On the aspect of error correction performance, comparing with the prior art utilizing middle-short code length non-cascaded polarization codes of the SCL decoding algorithm, the polarization code and multi-bit even parity check code cascaded error correction coding method has the advantages that frame error rate performance of a system can be remarkably improved, and a maximum likelihood bound (ML Bound), which cannot be broken through by the SCL decoding algorithm, can be remarkably broken through. On the aspect of engineering realization, according to the polarization code and multi-bit even parity check code cascaded error correction coding method, the outer code utilizes the multi-bit even parity check code, which is simple to code; the modified SCL decoding algorithm is utilized to decode, bit decision and even parity check are combined to be carried out in a decoding process, and compared with the original SCL decoding algorithm, the method provided by the invention does not increase the decoding complexity, and facilitates the engineering realization.

Description

A kind of error correction/encoding method of polarization code and the check code cascade of many bit even

Technical field

The invention belongs to Error Correction of Coding field, more specifically, belong to a kind of cascade system design promoting polarization code SCL decoding algorithm error-correcting performance, be specially a kind of polarization code and the error correction/encoding method of many bit even check code cascade.

Background technology

Polarization Coding owing to theory is perfect and has the encoding and decoding algorithm of lower complexity, is conducive to Project Realization to be widely studied after proposing as a kind of novel encoding scheme close to shannon limit. Polarization code SCL (SuccessiveCancellationList, successive elimination list) decoding algorithm propose after, simulation result shows that (L is number of paths to this decoding algorithm at lower complexity O (L Nlog (N)), N is code length) under, decoding error correcting capability can reach the error correcting capability of maximum likelihood decoder. But for adopting the short-and-medium code length non-cascaded polarization code of SCL decoding algorithm, still there is bigger gap in its error-correcting performance with shannon limit, and this gap cannot individually make up from increase number of paths. Therefore, it can the angle from cascade polarization code, promote the error-correcting performance of the SCL decoding algorithm of polarization code.

In traditional polarization code concatenated schemes, segmentation scheme (such as cascade LDPC (LowDensityParityCheck, low-density checksum) code) characteristic of concatenated code owing to obtaining is not suitable for SCL decoding algorithm, therefore, for the polarization code adopting SCL decoding algorithm, its error-correcting performance is without being obviously improved; Segmentation scheme (such as cascade CRC (CyclicalRedundancyCheck, cyclic redundancy check (CRC)) code) needs extra CRC check circuit, therefore brings certain hardware spending.

Summary of the invention

Disadvantages described above or Improvement requirement for prior art, the present invention proposes a kind of polarization code and the error correction/encoding method of many bit even check code cascade, purpose is in that to reduce encoder complexity, it is easy to Project Realization, and when without when being obviously improved decoding complexity and storage complexity, it is obviously improved polarization code error-correcting performance under SCL decoding algorithm, and this performance is substantially better than maximum likelihood decoder decoding performance.

The error correction/encoding method of a kind of polarization code provided by the invention and the check code cascade of many bit even, the cataloged procedure of the method is as follows:

Step 1 outer encoder encodes: information bit sequence carries out many bit even check code at outer encoder, obtains outer code codeword;

Step 2 outer code codeword maps: outer code codeword first to last bit is sequentially mapped to polarization code first to last on-fixed bit;

Step 3 inner encoder encodes: the on-fixed bit sequence of polarization code in step 2 is carried out polarization code coding, obtains concatenated code code word.

Improvement as technique scheme: in step 1, check bit in outer code codeword can concentrate on outer code codeword afterbody, if code length is N, information bit quantity is M, check equations quantity is K, check bit position number set is P={M+1, M+2, M+3, ..., M+K}, the element representation in set P is check bit on these bit positions of outer code, namely outer encoder coding codewordIn, bit sequenceFor information bit,For check bit.

In above-mentioned steps 1, the check bit in outer code codeword can also be distributed at outer code codeword equal intervals, if code length is N, information bit quantity is M, and check equations quantity is K, and outer code code length is M+K, and the spacing of adjacent check bit isWherein,Representing the lower integer taking x, check bit position number set is

In above-mentioned steps 1, check bit in outer code codeword can also be distributed by unequal interval in outer code codeword, namely anterior the closer to outer code codeword, check bit distribution more dispersion, more concentrate the closer to the distribution of outer code codeword afterbody check bit, according to this feature of check bit position distribution, obtain check bit position number set P.

In technique scheme, if code length is N, information bit quantity is M, and check equations quantity is K, it is assumed that the quantity concentrating on the check bit of afterbody is K₁, then the quantity of the check bit being above spacedly distributed is K-K₁, under unequal interval is distributed, the position number set of check bit is:

During described many bit even check code, check bit only verifies the bit before this bit, and unrelated with bit afterwards.

Outer code may be replaced by many bits odd check code.

The decoding of above-mentioned coded method adopts the SCL decoding algorithm revised to decode, namely bit decision is carried out according to SCL decoding algorithm during decoding information bit, during decoding check bit, carry out verification according to the court verdict of information bit in the even parity check equation at check bit place and obtain.

In general, by the contemplated above technical scheme of the present invention compared with prior art, have the advantages that

1, this programme is obviously improved polarization code error-correcting performance

Adopt the polarization code of the short-and-medium code length non-cascaded of SCL decoding algorithm, its error-correcting performance levels off to maximum likelihood decoder decoding performance, limited error recovery capability, even and if increase SCL decoding algorithm number of paths, FER performance will not be obviously improved, additionally increase number of paths and can linearly increase algorithm storage complexity and decoding complexity, be unfavorable for Project Realization. Under the SCL of same paths quantity decodes and calculates, the concatenated schemes that the present invention proposes is compared with the polarization code of non-cascaded, and the error-correcting performance of this programme promotes notable, and the error-correcting performance of this programme can substantially break through the error-correcting performance of maximum likelihood decoder.

2, this programme is without the lifting of obvious decoding complexity and storage complexity

This programme adopts the SCL decoding algorithm revised, and for original SCL decoding algorithm, it differs primarily in that: during algorithm decoding check bit, and the court verdict verification either directly through this check equations information bit obtains. Thus while need to carry out even parity check during decoding check bit, but eliminate path metric value sequence that original SCL decoding algorithm produces when decoding this class bit, the operation such as path is deleted, path duplication.Faint lifting is there is in this programme on storage complexity, namely need that to store information, the information bit of K check equations and the amount of storage of check bit positional information such as check equations corresponding to outer code on encoder with decoder respectively be faint for whole system.

3, this programme outer code coding is simple, it is easy to accomplish

This programme outer code adopts many bit even check code, and relative to the outer code scheme of other cascade, the inventive method can make the hardware circuit design of outer encoder simple, is conducive to Project Realization.

Accompanying drawing explanation

Fig. 1 is original SCL decoding algorithm schematic diagram;

Fig. 2 is the coding and decoding flow chart of the concatenated schemes that the present invention provides;

Fig. 3 is the schematic diagram that provide three kinds of the present invention determine even parity check code check bit position;

Fig. 4 is the SCL decoding algorithm schematic diagram of the correction that the present invention provides.

Detailed description of the invention

Owing to odd check code and even parity check code have identical character and error detecing capability, therefore many bit even check code of cascade of the present invention could alternatively be many bits odd check code, for the ease of this programme is illustrated, outer code all illustrates for many bit even check code herein.

In order to make the purpose of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated. Should be appreciated that specific embodiment described herein is only in order to explain the present invention, is not intended to limit the present invention. As long as just can be mutually combined additionally, technical characteristic involved in each embodiment of invention described below does not constitute conflict each other.

It is N for code length, sending information bit quantity is the polarization code of M, Polarization Coding technology is to be N number of bit channel (bitchannel) by a polarized circuit by N number of independent identically distributed channel-polarization, in this N number of bit channel, M the bit channel that channel capacity is maximum sends polarization code information bit, this bit channel is called on-fixed bit channel (unfrozenbitchannel), and the bit that on-fixed bit channel sends is also referred to as on-fixed bit (unfrozenbit); Other N-M bit channel is called fixed bit channel (frozenbitchannel), and the bit that fixed bit channel sends is called fixed bit (frozenbit).

If polarization code polarized circuit input list entries isBit u₁To u_NSending on the 1st to n-th bit channel successively, polarization code on-fixed bit channel sequence number set isFixed bit channel designator is designated as A^c, the element in set A meets as 1≤i < j≤M, a_i< a_j. then on-fixed bit sequence is designated asPolarization code fixed bit at transmitting-receiving two-end it is known that fixed bit sequenceIt is set to full 0. When known M information bit, it may be determined that on-fixed bit sequence u_A, so that it is determined that polarized circuit input list entriesPolarization code is encoded toG_NFor polarization code generator matrix.

Polarization code SCL decoding algorithm is the improvement of SC (SuccessiveCancellation, successive elimination) decoding algorithm. From bit u during the decoding of SCL decoding algorithm₁To u_NIt is sequentially carried out judgement, obtains list entriesDecoding result. SCL algorithm decoding process can retain at most the L parameter of SCL decoding algorithm (L be) bar decoding path, at decoding u_iTime, on every paths decoded go out sequenceUnique this path of sign. Original SCL decoding algorithm step is as follows:

Initialize input: i=1, number of paths L;

Step1: judge that whether i is less than or equal to N, is, then enter Step2; No, then enter Step5;

Step2: judge u_iWhether it is fixed bit, is, then enter Step3; No, then enter Step4;

Step3: by u on currently every paths_iDecision value be set to 0; I=i+1; Return Step1;

Step4: statistics current path quantity L ', current every paths is at u_iPlace can value 0 or 1, thus obtaining 2L ' bar alternative path, the metric of 2L ' paths respectively this path is at u_iThe probability of place's value 0 or 1:OrIf 2L '≤L, retain 2L ' paths; If 2L ' is > L, retain the path that L bar metric is maximum; I=i+1; Return Step1;

Step5: judgement sequence corresponding on the paths that outgoing route metric is maximum from L pathsJudgement sequenceIn on-fixed bit sequenceIt is polarization code information bit sequence decoding result;

Step6: terminate.

It is the polarization code employing SCL decoding algorithm schematic diagram of 4 if Fig. 1 is code length, wherein u₂For fixed bit, (u₁,u₃,u₄) for on-fixed bit, number of paths L=2, during decoding, at fixed bit u on every paths₂Place's judgement is 0, and other on-fixed bit then makes decisions according to path metric value.

The present invention provides a kind of polarization code and the error correction/encoding method of many bit even check code cascade, as in figure 2 it is shown, specifically include following steps:

Step 1 outer encoder encodes

Being N for code length, information bit quantity is M, and check equations quantity is the cascade system of K, then the length of outer code input information sequence is M, and the outer code codeword length of output is M+K. If the code word that outer encoder coding obtains isComprise M information bit and K even parity check bit. As it is shown on figure 3, according to the position distribution of K even parity check bit in outer code codeword, the present invention provides three kinds of methods determining check bit position:

Method one: check bit concentrates on outer code codeword afterbody. As shown in Fig. 3 (a), check bit position number set is P={M+1, M+2, M+3 ..., M+K}, the element representation in set P is check bit on these bit positions of outer code, namely outer encoder coding codewordIn, bit sequenceFor information bit,For check bit.

Method two: check bit is distributed at outer code codeword equal intervals. As shown in Fig. 3 (b), outer code code length is M+K, and the spacing of adjacent check bit isWherein,Representing the lower integer taking x, check bit position number set is

Method three: check bit is unequal interval distribution in outer code codeword. As shown in Fig. 3 (c), in method three, the feature of check bit unequal interval distribution is: anterior the closer to outer code codeword, check bit distribution more dispersion; More concentrate the closer to the distribution of outer code codeword afterbody check bit. According to this feature of check bit position distribution, obtain check bit position number set P.

In being embodied as, method three can adopt cooperative programs of said method one and method two, namely a part of check bit concentrates on afterbody, and another part check bit is spacedly distributed. Assume that the quantity concentrating on the check bit of afterbody is K₁, then the quantity of the check bit being above spacedly distributed is K-K₁, it is known that under unequal interval is distributed, the position number set of check bit is:. Work as K₁When=0, gather P₁For empty set, now method three is equivalent to method one; Work as K₁During=K, gather P₂For empty set, now method three is equivalent to method two.

Assume that the check bit location sets determined according to one of above-mentioned three kinds of methods is designated asp_jExpression jth (j=1,2,3 ..., K) individual check bit sequence number in outer code code word bits, check bitInformation bit position in the equation of place will from set S_j=1,2,3 ..., p_j-1} selects composition set T_j,Thus ensure check bit only verify this bit before bit and unrelated with the bit after this bit. Then check bitValue be: $x_{p_j}=\left(\underset{i\&Element;T_j}{\mathrm{\&Sigma;}}{x}_i\right)\mathrm{mod}2,j=\mathrm{1,2,3},...,K,$ Complete outer code coding.

Step 2 outer code codeword maps

Outer code codeword mapping refers to passes through these mapping relations bit as polarization code coding input using each bit in outer code codeword. If the on-fixed bit channel sequence number set of polarization code isFixed bit channel designator set is A^c, polarization code polarized circuit input list entries is designated asThe on-fixed bit sequence of polarization code isFixed bit value is full 0. Outer code codewordIt is mapped to on-fixed bit sequence u_AMode be: first bit x of outer code codeword₁To last bit x_M+KIt is sequentially mapped to first bit of on-fixed bit sequenceTo last bitNamely meetOr $u_A=x_1^{M+K}.$

By after mapping it can be seen that on-fixed bit channel a_P={ a_i| i ∈ P} is sent as the check bit of outer code; On-fixed bit channelOn be sent as outer code jth, (j=1 ..., K) individual check bit; On-fixed bit channelOn be sent as the information bit of outer code jth check equations.

Step 3 inner encoder encodes

ISN polarization code on-fixed bit sequence is obtained by step 2Polarization code fixed bit sequence is full 0, thus known polarization code polarized circuit input list entriesFormula is encoded, thus the code word that can obtain cascade system coding is according to polarization codeWherein G_NFor polarization code generator matrix.

Step 4 receiving terminal decodes

Cascade system decoder adopts the SCL decoding algorithm revised. Main correction: during decoding check bit, carry out verification according to the court verdict of information bit in the even parity check equation at check bit place and obtain, rather than make decisions according to the probability in original SCL decoding algorithm.

Concrete decoding procedure is as follows:

Initialize input: i=1, number of paths L;

Step1: judge that whether i is less than or equal to N, is, then enter Step2; No, then enter Step7;

Step2: judge u_iWhether it is fixed bit, is, then enter Step3; No, then enter Step4;

Step3: by u on currently every paths_iDecision value be set to 0; I=i+1; Return Step1;

Step4: judge u_iWhether it is check bit, is, then enter Step5; No, then enter Step6;

Step5: u on current every paths_iDecision value obtained by the information bit verification of judgement on this path: ${\hat{u}}_i=\left(\underset{k\&Element;a_{T_j}}{\mathrm{\&Sigma;}}{\hat{u}}_k\right)\mathrm{mod}2,i=i+1;$ Return Step1;

Step6: statistics current path quantity L ', current every paths is at u_iPlace can value 0 or 1, thus obtaining 2L ' bar alternative path, the metric of 2L ' paths respectively this path is at u_iThe probability of place's value 0 or 1:OrIf 2L '≤L, retain 2L ' paths; If 2L ' is > L, retain the path that L bar metric is maximum; I=i+1; Return Step1;

Step7: judgement sequence corresponding on the paths that outgoing route metric is maximum from L paths

Step8: terminate.

In decoding resultIn,It is outer code codeword decoding result, order setThenIt is the information bit decoding result of transmission.

It is the concatenated code of 4 that Fig. 4 show one code length of this programme, and check equations isAdopting the SCL (number of paths L=2) revised to carry out the schematic diagram decoded, as seen from the figure, two paths are at decoding u₃During bit, the direct basis of decision value of this bitCheck results obtain, and path metric value according to SCL decoding algorithm does not make decisions.

With an embodiment, the inventive method is described below, specific as follows.

Embodiment:

The embodiment of the present invention is, concatenated code code length is N=512, information bit quantity is M=240, the quantity of check equations is K=16, thus the quantity of known ISN polarization code on-fixed bit channel is 256, the quantity of fixed bit channel is 256, carries out polarization code structure under 2dB, respectively obtains the sequence number set of on-fixed bit channelSet A with fixed bit channel designator^c. receiving terminal decoder adopts the SCL decoding algorithm revised, and number of paths is set to L=32.

Step 1 outer encoder encodes

Information bit quantity is 240, and check equations quantity is 16, then outer code code length is 256, and note outer code codeword isThree kinds of methods that check bit position number set P according to the above description determines in conjunction with the embodiments, obtain set P as follows successively:

Method one, check bit concentrates on outer code codeword afterbody. This shows in outer codeBit in, rear 16 bits, namelyFor even parity check bit; Front 240 bits, namelyFor information bit, then gather P={241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256}.

Method two, check bit is distributed at outer code codeword equal intervals. This shows in outer codeBit in, x_1×16, x_2×16, x_3×16..., x_16×16For check bit, all the other 240 bits are information bit, then gather P={16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256}.

Method three, check bit is unequal interval distribution in outer code codeword. Assume, in unequal interval is distributed, to concentrate on the quantity K of the check bit of afterbody₁=8, the check bit quantity being above spacedly distributed is K-K₁=8, this shows in outer codeBit in, x_1×31, x_2×31, x_3×31..., x_8×31, x₂₄₉, x₂₅₀, x₂₅₁..., x₂₅₆For check bit, all the other 240 bits are information bit, in conjunction with this example, then gather P={31,62,93,124,155,186,217,248,249,250,251,252,253,254,255,256}.

For the set P that method two obtains, the determination of information bit position in each check equations and the coding of each even parity check equation are described.

Known P={16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256}, namely the check bit of first check equations is x₁₆, in the equation, the position of information bit will from set S₁=1,2,3 ... and in select, gather S₁In element choose whether to participate in this check equations according to probability α=0.5, thus obtaining first check equations information bit location sets is T₁=6,8,10,11}, therefore first check bit x₁₆Coding formula as follows:

$x_{16}=x_6\&CirclePlus;x_8\&CirclePlus;x_{10}\&CirclePlus;x_{11}---\left(1\right)$

May determine that the value of other 15 check bits in the manner described above, thus completing outer code coding.

Step 2 outer code codeword maps

The code word that known outer encoder obtains isPolarization code on-fixed bit channel set is A={a₁,a₂,a₃,...,a₂₅₆, by code wordThe 1st to 256 bits be sequentially mapped to the 1st to 256 on-fixed bits of polarization code, then polarization code on-fixed bit sequence is

It can be seen that on-fixed bit channel a after mapping_P={ a_i| i ∈ P} sends the check bit of outer code; On-fixed bit channelOn be sent as outer code jth, (j=1 ..., 16) individual check bit; On-fixed bit channelOn be sent as the information bit of outer code jth check equations.With method two obtain P={16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256} for example, then a_P={ a_i| i ∈ P}={a₁₆,a₃₂,a₄₈,a₆₄,a₈₀,a₉₆,a₁₁₂,a₁₂₈,a₁₄₄,a₁₆₀,a₁₇₆,a₁₉₂,a₂₀₈,a₂₂₄,a₂₄₀,a₂₅₆, send outer code check bit; On-fixed bit channelThe 1st check bit of upper transmission outer code; On-fixed bit channelThe information bit of upper the 1st check equations of transmission outer code. Can obtain successivelyEtc. situation.

Step 3 inner encoder encodes

ISN polarization code on-fixed bit sequence is obtained by step 2Polarization code fixed bit sequence is full 0, thus known polarization code polarized circuit input list entriesFormula is encoded, thus the code word that can obtain cascade system coding is according to polarization codeWherein G_NFor polarization code generator matrix.

The decoding of step 4 cascade system

The decoding of cascade system adopts the SCL decoding algorithm revised, and this algorithm differs primarily in that with original SCL decoding algorithm, and during decoding check bit, check bit decision value directly carries out verification according to the information bit decision value of this check equations and obtains. For first check equations, when 32 paths are decoded toDuring bit, forThe judgement of bit then carries out verification according to the decision value of information bit in first check equations and obtains, and concrete formula is as follows:

${\hat{u}}_{a_{16}}={\hat{u}}_{a_6}\&CirclePlus;{\hat{u}}_{a_8}\&CirclePlus;{\hat{u}}_{a_{10}}\&CirclePlus;{\hat{u}}_{a_{11}}---\left(2\right)$

And for the bit decision on the on-fixed bit channel outside set P, then the decoding principle according to SCL decoding algorithm makes decisions. According to the SCL decoding algorithm of this correction, such that it is able to obtain the decoding result of concatenated codeIn decoding resultIn,It is outer code codeword decoding result, order setThenIt is the information bit decoding result of transmission.

Those skilled in the art will readily understand; the foregoing is only presently preferred embodiments of the present invention; not in order to limit the present invention, all any amendment, equivalent replacement and improvement etc. made within the spirit and principles in the present invention, should be included within protection scope of the present invention.

Claims (9)

1. an error correction/encoding method for polarization code and the check code cascade of many bit even, the cataloged procedure of the method is as follows:

Step 1 outer encoder encodes: information bit sequence carries out many bit even check code at outer encoder, obtains outer code codeword;

Step 2 outer code codeword maps: outer code codeword first to last bit is sequentially mapped to polarization code first to last on-fixed bit;

Step 3 inner encoder encodes: the on-fixed bit sequence of polarization code in step 2 is carried out polarization code coding, obtains concatenated code code word.

2. the error correction/encoding method of polarization code as claimed in claim 1 and the check code cascade of many bit even, it is characterised in that in step 1, check bit in outer code codeword concentrates on outer code codeword afterbody, if code length is N, information bit quantity is M, check equations quantity is K, check bit position number set is P={M+1, M+2, M+3, ..., M+K}, the element representation in set P is check bit on these bit positions of outer code, namely outer encoder coding codewordIn, bit sequenceFor information bit,For check bit.

3. the error correction/encoding method of polarization code as claimed in claim 1 and the check code cascade of many bit even, it is characterized in that, in step 1, check bit in outer code codeword is distributed at outer code codeword equal intervals, if code length is N, information bit quantity is M, and check equations quantity is K, outer code code length is M+K, and the spacing of adjacent check bit isWherein,Representing the lower integer taking x, check bit position number set is

4. the error correction/encoding method of polarization code as claimed in claim 1 and the check code cascade of many bit even, it is characterized in that, in step 1, check bit in outer code codeword is unequal interval distribution in outer code codeword, namely anterior the closer to outer code codeword, check bit distribution more dispersion, more concentrate the closer to the distribution of outer code codeword afterbody check bit, according to this feature of check bit position distribution, obtain check bit position number set P.

5. the error correction/encoding method of polarization code as claimed in claim 4 and the check code cascade of many bit even, it is characterised in that setting code length as N, information bit quantity is M, and check equations quantity is K, it is assumed that the quantity concentrating on the check bit of afterbody is K₁, then the quantity of the check bit being above spacedly distributed is K-K₁, under unequal interval is distributed, the position number set of check bit is:

6. the error correction/encoding method of polarization code as claimed in claim 1 and the check code cascade of many bit even, it is characterised in that during described many bit even check code, check bit only verifies the bit before this bit, and unrelated with bit afterwards.

7. such as the error correction/encoding method of the polarization code as described in arbitrary in claim 1 to 6 and the check code cascade of many bit even, it is characterised in that outer code replaces with many bits odd check code.

8. the error correction/encoding method of polarization code as described in claim 1 to 6 and the check code cascade of many bit even, it is characterized in that, the decoding of the method adopts the SCL decoding algorithm revised to decode, namely bit decision is carried out according to SCL decoding algorithm during decoding information bit, during decoding check bit, carry out verification according to the court verdict of information bit in the even parity check equation at check bit place and obtain.

9. the error correction/encoding method of polarization code as claimed in claim 8 and the check code cascade of many bit even, it is characterised in that the detailed process of described decoding is:

Initialize input: i=1, number of paths L;

Step1: judge that whether i is less than or equal to N, is, then enter Step2; No, then enter Step7;

Step2: judge u_iWhether it is fixed bit, is, then enter Step3; No, then enter Step4;

Step3: by u on currently every paths_iDecision value be set to 0; I=i+1; Return Step1;

Step4: judge u_iWhether it is check bit, is, then enter Step5; No, then enter Step6;

Step5: u on current every paths_iDecision value obtained by the information bit verification of judgement on this path:I=i+1; Return Step1;

Step6: statistics current path quantity L ', current every paths is at u_iPlace can value 0 or 1, thus obtaining 2L ' bar alternative path, the metric of 2L ' paths respectively this path is at u_iThe probability of place's value 0 or 1:OrIf 2L '≤L, retain 2L ' paths; If 2L ' is > L, retain the path that L bar metric is maximum; I=i+1; Return Step1;

Step7: judgement sequence corresponding on the paths that outgoing route metric is maximum from L paths

Step8: terminate.