CN105515590A - Successive cancellation list polarization code decoding algorithm with effective low complexity based on random binary data flows and decoding structural frame thereof - Google Patents

Successive cancellation list polarization code decoding algorithm with effective low complexity based on random binary data flows and decoding structural frame thereof Download PDF

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CN105515590A
CN105515590A CN201510907710.7A CN201510907710A CN105515590A CN 105515590 A CN105515590 A CN 105515590A CN 201510907710 A CN201510907710 A CN 201510907710A CN 105515590 A CN105515590 A CN 105515590A
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CN105515590B (en
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张川
梁霄
尤肖虎
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Southeast University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes

Abstract

The invention discloses a successive cancellation list polarization code decoding algorithm with effective low complexity based on random binary data flows and a decoding structural frame thereof. The algorithm comprises the steps of converting received vectors to be decoded into corresponding input probability values through a channel message scaling algorithm; generating corresponding random binary data flows from the computed input probability values, and respectively inputting the data flows into two basic disk-type decoding frames; obtaining the conditional probability values of decoding through computing the data flows by the mixed node of the two basic disk-type decoding frames; working out the conditional probability random data flows of four paths by a phase inverter; obtaining the final judgment of the path probabilities through allowing the four condition probabilities to pass through an AND gate; through the computation of a feedback module, integrating signals, feeding back into the basic disk-type frames, allowing the data flows to pass through the basic disk-type decoding frames for the second time, and thereby obtaining the conditional probability values; and obtaining the optimal path decoding result. According to the algorithm provided by the invention, the complexity of the system is reduced, and meanwhile the random data flow decoding performance is improved.

Description

List polarization code decoding algorithm and decoding framework thereof are offset in a kind of effective low complex degree serial based on random binary data stream
Technical field
The present invention relates to the efficient coding of coding techniques polarization code, be specially a kind of ground complexity serial being applicable to polarization code and offset list decoding and decoding framework thereof.
Background technology
propose, polar code is the first kind of chnnel coding, almost can realize the capacity (B-DMCs) of symmetrical binary system input discrete memoryless channel(DMC).Because its lower computation complexity is O (NlogN), wherein N is polarization code length; And the decoding architecture of fast Fourier transform FastFourierTransformation (FFT) form, decoding successivecancellation (SC) algorithm is offset in serial has become one of the decoding algorithm that the most effectively polarizes.But compared to maximum likelihood maximumlikelihood (ML) decoder, the decoding performance that decoder is offset in serial still has larger decline.In order to reduce the performance gap brought by the suboptimum Path selection of traditional serial counteracting decoder, list serial is offset decoding algorithm (listSCpolardecoder) and is arisen at the historic moment.After adding list (L), bring the chance of more Path selection.Simulation result shows, list SC pole decoder can surmount the error rate of famous LDPC code.
The major defect that list decoding device is offset in serial is that, along with the increase of list L size, the complexity of decoder linearly increases.In other words, in order to realize better performance, list decoding device is offset in serial must suffer greatly hardware cost, particularly when list L is sizable time.In addition, for the application scenarios of some height noise, list decoding device noise resisting ability deficiency is offset in existing serial.In order to solve the problem, the present invention proposes the polarity decoding algorithm based on random binary data stream, namely introduce random data stream as arithmetic core.Have benefited from the advantage of random decoding, list decoding device is offset in serial can reach good bit error rate performance, reduces complexity and fault-tolerance.But directly application offsets list decoding device based on the serial of random data stream in practice, due to the continuous loss of random sequence randomness in computing, will cause the degradation of decoding performance.In the present invention, a kind of " the double scheme of probability " DPA (DoublingProbabilityApproach) is proposed, to improve decoding performance.Give the corresponding hardware structure of above-mentioned decoding algorithm simultaneously.
Summary of the invention
For above-mentioned the deficiencies in the prior art, the object of this invention is to provide a kind of effective low complex degree serial based on random binary data stream and offset list polarization code decoding algorithm and decoding framework thereof, to reduce the complexity of whole system, improve the performance of random data stream decoding simultaneously.
For achieving the above object, the present invention is by the following technical solutions:
A list polarization code decoding algorithm is offset in effective low complex degree serial based on random binary data stream, comprises the following steps:
(1) the to be decoded vectorial y will received i=(y 1..., y n) by changing corresponding input probability into after channel massage convergent-divergent algorithm value, wherein α is channel zoom factor, and e is natural number constant, and N is polarization code code length; (2) input probability value corresponding for the N number of code word calculated is generated by CPU the random binary data stream that length corresponding to N group is 1024, namely each probable value random binary data stream that length is 1024 represents; This N group data stream step-by-step is input to respectively the input of two basic dish-shaped decoding frameworks of decoding framework, the input data of two framings are identical;
(3) data flow is by two groups of log 2obtain after the calculating of the basic dish-shaped decoding framework mixed node of N level the conditional probability value of decoding with
(4) the conditional probability random data stream of four paths is calculated by inverter with
(5) four conditional probabilities are realized finally differentiating path probability with door respectively by one;
P ( u ^ 1 i ) = P ( u ^ 1 i - 1 ) p ( u i = u ^ i | u ^ 1 i - 1 ) Circulation tire out multiplication:
By four probable values obtained two optimal paths corresponding to two maximums are chosen by sequence;
Result is passed into " in the double module of probability " and carry out overall probability amplification, and store routing footpath by memory;
By corresponding for two selected paths value feed back in this step with door input, wait for lower one deck four set condition probability arrival, constantly circulation is tired takes advantage of;
(6) by the calculating of feedback module, i decoding value in two paths selected is integrated into a signal by certain rule, feeds back in basic dish-shaped framework, data flow again by basic dish-shaped decoding framework, and obtains the conditional probability value of code with
(7) repeat above-mentioned steps (4), (5) and (6), until N number of code word has all been translated, thus obtain optimal path decode results u ^ 1 N = ( u ^ 1 , ... , u ^ N ) .
A kind of based on random binary data stream list serial counteracting decoding framework, it comprises two basic dish-shaped decoding frameworks, and two basic dish-shaped decoding frameworks connect list nucleus module respectively; Also comprise two inverters, two inverters are parallel in the connection line of two basic dish-shaped decoding frameworks and list nucleus module respectively; Table nucleus module is connected with feedback module.
Described basic dish-shaped decoding framework contains N-1 mixed node module, and this N-1 node module is divided into log 2n level 2 × 1 form, this framework is connected with one for providing the external feedback module of allotment information.
Described mixed node module is owing to using binary data stream as deal with data, mixed node module is single-bit computing herein, described mixed node module comprises a single input and door, one two input or door, one two input not gate, one two input XOR gate, a JK flip-flop, two two input data selectors, wherein, the input input random data stream of two input XOR gate, output connects the input of the two or two input data selector; The input input random data stream of two input not gates, exports the input of termination the or two input data selector; The input termination random data stream of the one or two input data selector, output distinguishes order input and door and two inputs or the input of door; Single input and door and two input or the input of door all connects random data stream, and single input and door and two input or the output of door all connects the input of JK flip-flop; Output termination the two or two input data selector of JK flip-flop.
Described list nucleus module comprises 4 and door, and 4 are connected with order module with Men Jun, and order module connects the double module of probability, and probability double model calling memory memory module, memory memory module connects described 4 and door respectively.
The invention has the beneficial effects as follows:
Invention introduces random binary data stream offsets decoding calculating core as polarization code list serial, such operation, by originally parallel Data Computation Unit, has changed the unit by single-bit and single-bit probabilities data-flow computation into.Reduce the complexity of whole system largely.By " channel massage scalable scheme " ChannelMessageScaling (CMS), (DoublingProbabilityApproach significantly improves the performance of random data stream decoding with " probability is double " DPA simultaneously.Specific as follows:
(1) instead of the rate of specific gravity in traditional SC decoding by the probabilistic information representated by random binary data stream, computing between ingenious utilization bit, reduces the hardware complexity of whole system largely.The complexity of tradition SC decoder is O (10qN), and complexity of the present invention is O (7LN), and wherein q gets 10, L usually for quantification length is that list length gets 1 or 2 herein, and N is polarization code length;
(2) by " channel massage scalable scheme " ChannelMessageScaling (CMS), (DoublingProbabilityApproach significantly improves the performance of random data stream decoding with " probability is double " DPA in the present invention;
(3) quantize length q in the present invention larger, the length of binary data stream is larger, and result of calculation is more accurate, and corresponding time delay is longer.And the Modulatory character of random binary data stream length is strong, data flow length can according to accuracy allotment needed for system, and not influential system framework.
(4) the present invention gives the detailed effective low complex degree serial based on random binary data stream simultaneously and offsets list polarization code decoding algorithm, has built complete hardware architecture platform according to this algorithm design simultaneously.
Accompanying drawing explanation
Fig. 1 is the performance of BER contrast in 64 bit polarization code decodings under different α ∈ [0,1] value;
Fig. 2 is the error bit ability comparison diagram of random data stream SC decoding when using traditional SC decoding, directly random data stream SC decoding and channel to be scaled 0.5 respectively;
Fig. 3 is list length when being 2, and the decoding path based on random binary data stream selects schematic diagram;
The bit error rate comparison diagram that Fig. 4 is random data stream decoding after " probability is double " DPA (DoublingProbabilityApproach) and traditional SC decoding performance;
Fig. 5 to be list length be 2 offset decoding framework based on random binary data stream list serial;
Fig. 6 is the basic dish-shaped decoding framework of 8bit polarization code decoding based on random binary data stream;
Fig. 7 is the framework map of mixed node module;
Fig. 8 is the frame diagram of list nucleus module.
Embodiment
Below in conjunction with accompanying drawing, the present invention is further described.
1, the list serial based on random binary data stream offsets polarization code decoding algorithm, wherein list length L=1
1) traditional SC decoder algorithms
Consider a polarization code (N, K, A), wherein N represents the code length of polarization code, and K represents effective information number in polarization code, and A represents effective information bit set.If the vector to be decoded that receiving terminal receives is y i=(y 1..., y n), the decode results of receiving terminal is expressed as if u ibe not effective information bit, we will zero setting.Otherwise decoding bit can be expressed as:
u ^ i = 0 , i f - W N ( i ) ( y 1 N , u ^ 1 i - 1 | 0 ) &GreaterEqual; W N ( i ) ( y 1 N , u ^ 1 i - 1 | 1 ) , 1 , i f - W N ( i ) ( y 1 N , u ^ 1 i - 1 | 0 ) < W N ( i ) ( y 1 N , u ^ 1 i - 1 | 1 ) ,
Wherein, define transmission probability.Traditional SC decoder completes decoding by two basic computational ele-ment and calculates, and is referred to as f node unit and g node unit.The computing formula of these two nodes is:
f ( a , b ) = 1 + a b a + b
g ( a , b , u ^ s u m ) = a 1 - 2 u ^ s u m b
Wherein a and b represents two the input data entering each node calculate.
Traditional SC decoder meets FFT dish decoding rule.
2) based on the SC decoder algorithms of random binary data stream
Be different from the operating basis that traditional SC decoder uses rate of specific gravity to decode as decoding, the present invention introduces random binary data stream to carry out decoding calculating.First the computing formula between rate of specific gravity is revised as the computing formula on corresponding probability, then represents these probability by the form of random binary data stream.
Random binary data stream representation is as follows: utilize CPU to generate the binary system random data stream agreeing to length.Wherein the number proportion of bit " 1 " is corresponding probable value.Herein because data flow has randomness, still only know the corresponding proportion of bit in data flow " 1 ", but do not know its particular location.That is the random binary data stream of an expression probability is not unique.Table 1 gets 10 for data flow length, gives several different situations that probability is expressed as 0.6:
Table 1
Decoding in the present invention calculates based on probability, therefore decoding formula is rewritten as following form: wherein represent
p ( u i = u ^ i | u ^ 1 i - 1 ) = W N ( i ) ( y 1 N , u ^ 1 i - 1 | u i = u ^ i ) &Sigma; u i &Element; { 0 , 1 } W N ( i ) ( y 1 N , u ^ 1 i - 1 | u i )
Wherein representative differentiates decode results conditional probability, the probability calculation expression formula of again pushing over above-mentioned f node and g node is in this case as follows:
Pr f＝Pr a(1-Pr b)+Pr b(1-Pr a)
Pr g = ( 1 - Pr a ) Pr b Pr a ( 1 - Pr b ) + ( 1 - Pr a ) Pr b
Wherein Pr awith Pr brepresent the input probability value in cell node calculating, Pr fwith Pr grepresent the output probability value in cell node calculating.But the bit conditional probability that can only be obtained by the dish-shaped computing framework of these two formula compositions in differentiation but the bit probabilities of final decoding can not be obtained the bit probabilities formula of final decoding is as follows:
P ( u ^ 1 i ) = P ( u ^ 1 i - 1 ) p ( u i = u ^ i | u ^ 1 i - 1 )
When list size L is 1 time, owing to not needing to carry out the comparison between each path, so conditional probability herein can directly as final decoding bit probabilities, and not need to do tired multiplication.
3) " channel massage scalable scheme " ChannelMessageScaling (CMS)
Due in the region that signal to noise ratio is high, the channel information of binary data stream representative will cause the weak of its random nature.If so directly adopt random binary data stream to replace traditional rate of specific gravity to carry out decoding calculating, although save hardware resource largely, the bit error rate curve performance of decoding differs greatly relative to traditional SC decoding.In the present invention, employing " channel massage scalable scheme " ChannelMessageScaling (CMS) improves the decoding performance in random data stream scheme to a certain extent.
Receiving terminal vector y ioriginal channel likelihood ratio can be expressed as LR (y i)=4y i/ N 0, wherein N 0it is the monolateral noise power of system." channel massage scalable scheme " introduces a channel zoom factor α ∈ [0,1], then new channel likelihood ratio can be expressed as:
LR′(y i)＝αN 0LR(y i)＝4αy i
The channel likelihood ratio LR ' (y of new reception vector i) for generation of being applicable to the most initial input probability value representing probability in the present invention with binary data stream, formula is as follows:
Pr ( y i = 1 ) &ap; 1 e - LR &prime; ( y i ) + 1 = 1 e - 4 &alpha;y i + 1
Channel zoom factor is the real number in α ∈ [0,1] interval, and the Rational choice of this coefficient has had influence on the quality of decoding performance.Fig. 1 gives the contrast of the performance of BER in 64 bit polarization code decodings under different α ∈ [0,1] value, and wherein choosing random data stream length is 1024.When can find out α=0.5, gain is maximum, best performance.
Therefore employing channel zoom factor is the SC decoding based on binary system random data stream of 0.5 in the present invention.The error bit ability comparison diagram of random data stream SC decoding Fig. 2 uses traditional SC decoding, directly random data stream SC decoding and channel to be scaled 0.5 respectively under giving different polarization code length situation time.
2, the list serial based on random binary data stream offsets polarization code decoding algorithm, wherein list length L=2
1) based on the list SC decoder algorithms of random binary data stream
When list length is greater than 1, will select in every one deck 2L path candidate, optimum L paths, we can not again by conditional probability herein directly as the foundation of Path selection, but will according to final bit probabilities carry out preferentially path selection.
Fig. 3 gives when list length is 2, and the decoding path based on random binary data stream selects schematic diagram.In figure represent the conditional probability of the jth paths of i-th layer of bit decision.Often adjudicate one deck downwards, need to tire out and take advantage of new conditional probability.Two path candidates are obtained at ground floor with four path candidates are obtained at the second layer P 1 2 = p 1 1 p 1 2 = p ( u 2 = 0 | u 1 = 0 ) , P 2 2 = p 1 1 p 2 2 = p ( u 2 = 1 | u 1 = 0 ) , P 3 2 = p 2 1 p 3 2 = p ( u 2 = 0 | u 1 = 1 ) With P 4 2 = p 2 1 p 4 2 = p ( u 2 = 1 | u 1 = 1 ) , In the final bit probability values of this four paths, select two optimum probabilities, two optimal paths (as shown in black surround) the most, and abandon two poor paths (as shown in grey frame); The downward one deck of continuity selected path differentiates, from four path candidates, still select preferably two relatively; By that analogy, until calculate n-th layer, in four path candidates, select optimal path this decode results the most.
2) " probability is double " DPA (DoublingProbabilityApproach)
Increase the size of list L, being the selection in order to increase sub-optimal path in essence, avoiding optimal decoding result not in every one deck decoding, to be all in optimal decoding state.The decoding performance of L=2 has remarkable lifting than the identical decoding performance arranging lower L=1 in theory, but we do not see expected result in simulations.This is owing to having related to when calculating path judges probable value tired multiplication.Due to the probable value herein related to be all be less than 1 number, so arrived by constantly tired multiplied be one much smaller than 1 minimum number.Due to probable value too small, the probable value accuracy represented by random binary data stream obtains challenge.Result in overall error bit ability and not fully up to expectations.
The present invention adopts " probability is double " DPA (DoublingProbabilityApproach) to promote random performance in calculating is lost.Because Path selection is each time all that probable value in same layer compares, as long as therefore retain its relative size information, do not need absolute size information.When owning in same layer when value is all less than 0.5, the probable value of one deck is all carried out double process by unification of the present invention, and as new bring lower one deck into continue to calculate.Specific algorithm is expressed as follows:
Fig. 4 gives the bit error rate comparison diagram of the random data stream decoding after " probability is double " DPA (DoublingProbabilityApproach) and traditional SC decoding performance, wherein random binary data stream length is can find out in 1024. figure, and DPA algorithm effectively improves the decoding algorithm performance based on random binary data stream.Decoding algorithm performance boost of the present invention has been arrived on traditional SC algorithm performance.
Concrete operations of the present invention are as follows:
Fig. 5 give list length be 2 offset decoding framework based on random binary data stream list serial.It comprises two basic dish-shaped decoding frameworks, and the output of these two frameworks is with two basic dish-shaped decoding frameworks connect list nucleus module respectively; Also comprise two inverters, two inverters are parallel in the connection line of two basic dish-shaped decoding frameworks and list nucleus module respectively; Table nucleus module is connected with feedback module.Realize binary system random data stream probability get complementary operation by adding two inverters, thus obtain with represent that the random data stream of probability passes into list nucleus module by these four groups, from four paths, preferentially choose two optimal solutions, path N1 and N2. translates to obtain code element by feedback module in two paths calculating, feed back to basic dish-shaped decoding framework, thus provide four paths of code value, and screen.From husband's above-mentioned steps until N bit polarization code has all been translated.
Fig. 6 gives the basic dish-shaped decoding framework based on random binary data stream of 8bit polarization code decoding.Wherein contain 7 mixed node modules (namely needing N-1 mixed node module) in basic dish-shaped framework square frame, these 7 modules are divided into 3 grades and (are namely divided into log 2n level) 2 × 1 forms.This framework also needs an external feedback module to provide allotment information, and it is good by decoding fed back in basic dish-shaped framework by the combination of certain rule, thus crack next code value this is the process of a continuous loop iteration.The complexity of this module is O (7N), and under same case, the dish-shaped basic framework complexity of traditional SC decoding is O (10qN), and wherein q is for quantizing length, and random binary data stream length corresponding is with it 2 q.
Fig. 7 gives the framework map of mixed node module.In dish-shaped data flow trend due to decoding herein, f node is consistent with the computing framework of g node, therefore the new probability formula of this module foundation f node and g node designs, and has merged the function of f node and g node two computing formula.Select to export different probability data stream by damping factor k, namely export f node calculate result during k=0, during k=1, export g node calculate result.Mixed node module is owing to using binary data stream as deal with data, mixed node module is single-bit computing herein, described mixed node module comprises a single input and door, one two input or door, one two input not gate, one two input XOR gate, a JK flip-flop, two two input data selectors, wherein, the input input random data stream of two input XOR gate, output connects the input of the two or two input data selector; The input input random data stream of two input not gates, exports the input of termination the or two input data selector; The input termination random data stream of the one or two input data selector, output distinguishes order input and door and two inputs or the input of door; Single input and door and two input or the input of door all connects random data stream, and single input and door and two input or the output of door all connects the input of JK flip-flop; Output termination the two or two input data selector of JK flip-flop.
Fig. 8 gives the frame diagram of list nucleus module.List nucleus module comprises 4 and door, and 4 are connected with order module with Men Jun, and order module connects the double module of probability, and probability double model calling memory memory module, memory memory module connects described 4 and door respectively.Achieved with door by one the tired multiplication of circulation.By four probable values obtained two optimal paths corresponding to two maximums are chosen by sequence.Result is passed into " in the double module of probability " and carry out overall probability amplification, and store routing footpath by memory.
This framework concrete operations flow process is as follows:
I. the to be decoded vectorial y will received i=(y 1..., y n) by changing corresponding input probability into after channel massage convergent-divergent algorithm value, wherein α is channel zoom factor;
Ii. the input probability value calculated is generated by CPU the random binary data stream that corresponding length is 1024, this N group data stream step-by-step is input to respectively the input (the input data of two framings are identical) of two basic dish-shaped decoding frameworks of Fig. 6 decoding framework;
Iii. data flow is by two groups of log 2obtain after the calculating of the basic dish-shaped decoding framework mixed node of N level the conditional probability value of decoding with
Iv. the conditional probability random data stream of four paths is calculated by inverter with
V. four conditional probabilities are realized finally differentiating path probability with door respectively by one
circulation tire out multiplication.By four probable values obtained two optimal paths corresponding to two maximums are chosen by sequence.Result is passed into " in the double module of probability " and carry out overall probability amplification, and store routing footpath by memory.By corresponding for two selected paths value feed back in this step with door input, wait for lower one deck four set condition probability arrival, constantly circulation is tired takes advantage of;
Vi. by the calculating of feedback module, i decoding value in two paths selected is integrated into a signal by certain rule, feeds back in basic dish-shaped framework, data flow again by basic dish-shaped decoding framework, and obtains the conditional probability value of code with
Vii. above-mentioned steps IV, step V and step VI is repeated, until N number of code word has all been translated.Thus obtain optimal path decode results u ^ 1 N = ( u ^ 1 , ... , u ^ N ) .
It is 10 that table 2 gives quantification length q, when corresponding random binary data stream length l is 1024, and the hardware resource consumption that the complexity of three kinds of schemes and 8bit decode.(quantize length q larger, the length of binary data stream is larger, and result of calculation is more accurate, and corresponding time delay is longer.And the Modulatory character of data flow length is strong, data flow length can according to accuracy allotment needed for system, and not influential system framework.)
Table 2
The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (5)

1. a list polarization code decoding algorithm is offset in the effective low complex degree serial based on random binary data stream, it is characterized in that: comprise the following steps:
(1) the to be decoded vectorial y will received i=(y 1..., y n) by changing corresponding input probability into after channel massage convergent-divergent algorithm value, wherein α is channel zoom factor, and e is natural number constant, and N is polarization code code length;
(2) input probability value corresponding for the N number of code word calculated is generated by CPU the random binary data stream that length corresponding to N group is 1024, namely each probable value random binary data stream that length is 1024 represents; This N group data stream step-by-step is input to respectively the input of two basic dish-shaped decoding frameworks of decoding framework, the input data of two framings are identical;
(3) data flow is by two groups of log 2obtain after the calculating of the basic dish-shaped decoding framework mixed node of N level the conditional probability value of decoding with
(4) the conditional probability random data stream of four paths is calculated by inverter with
(5) four conditional probabilities are realized finally differentiating path probability with door respectively by one;
P ( u ^ 1 i ) = P ( u ^ 1 i - 1 ) p ( u i = u ^ i | u ^ 1 i - 1 ) Circulation tire out multiplication:
By four probable values obtained two optimal paths corresponding to two maximums are chosen by sequence;
Result is passed into " in the double module of probability " and carry out overall probability amplification, and store routing footpath by memory;
By corresponding for two selected paths value feed back in this step with door input, wait for lower one deck four set condition probability arrival, constantly circulation is tired takes advantage of;
(6) by the calculating of feedback module, i decoding value in two paths selected is integrated into a signal by certain rule, feeds back in basic dish-shaped framework, data flow again by basic dish-shaped decoding framework, and obtains the conditional probability value of code with
(7) repeat above-mentioned steps (4), (5) and (6), until N number of code word has all been translated, thus obtain optimal path decode results u ^ 1 N = ( u ^ 1 , ... , u ^ N ) .
2. offset a decoding framework based on random binary data stream list serial, it is characterized in that: it comprises two basic dish-shaped decoding frameworks, two basic dish-shaped decoding frameworks connect list nucleus module respectively; Also comprise two inverters, two inverters are parallel in the connection line of two basic dish-shaped decoding frameworks and list nucleus module respectively; Table nucleus module is connected with feedback module.
3. offset decoding framework based on random binary data stream list serial as claimed in claim 2, it is characterized in that: described basic dish-shaped decoding framework contains N-1 mixed node module, and this N-1 node module is divided into log 2n level 2 × 1 form, this framework is connected with one for providing the external feedback module of allotment information.
4. offset decoding framework based on random binary data stream list serial as claimed in claim 3, it is characterized in that: described mixed node module is owing to using binary data stream as deal with data, mixed node module is single-bit computing herein, described mixed node module comprises a single input and door, one two input or door, one two input not gate, one two input XOR gate, a JK flip-flop, two two input data selectors, wherein, the input input random data stream of two input XOR gate, output connects the input of the two or two input data selector, the input input random data stream of two input not gates, exports the input of termination the or two input data selector, the input termination random data stream of the one or two input data selector, output distinguishes order input and door and two inputs or the input of door, single input and door and two input or the input of door all connects random data stream, and single input and door and two input or the output of door all connects the input of JK flip-flop, output termination the two or two input data selector of JK flip-flop.
5. offset decoding framework based on random binary data stream list serial as claimed in claim 3, it is characterized in that: described list nucleus module comprises 4 and door, 4 are connected with order module with Men Jun, order module connects the double module of probability, probability double model calling memory memory module, memory memory module connects described 4 and door respectively.
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CN106877884A (en) * 2017-02-01 2017-06-20 东南大学 A kind of polarization code coding method for reducing decoding path division
CN108063623A (en) * 2018-01-05 2018-05-22 重庆邮电大学 A kind of the serial of Polar codes for reducing complexity eliminates interpretation method
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