CN102324998B - Raptor Codes encoding/decoding method suitable for medium/short code lengths of additive white Gaussian noise channel - Google Patents

Raptor Codes encoding/decoding method suitable for medium/short code lengths of additive white Gaussian noise channel Download PDF

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CN102324998B
CN102324998B CN 201110121121 CN201110121121A CN102324998B CN 102324998 B CN102324998 B CN 102324998B CN 201110121121 CN201110121121 CN 201110121121 CN 201110121121 A CN201110121121 A CN 201110121121A CN 102324998 B CN102324998 B CN 102324998B
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sign indicating
codes
indicating number
node
check
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CN102324998A (en
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彭瑶
张朝阳
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Zhejiang University ZJU
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Abstract

The invention discloses a Raptor Codes encoding/decoding method suitable for medium/short code lengths of an additive white Gaussian noise channel. According to the method disclosed by the invention, the degree distribution of the inner codes, i.e. LT (Linear-Time) Codes, of the Raptor Codes which are more suitable for the medium/short code lengths is proposed; and the improved PEG (Progressive Edge-Growth) algorithm is used for encoding the inner codes, i.e. the LT codes, of the Raptor Codes, wherein the encoding manner consists of two PEG encoding manners, i.e. independently carrying out PEG composition on the LT Codes and carrying out the PEG composition on the LT Codes through combining with outer codes, i.e. LDPC (Low Density Parity Check) Codes, thus the problem that excessive shortloops appear in a Tanner graph, caused by randomly selecting information packets in an LT encoding stage, is solved. With the adoption of the method disclosed by the invention, the effectiveness for the transfer of soft information when the BP (Background Processing) iterative decoding is carried out is therefore enhanced, the performance better than that of a random composition manner is obtained, and the more reliable transmission for the rateless codes with the medium/short code lengths is realized.

Description

The Raptor Codes coding and decoding method that is suitable for the short-and-medium code length of additive white gaussian noise channels
Technical field
The present invention relates to wireless communication field, relate in particular to a kind of Raptor Codes coding and decoding method that is suitable for the short-and-medium code length of additive white gaussian noise channels.
Background technology
When the traditional chnnel coding of design, need to estimate channel parameter by channel condition information (CSI) earlier that the linear block codes that to design a cbr (constant bit rate) according to this then be R is as LDPC sign indicating number, RA sign indicating number, convolution code etc.Because the unsteadiness of channel status, actual channel parameter may be greater than or less than estimated channel parameter, and the previous case can't realize reliable transmission, needs to use the block code of lower code check; Latter event then can cause the wasting of resources, because can use higher code check linear block codes.In order to make more reliably transmission effectively of linear block codes, a kind of punching technology based on the LDPC sign indicating number (see " Rate-compatible puncturing of low-density parity-check codes; " in IEEE Trans. Information Thoery, vol. 50. no. 11, pp.2824-2836, Nov. 2004.) be suggested, though this method has guaranteed reliability of information transmission and validity, but need by a large amount of feedback mechanisms, for example ARQ (Auto Repeat-Request).How select adaptively under the situation that need not to feed back and the code check of channel matched transmits, we consider no-rate codes (Rateless Codes).
The coded system that is different from traditional cbr (constant bit rate), no-rate codes is to have the adaptive link fit characteristics, it need not to set fixing code check at transmitting terminal, but produce encoded packets in some way continuously and send, receiving terminal also is indifferent to the reception condition of each encoded packets, and be the total amount of being concerned about the encoded packets that receives, therefore there is not the mechanism of feedback and re-transmission.After the encoded packets that has received some, the receiving terminal trial and error decoding, if the unsuccessful received code bag that then continues attempts continuing decoding then, receiving terminal repeats this process up to decoding success always, at this moment one of receiving terminal transmission simply feeds back signal to transmitting terminal and informs that it stops to send encoded packets, has so just finished whole transmission course.Therefore the code check of actual transmissions depends on the number of the encoded packets of actual transmission, just depends on current channel status.And how coded system reasonable in design is so that the code check of actual transmissions approaches the key that channel capacity becomes the design no-rate codes as best one can.
At first, Rateless code is causing to show great attention to and (is seeing " LT Codes " except deleting superior function on the channel because of it, Proceedings of the 43rd Annual IEEE Symposium on foundation of Computer Science), but LT sign indicating number and be not suitable for awgn channel.Shokrollahi is for having proposed the no-rate codes that the coding and decoding complexity can not increase along with code length except deleting channel, be called Raptor Codes(and see " Raptor Codes ", IEEE Transactions on Information Theory, Vol.52, No.6, June 2006), it passes through the LDPC sign indicating number as outer sign indicating number and the cascade of LT sign indicating number.The Raptor Codes(that Ravi Palanki has proposed to be suitable for AWGN sees " Rateless codes on noisy channels "; Available at www.merl.com/papers/TR2003-124/); and provided suitable degree and distributed; because distributing, this degree draws under the prerequisite that is acyclic in hypothesis Tanner figure; under the very long situation of code length; this hypothesis can be set up approx; and in actual conditions; because the restriction of hardware aspect; usually can select short code; under short-and-medium code length; Raptor Codes ISN LT sign indicating number selects the coded system of several precoding bags to construct a large amount of becates randomly; this independence for information in the BP algorithm is propagated and is harmful to, and under short-and-medium code length, this degree distribution mode is also reasonable inadequately.
Summary of the invention
The objective of the invention is to overcome the deficiencies in the prior art, a kind of Raptor Codes coding and decoding method that is suitable for the short-and-medium code length of additive white gaussian noise channels is provided;
Be suitable for the Raptor Codes coding and decoding method of the short-and-medium code length of additive white gaussian noise channels, it is characterized in that comprising coding method and interpretation method.
The step of coding method is as follows:
1) setting transmitting terminal will send Individual message packets, each packet contains several data bits, and comprises that a cyclic redundancy check (CRC) code is used as decoder and judges whether successful foundation of decoding, usefulness
Figure 758193DEST_PATH_IMAGE002
The expression message packets, subscript
Figure 743467DEST_PATH_IMAGE003
Be the numbering of message packets,
Figure 115543DEST_PATH_IMAGE004
, the transmitting terminal of encoding adopts Raptor Codes to encode, and Raptor Codes is the outer sign indicating number of LDPC sign indicating number conduct by high code check, and cascade LT Codes composition, use
Figure 920687DEST_PATH_IMAGE005
The precoding bag that the expression message packets generates through LDPC coding back,
Figure 787143DEST_PATH_IMAGE006
, use
Figure 626924DEST_PATH_IMAGE007
The encoded packets that expression generates through LT Codes coding back,
Figure 169900DEST_PATH_IMAGE008
2) Tanner according to the outer sign indicating number of Linear-Time PEG algorithm generation LDPC schemes,
Figure 727921DEST_PATH_IMAGE001
Precoding obtains individual message packets through LDPC
Figure 132488DEST_PATH_IMAGE009
Individual precoding bag, the Tanner of outer sign indicating number LDPC schemes the check matrix of corresponding LDPC sign indicating number
Figure 92354DEST_PATH_IMAGE010
It is a upper triangular matrix;
3) the employing degree distributes
Figure 806232DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 399019DEST_PATH_IMAGE012
, wherein
Figure 2011101211218100002DEST_PATH_IMAGE013
Be the numbering of encoded packets,
Figure 856545DEST_PATH_IMAGE008
, generate in conjunction with the selection mode of LDPC sign indicating number by improved PEG algorithm edged by the selection mode of improved PEG algorithm edged or with the LT sign indicating number independently with the LT sign indicating number then
Figure 670917DEST_PATH_IMAGE009
Dimension two element field vector
Figure 303499DEST_PATH_IMAGE014
,
Figure 570532DEST_PATH_IMAGE009
The number of element " 1 " is in the dimension two element field vector
Figure 831749DEST_PATH_IMAGE012
4)
Figure 500628DEST_PATH_IMAGE009
Dimension two element field vector
Figure 307041DEST_PATH_IMAGE014
In element
Figure 61371DEST_PATH_IMAGE015
Value be " 0 " or " 1 ", element
Figure 126279DEST_PATH_IMAGE016
Be corresponding being numbered of " 1 " expression
Figure 649664DEST_PATH_IMAGE017
The precoding bag of LDPC Codes
Figure 626978DEST_PATH_IMAGE005
Selected, the precoding bag that these are selected adopts the value that obtains behind the following formula operation to be the encoded packets of LT Codes by bit
Figure 930921DEST_PATH_IMAGE007
Value:
Transmitting terminal is encoded according to above formula, produces encoded packets continuously and sends into awgn channel, informs that up to receiving terminal it stops to send;
The step of interpretation method is as follows:
5) receiving terminal at first receives
Figure 662564DEST_PATH_IMAGE019
Individual aliasing the Raptor Codes encoded packets of noise;
6) receiving terminal continues to receive Individual encoded packets, the encoded packets sum that receives becomes
Figure 788969DEST_PATH_IMAGE021
, code check
Figure 943483DEST_PATH_IMAGE022
Along with
Figure 175881DEST_PATH_IMAGE023
Continuous growth and change;
7) the Seed reconstruct Tanner figure that the decoder basis is the same with transmitting terminal, basis receives then
Figure 9845DEST_PATH_IMAGE023
Individual encoded packets obtains posterior probability, posterior probability is sent into Tanner figure carry out the BP iterative decoding;
8) according to the correct decoding whether of the cyclic redundancy check (CRC) code judgment data bag in each bag, if decoding success then changes step 9) over to; Otherwise change step 6) over to;
9) decoding finishes, and receiving terminal sends signal by feedback channel and tells that transmitting terminal stops to send.
Describedly with the LT sign indicating number by the selection mode step of improved PEG algorithm edged be independently:
1) sign indicating number of not considering the LDPC part is schemed, and according to the independent composition of improved PEG algorithm, the bigraph (bipartite graph) of initialization LT sign indicating number only contains among the figure at first to LT Individual variable node through the LDPC coding
Figure 656038DEST_PATH_IMAGE024
2) the employing degree distributes
Figure 70839DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 13387DEST_PATH_IMAGE012
,
Figure 264371DEST_PATH_IMAGE013
The numbering of corresponding encoded packets,
Figure 950567DEST_PATH_IMAGE008
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 219874DEST_PATH_IMAGE025
3) to newly-increased check-node
Figure 71604DEST_PATH_IMAGE009
Select a variable node to be attached thereto in the individual variable node randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph)
Figure 358229DEST_PATH_IMAGE024
,
Figure 685305DEST_PATH_IMAGE027
And the annexation on limit between them, upgrade check-node
Figure 537634DEST_PATH_IMAGE025
Arrive
Figure 950160DEST_PATH_IMAGE009
Distance between the individual variable node is selected one and check-node
Figure 40476DEST_PATH_IMAGE025
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
Figure 35108DEST_PATH_IMAGE025
When variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to
Figure 490360DEST_PATH_IMAGE012
Individual precoding bag is selected to finish.
Describedly with the LT sign indicating number in conjunction with the LDPC sign indicating number by the selection mode step of improved PEG algorithm edged be:
1) the sign indicating number figure that has constructed in conjunction with LDPC part carries out composition to the LT sign indicating number on the existing basis of LDPC sign indicating number, and the bigraph (bipartite graph) of initialization Raptor Codes contains the LDPC coded portion among the figure
Figure 186921DEST_PATH_IMAGE028
Individual check-node
Figure 753031DEST_PATH_IMAGE029
,
Figure 867749DEST_PATH_IMAGE009
Individual variable node through the LDPC coding
Figure 493902DEST_PATH_IMAGE024
, and the limit of link variable node and check-node;
2) distribute according to degree
Figure 677759DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 860610DEST_PATH_IMAGE012
, The numbering of corresponding encoded packets,
Figure 876156DEST_PATH_IMAGE008
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 295112DEST_PATH_IMAGE026
3) to newly-increased check-node
Figure 276023DEST_PATH_IMAGE009
Select a variable node to be attached thereto in the individual variable node randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph) ,
Figure 153160DEST_PATH_IMAGE024
, And the annexation on limit between them, upgrade check-node
Figure 792269DEST_PATH_IMAGE025
Arrive
Figure 744176DEST_PATH_IMAGE009
Distance between the individual variable node is selected one and check-node
Figure 389921DEST_PATH_IMAGE025
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
Figure 905216DEST_PATH_IMAGE025
When variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to
Figure 437959DEST_PATH_IMAGE012
Individual precoding bag is selected to finish.
The present invention utilizes improved PEG algorithm that the ISN LT sign indicating number of Raptor Codes is encoded, to avoid occurring too much becate among the Tanner figure, thereby solve Raptor Codes because cause the problem of too much becate in the ISN LT coded portion coded system that employing is selected at random to the precoding bag, and then improved the validity that soft information is transmitted when the BP iterative decoding.Several degree that proposed to be more suitable for the Raptor Codes of short-and-medium code length simultaneously distribute, and in conjunction with the PEG encryption algorithm, have realized that the no-rate codes of short-and-medium code length transmits effectively reliably.
Description of drawings
Fig. 1 is the Tanner figure of LDPC Codes;
Fig. 2 is the Tanner figure of Raptor Codes " whole figure decoding ";
Fig. 3 is to the LT Codes Tanner figure of composition independently with improved PEG algorithm;
Fig. 4 schemes with the Tanner of improved PEG algorithm to LT Codes composition in conjunction with LDPC Codes;
Fig. 5 is that the PEG-Raptor Codes of the independent composition of LT sign indicating number distributes with the employing degree
Figure 810035DEST_PATH_IMAGE030
Raptor Codes and the bit error rate comparison diagram that adopts the Raptor Codes in the document " Rateless codes on noisy channels ", the message data packet length
Figure 880759DEST_PATH_IMAGE031
, signal to noise ratio
Fig. 6 is the PEG-Raptor Codes and the distribution of employing degree in conjunction with the LT sign indicating number of LDPC Codes composition
Figure 646382DEST_PATH_IMAGE033
Raptor Codes and the bit error rate comparison diagram that adopts the Raptor Codes in the document " Rateless codes on noisy channels ", the message data packet length
Figure 127042DEST_PATH_IMAGE031
, signal to noise ratio
Figure 498112DEST_PATH_IMAGE032
Embodiment
Be suitable for the Raptor Codes coding and decoding method of the short-and-medium code length of additive white gaussian noise channels, it is characterized in that comprising coding method and interpretation method;
The step of coding method is as follows:
1) setting transmitting terminal will send
Figure 89630DEST_PATH_IMAGE001
Individual message packets, each packet contains several data bits, and comprises that a cyclic redundancy check (CRC) code is used as decoder and judges whether successful foundation of decoding, usefulness
Figure 846234DEST_PATH_IMAGE002
The expression message packets, subscript
Figure 576423DEST_PATH_IMAGE003
Be the numbering of message packets,
Figure 356160DEST_PATH_IMAGE004
, the transmitting terminal of encoding adopts Raptor Codes to encode, and Raptor Codes is the outer sign indicating number of LDPC sign indicating number conduct by high code check, and cascade LT Codes composition, use
Figure 813687DEST_PATH_IMAGE005
The precoding bag that the expression message packets generates through LDPC coding back,
Figure 628059DEST_PATH_IMAGE006
, use
Figure 263571DEST_PATH_IMAGE007
The encoded packets that expression generates through LT Codes coding back,
Figure 530604DEST_PATH_IMAGE008
2) Tanner according to the outer sign indicating number of Linear-Time PEG algorithm generation LDPC schemes,
Figure 791821DEST_PATH_IMAGE001
Precoding obtains individual message packets through LDPC
Figure 270819DEST_PATH_IMAGE009
Individual precoding bag, the Tanner of outer sign indicating number LDPC schemes the check matrix of corresponding LDPC sign indicating number
Figure 264183DEST_PATH_IMAGE010
It is a upper triangular matrix;
3) the employing degree distributes
Figure 80829DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 630891DEST_PATH_IMAGE012
, wherein
Figure 216593DEST_PATH_IMAGE013
Be the numbering of encoded packets,
Figure 646437DEST_PATH_IMAGE008
, generate in conjunction with the selection mode of LDPC sign indicating number by improved PEG algorithm edged by the selection mode of improved PEG algorithm edged or with the LT sign indicating number independently with the LT sign indicating number then
Figure 701112DEST_PATH_IMAGE009
Dimension two element field vector , The number of element " 1 " is in the dimension two element field vector
4)
Figure 621477DEST_PATH_IMAGE009
Dimension two element field vector
Figure 700292DEST_PATH_IMAGE014
In element
Figure 8389DEST_PATH_IMAGE015
Value be " 0 " or " 1 ", element
Figure 780036DEST_PATH_IMAGE016
Be corresponding being numbered of " 1 " expression
Figure 792991DEST_PATH_IMAGE017
The precoding bag of LDPC Codes
Figure 488546DEST_PATH_IMAGE005
Selected, the precoding bag that these are selected adopts the value that obtains behind the following formula operation to be the encoded packets of LT Codes by bit
Figure 841030DEST_PATH_IMAGE007
Value:
Figure 845895DEST_PATH_IMAGE018
Transmitting terminal is encoded according to above formula, produces encoded packets continuously and sends into awgn channel, informs that up to receiving terminal it stops to send;
The step of interpretation method is as follows:
5) receiving terminal at first receives
Figure 96879DEST_PATH_IMAGE019
Individual aliasing the Raptor Codes encoded packets of noise;
6) receiving terminal continues to receive
Figure 517496DEST_PATH_IMAGE020
Individual encoded packets, the encoded packets sum that receives becomes
Figure 52382DEST_PATH_IMAGE021
, code check
Figure 165832DEST_PATH_IMAGE022
Along with
Figure 904112DEST_PATH_IMAGE023
Continuous growth and change;
7) the Seed reconstruct Tanner figure that the decoder basis is the same with transmitting terminal, basis receives then
Figure 128420DEST_PATH_IMAGE023
Individual encoded packets obtains posterior probability, posterior probability is sent into Tanner figure carry out the BP iterative decoding;
8) according to the correct decoding whether of the cyclic redundancy check (CRC) code judgment data bag in each bag, if decoding success then changes step 9) over to; Otherwise change step 6) over to;
9) decoding finishes, and receiving terminal sends signal by feedback channel and tells that transmitting terminal stops to send.
Describedly with the LT sign indicating number by the selection mode step of improved PEG algorithm edged be independently:
1) sign indicating number of not considering the LDPC part is schemed, and according to the independent composition of improved PEG algorithm, the bigraph (bipartite graph) of initialization LT sign indicating number only contains among the figure at first to LT
Figure 252234DEST_PATH_IMAGE009
Individual variable node through the LDPC coding
Figure 346704DEST_PATH_IMAGE024
2) the employing degree distributes
Figure 759231DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 849547DEST_PATH_IMAGE012
,
Figure 844179DEST_PATH_IMAGE013
The numbering of corresponding encoded packets,
Figure 33852DEST_PATH_IMAGE008
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 995991DEST_PATH_IMAGE025
3) to newly-increased check-node
Figure 562102DEST_PATH_IMAGE026
Figure 676820DEST_PATH_IMAGE009
Select a variable node to be attached thereto in the individual variable node randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph)
Figure 99711DEST_PATH_IMAGE024
, And the annexation on limit between them, upgrade check-node
Figure 669680DEST_PATH_IMAGE025
Arrive
Figure 560276DEST_PATH_IMAGE009
Distance between the individual variable node is selected one and check-node
Figure 419648DEST_PATH_IMAGE025
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
Figure 838603DEST_PATH_IMAGE025
When variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to
Figure 12095DEST_PATH_IMAGE012
Individual precoding bag is selected to finish.
Describedly with the LT sign indicating number in conjunction with the LDPC sign indicating number by the selection mode step of improved PEG algorithm edged be:
1) the sign indicating number figure that has constructed in conjunction with LDPC part carries out composition to the LT sign indicating number on the existing basis of LDPC sign indicating number, and the bigraph (bipartite graph) of initialization Raptor Codes contains the LDPC coded portion among the figure
Figure 85094DEST_PATH_IMAGE028
Individual check-node
Figure 866099DEST_PATH_IMAGE029
,
Figure 962231DEST_PATH_IMAGE009
Individual variable node through the LDPC coding
Figure 736152DEST_PATH_IMAGE024
, and the limit of link variable node and check-node;
2) distribute according to degree
Figure 601340DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 553246DEST_PATH_IMAGE012
,
Figure 198991DEST_PATH_IMAGE034
The numbering of corresponding encoded packets, , increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 247030DEST_PATH_IMAGE026
3) to newly-increased check-node
Figure 619105DEST_PATH_IMAGE025
Figure 689830DEST_PATH_IMAGE009
Select a variable node to be attached thereto in the individual variable node randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph) ,
Figure 393136DEST_PATH_IMAGE024
,
Figure 936113DEST_PATH_IMAGE027
And the annexation on limit between them, upgrade check-node
Figure 41603DEST_PATH_IMAGE025
Arrive
Figure 898701DEST_PATH_IMAGE009
Distance between the individual variable node is selected one and check-node
Figure 655304DEST_PATH_IMAGE025
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
Figure 306865DEST_PATH_IMAGE025
When variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to Individual precoding bag is selected to finish.
Embodiment
Be suitable for the Raptor Codes coding and decoding method of the short-and-medium code length of additive white gaussian noise channels, comprise coding method and interpretation method;
Its coding method is as follows:
1) considers that transmitting terminal will send
Figure 622757DEST_PATH_IMAGE031
Individual message packets, each packet contains several data bits, and comprises a cyclic redundancy check (CRC) code, and this cyclic redundancy check (CRC) code adopts CRC16, is used as decoder and judges whether successful foundation of decoding.With
Figure 171550DEST_PATH_IMAGE002
The expression message packets, subscript
Figure 72641DEST_PATH_IMAGE003
Be the numbering of message packets, The transmitting terminal of encoding adopts Raptor Codes to encode, and it is the outer sign indicating number of LDPC sign indicating number conduct by high code check, and cascade LT Codes composition, use
Figure 600892DEST_PATH_IMAGE005
The precoding bag that the expression message packets generates through LDPC coding back,
Figure 837748DEST_PATH_IMAGE036
, use
Figure 96691DEST_PATH_IMAGE007
The encoded packets that expression generates through LT Codes coding back,
Figure 913338DEST_PATH_IMAGE008
Encoder produces encoded packets as follows:
2) at first according to Linear-Time PEG algorithm (see " Regular and Irregular Progressive Edge-Growth Tanner Graphs ", IEEE Transactions On Information Theory, Vol. 51, No. 1, January 2005) and generate the Tanner figure of outer sign indicating number LDPC,
Figure 650349DEST_PATH_IMAGE031
Individual message packets is used
Figure 986784DEST_PATH_IMAGE002
Expression, precoding obtains through LDPC
Figure 416628DEST_PATH_IMAGE037
Individual precoding bag is used
Figure 454991DEST_PATH_IMAGE005
Expression.This Tanner figure has
Figure 808743DEST_PATH_IMAGE037
Individual variable node and
Figure 514531DEST_PATH_IMAGE038
Individual check-node.The Tanner of LDPC Codes schemes as shown in Figure 1, and wherein circle is variable node (v-node), is designated as , the encoded packets of corresponding LDPC Codes
Figure 391669DEST_PATH_IMAGE040
; Square frame represents check-node (c-node), is designated as
Figure 470483DEST_PATH_IMAGE041
The LDPC Codes that generates with Linear-Time PEG algorithm is systematic code, so back 1900 nodes among its Tanner figure Represent message packets
Figure 536845DEST_PATH_IMAGE043
The number of degrees of the variable node of this Tanner are fixed, and the number of degrees of preceding 5 nodes are 1, and next 800 node number of degrees are 2, and the number of degrees of last 1195 nodes are 3.Press Linear-Time PEG algorithm and be the annexation of each variable node selection with check-node.Tanner schemes the check matrix of corresponding LDPC sign indicating number
Figure 563182DEST_PATH_IMAGE044
Be a upper triangular matrix:
Figure 445688DEST_PATH_IMAGE045
Then the value of the encoded packets of LDPC Codes can be obtained by following formula:
Figure 860489DEST_PATH_IMAGE046
3) distribute according to degree For encoded packets is selected the number of degrees
Figure 54021DEST_PATH_IMAGE012
, wherein
Figure 536955DEST_PATH_IMAGE034
Be the numbering of encoded packets,
Figure 822574DEST_PATH_IMAGE008
, then according to making the LT sign indicating number independently by the selection mode of improved PEG algorithm edged or make the LT sign indicating number generate 2000 dimension two element field vectors in conjunction with the LDPC sign indicating number by the selection mode of improved PEG algorithm edged
Figure 670444DEST_PATH_IMAGE014
, the number of element " 1 " is in the 2000 dimension two element field vectors
Figure 657991DEST_PATH_IMAGE012
4) 2000 dimension two element field vectors
Figure 695349DEST_PATH_IMAGE014
In element
Figure 22425DEST_PATH_IMAGE015
Value be " 0 " or " 1 ", element
Figure 369093DEST_PATH_IMAGE016
Be corresponding being numbered of " 1 " expression
Figure 781619DEST_PATH_IMAGE047
The precoding bag of LDPC Codes
Figure 354159DEST_PATH_IMAGE005
Selected, the precoding bag that these are selected is done the encoded packets that the value that obtains behind the Modulo-two operation is LT Codes by bit
Figure 535741DEST_PATH_IMAGE007
Value:
Figure 53310DEST_PATH_IMAGE048
Transmitting terminal is encoded according to above rule, produces encoded packets continuously and sends into awgn channel, informs that up to receiving terminal it stops to send.
The interpretation method of no-rate codes comprises the steps:
5) receiving terminal at first receives
Figure 953133DEST_PATH_IMAGE049
Individual aliasing the Raptor Codes encoded packets of making an uproar living.
6) receiving terminal continues to receive
Figure 332293DEST_PATH_IMAGE050
Individual encoded packets, the encoded packets sum that receive this moment becomes
Figure 430699DEST_PATH_IMAGE021
, code check
Figure 56852DEST_PATH_IMAGE022
Along with
Figure 257021DEST_PATH_IMAGE023
Continuous growth and change.
7) decoder can be schemed by the basis Seed reconstruct Tanner the same with transmitting terminal, and basis receives then Individual encoded packets obtains their posterior probability (LLR), these posterior probability is sent into Tanner figure carry out the BP iterative decoding.
8) according to the correct decoding whether of the cyclic redundancy check (CRC) code judgment data bag in each bag, if decoding success then changes step 9) over to; Otherwise change step 6) over to.
9) decoding finishes, and receiving terminal sends signal by feedback channel and tells that transmitting terminal stops to send.
Therefore when can't correct decoding with the encoded packets that has received, receiving terminal needs reception again Individual encoded packets, the Tanner figure of Raptor Codes increases thereupon, and the new Tanner figure of receiving terminal utilization carries out new round decoding iteration.
Expression for convenience, we namely receive with the variation that the inverse of code check is portrayed code check
Figure 189839DEST_PATH_IMAGE023
During individual bag:
Figure 798675DEST_PATH_IMAGE052
Therefore whenever new reception
Figure 34484DEST_PATH_IMAGE020
During individual encoded packets, code check changes also can be used
Figure 855285DEST_PATH_IMAGE053
Expression:
Figure 823241DEST_PATH_IMAGE054
Raptor Codes is made of outer sign indicating number LDPC Codes and ISN LT Codes, when carrying out the BP iterative decoding, can be directly the Tanner figure of LDPC Codes and LT Codes be merged into one " whole figure ", finishes decoding " whole scheme ", as shown in Figure 2.Wherein the information initializing of precoding bag is 0.
The ISN LT Codes of Raptor Codes more in short-term, can form a large amount of becates if the mode that the precoding bag is taked to select at random generates encoded packets at code length in Tanner figure, these becates have directly influenced the performance of decoding.Will enlarge loop as can be known from the encoder design of LT, crucial problem is exactly how to produce
Figure 981690DEST_PATH_IMAGE014
Problem.In order to improve the performance of Raptor Codes, with improved PEG algorithm application on LT Codes.
The described selection mode of pressing improved PEG algorithm edged with the LT sign indicating number independently:
The sign indicating number that is different from fixed rate, the bigraph (bipartite graph) of the ISN LT sign indicating number of Raptor Codes constantly enlarge along with the continuous increase of encoded packets.Do not consider the sign indicating number figure of LDPC part, to the independent composition of the LT improved PEG algorithm of foundation, length local optimum in the Tanner of Raptor Codes figure of accomplishing loop.
Here be noted that traditional PEG algorithm is the degree distribution by given information node, to the information node edged, and makes the number of degrees of check-node be tending towards unified.For LT Codes then be by to check-node by PEG algorithm edged so that the loop maximum, the degree of check-node distributes
Figure 240764DEST_PATH_IMAGE011
Definite, it is unified but at random that the degree of variable node does not need.The Tanner figure of the PEG structure of LT sign indicating number has two category nodes as shown in Figure 3 among the figure, wherein circle is variable node (v-node), and the variable node of first row is also referred to as information node, and is total
Figure 371531DEST_PATH_IMAGE037
Individual, note is done
Figure 572705DEST_PATH_IMAGE039
, corresponding to the precoding bag behind the LDPC Codes coding, also be the packets of information of LT Codes this moment
Figure 156133DEST_PATH_IMAGE040
, and they are without channel, the initial information when the BP iteration is 0; Below a behavior coding nodes, be designated as
Figure 218898DEST_PATH_IMAGE055
, the encoded packets of corresponding LT Codes
Figure 266489DEST_PATH_IMAGE056
, these encoded packets are received termination through channel and receive.Box indicating check-node (c-node) is designated as among the figure
Figure 576247DEST_PATH_IMAGE057
Check-node and coding nodes are annexation one to one, and the mould 2 of all variable nodes that link to each other with check-node and be 0, this has just embodied in the cataloged procedure and for the number of degrees has been
Figure 460021DEST_PATH_IMAGE012
Encoded packets select
Figure 513427DEST_PATH_IMAGE012
Individual precoding bag carries out mould 2 Hes.Because the characteristic of Rateless, the Tanner figure of LT Codes is along with the process of coding constantly enlarges, an encoded packets Tanner of every increase figure will increase a coding nodes and check-node and corresponding limit newly, because the number of degrees of each coding nodes are 1, to the ring among the Tanner figure without any influence, so the time can ignore these nodes at structure Tanner figure.
According to the independent composition of improved PEG algorithm, its step is as follows to LT:
1) bigraph (bipartite graph) of initialization LT sign indicating number only contains among the figure at first
Figure 415524DEST_PATH_IMAGE037
Individual variable node through the LDPC coding
Figure 896184DEST_PATH_IMAGE039
2) distribute according to degree
Figure 998745DEST_PATH_IMAGE011
For encoded packets is selected the number of degrees
Figure 918159DEST_PATH_IMAGE012
,
Figure 612446DEST_PATH_IMAGE013
The numbering of corresponding encoded packets,
Figure 77057DEST_PATH_IMAGE008
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 122373DEST_PATH_IMAGE026
3) be newly-increased check-node
Figure 579899DEST_PATH_IMAGE025
Figure 128692DEST_PATH_IMAGE037
Individual variable node
Figure 29783DEST_PATH_IMAGE039
In select a variable node to be attached thereto randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph)
Figure 296816DEST_PATH_IMAGE039
,
Figure 292454DEST_PATH_IMAGE027
And the annexation on limit between them, upgrade check-node
Figure 774382DEST_PATH_IMAGE025
Arrive
Figure 33325DEST_PATH_IMAGE037
Distance between the individual variable node, select one with its variable node apart from maximum, and between them edged, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to Individual precoding bag is selected to finish.
Selection to variable node in the step 3) is at random, and this selects the variable node of number of degrees minimum different with traditional PEG method, is this improved place of PEG algorithm, is more suitable for Raptor Codes than conventional method.
In the step 4) when the choice variable node, if apart from check-node
Figure 586983DEST_PATH_IMAGE025
When variable node farthest has several, then choose one randomly in them, this also is to change the improved place of PEG algorithm.
The degree that document " Rateless codes on noisy channels " has provided the LT part of the Raptor Codes that is suitable for awgn channel distributes
Figure 920488DEST_PATH_IMAGE058
, as shown in table 1:
Table 1
Figure 147070DEST_PATH_IMAGE059
Figure 388696DEST_PATH_IMAGE030
Figure 742448DEST_PATH_IMAGE033
Figure 182656DEST_PATH_IMAGE060
Figure 783402DEST_PATH_IMAGE061
0.007969 0.493570 0.166220 0.072646 0.082558
Figure 59794DEST_PATH_IMAGE062
Figure 404187DEST_PATH_IMAGE063
Figure 964482DEST_PATH_IMAGE064
Figure 499816DEST_PATH_IMAGE066
0.056058 0.037229 0.055590 0.025023 0.003135
When code length more in short-term because
Figure 444639DEST_PATH_IMAGE059
Ratio very little, start the quantity of the encoded packets of decoding as BP, be very easy to cause decoding failure, therefore at code length more in short-term, the ratio of degree of increasing by 1 suitably.And
Figure 797123DEST_PATH_IMAGE065
,
Figure 284211DEST_PATH_IMAGE066
Then can increase the quantity of becate etc. the existence of the very large number of degrees, also decoding performance be exerted an influence.Right
Figure 784463DEST_PATH_IMAGE058
Do a little adjustment, the ratio of increase degree 1 reduces the big number of degrees, obtains
Figure 470659DEST_PATH_IMAGE067
:
Table 2
Figure 490699DEST_PATH_IMAGE059
Figure 666465DEST_PATH_IMAGE030
Figure 591696DEST_PATH_IMAGE033
Figure 956129DEST_PATH_IMAGE061
0.029824 0.485949 0.158552 0.070614 0.080263
Figure 262794DEST_PATH_IMAGE063
Figure 290793DEST_PATH_IMAGE068
Figure 534692DEST_PATH_IMAGE069
0.055053 0.036194 0.055481 0.028070
Weigh the distribution situation of encircling among the Tanner figure of LT Codes with the shortest loop-length through each precoding bag, for
Figure 989944DEST_PATH_IMAGE037
Individual precoding bag in the verification bag quantity that generates is
Figure 699887DEST_PATH_IMAGE070
The time, it is as shown in table 3 to obtain among the LT sign indicating number Tanner figure the becate distribution situation of each precoding bag:
Table 3
Figure 328314DEST_PATH_IMAGE071
As seen the PEG algorithm has improved the situation that has a large amount of becates among the Tanner figure greatly.Fig. 5 is that the PEG-Raptor Codes of the independent composition of LT sign indicating number distributes with the employing degree
Figure 364403DEST_PATH_IMAGE030
Raptor Codes and adopt Raptor Codes in the document " Rateless codes on noisy channels " in the message packets that adopts equal length
Figure 803606DEST_PATH_IMAGE072
, identical signal to noise ratio
Figure DEST_PATH_IMAGE073
Under the performance comparison diagram.Plant at identical degree branch as can be seen, the performance of PEG-Raptor Codes is better than the performance of the Raptor Codes of LT random configuration, and simultaneously owing to spend the improvement that distributes, the employing degree distributes The performance of Raptor Codes also be better than the Raptor Codes that provides in the document.
The described selection mode of pressing improved PEG algorithm edged with the LT sign indicating number in conjunction with the LDPC sign indicating number:
Sign indicating number figure in conjunction with the LDPC part has been constructed carries out composition to the LT sign indicating number on the existing basis of LDPC sign indicating number, realizes length global optimum in the Tanner of Raptor Codes figure of loop, and its step is as follows:
1) bigraph (bipartite graph) of initialization Raptor Codes contains the LDPC coded portion among the figure
Figure 170314DEST_PATH_IMAGE074
Individual check-node
Figure 326488DEST_PATH_IMAGE075
,
Figure 185860DEST_PATH_IMAGE076
Individual variable node through the LDPC coding , and the limit of link variable node and check-node;
2) distribute according to degree
Figure 515658DEST_PATH_IMAGE078
For encoded packets is selected the number of degrees
Figure 588657DEST_PATH_IMAGE012
,
Figure 556613DEST_PATH_IMAGE013
The numbering of corresponding encoded packets, , increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
Figure 260223DEST_PATH_IMAGE025
3) to newly-increased check-node
Figure 342896DEST_PATH_IMAGE076
Select a variable node to be attached thereto in the individual variable node randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4) according to existing node in the bigraph (bipartite graph)
Figure 660745DEST_PATH_IMAGE075
,
Figure 238357DEST_PATH_IMAGE077
,
Figure 223631DEST_PATH_IMAGE080
And the annexation on limit between them, upgrade check-node
Figure 346439DEST_PATH_IMAGE025
Arrive
Figure 213900DEST_PATH_IMAGE076
Distance between the individual variable node, select one with its variable node apart from maximum, and between them edged, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5) repeating step 4) up to
Figure 267307DEST_PATH_IMAGE012
Individual precoding bag is selected to finish.
In the step 4) when the choice variable node, if the range coding node
Figure 920136DEST_PATH_IMAGE025
When variable node farthest has several, then in them, choose one randomly.
LT Codes schemes as shown in Figure 4 in conjunction with the Tanner that outer sign indicating number LDPC Codes carries out the PEG structure.
The degree that PEG-Raptor Codes in conjunction with the LDPC composition is adopted distributes
Figure 400796DEST_PATH_IMAGE081
As shown in table 4:
Table 4
Figure 21133DEST_PATH_IMAGE059
Figure 422771DEST_PATH_IMAGE030
Figure 382637DEST_PATH_IMAGE033
Figure 96515DEST_PATH_IMAGE060
Figure 876252DEST_PATH_IMAGE061
0.029824 0.485949 0.158552 0.070614 0.080263
Figure 84511DEST_PATH_IMAGE062
Figure 783663DEST_PATH_IMAGE082
Figure 863745DEST_PATH_IMAGE083
0.055053 0.036194 0.055481 0.028070
Weigh the distribution situation of encircling among the Tanner figure of whole Raptor Codes with the shortest loop-length through each precoding bag, for
Figure 124962DEST_PATH_IMAGE076
Individual precoding bag in the verification bag quantity that generates is
Figure 793841DEST_PATH_IMAGE084
The time, it is as shown in table 5 to obtain among the Raptor sign indicating number Tanner figure the becate distribution situation of each precoding bag:
Table 5
Figure 600254DEST_PATH_IMAGE085
As seen improved the situation that has a large amount of becates among the Tanner figure of whole Raptor Codes greatly in conjunction with the PEG algorithm of the LT Codes of LDPC part.Fig. 6 is that the PEG-Raptor Codes of whole composition distributes with the employing degree
Figure 416900DEST_PATH_IMAGE033
Raptor Codes and adopt Raptor Codes in the document " Rateless codes on noisy channels " in the message packets that adopts equal length
Figure 419492DEST_PATH_IMAGE072
, identical signal to noise ratio
Figure 752996DEST_PATH_IMAGE073
Under the performance comparison diagram.Plant at identical degree branch as can be seen, the performance of the PEG-Raptor Codes of whole composition is better than the performance of the Raptor Codes of LT sign indicating number random configuration, and simultaneously owing to spend the improvement that distributes, the employing degree distributes
Figure 979578DEST_PATH_IMAGE033
The performance of Raptor Codes also be better than the Raptor Codes that provides in the document.

Claims (1)

1. a Raptor Codes coding and decoding method that is suitable for the short-and-medium code length of additive white gaussian noise channels is characterized in that comprising coding method and interpretation method;
The step of coding method is as follows:
1) set transmitting terminal and will send m message packets, each packet contains several data bits, and comprises that whether successful a cyclic redundancy check (CRC) code be used as decoder and judge and decipher foundation, uses s jThe expression message packets, subscript j is the numbering of message packets, j=1,2 ..., m, the transmitting terminal of encoding adopts Raptor Codes to encode, and Raptor Codes is the outer sign indicating number of LDPC sign indicating number conduct by high code check, and cascade LT Codes composition, use a lThe precoding bag that the expression message packets generates through LDPC coding back, l=1,2 ..., n uses t iThe encoded packets that expression generates through LT Codes coding back, i=1,2 ...;
2) according to the Tanner figure of the outer sign indicating number of Linear-Time PEG algorithm generation LDPC, precoding obtains n precoding bag to m message packets through LDPC, and the Tanner of sign indicating number LDPC schemes the check matrix H of corresponding LDPC sign indicating number outward (n-m) * nIt is a upper triangular matrix;
3) employing degree distribution Ω (x) selects number of degrees d for encoded packets i, wherein i is the numbering of encoded packets, i=1,2 ..., then with the LT sign indicating number independently by the selection mode of improved PEG algorithm edged or with the LT sign indicating number in conjunction with the LDPC sign indicating number by the selection mode of improved PEG algorithm edged generate n tie up the two element field vector
Figure FDA00003379171100012
, the number of element " 1 " is d in the n dimension two element field vector i
4) n dimension two element field vector
Figure FDA00003379171100013
In element
Figure FDA00003379171100014
Value be " 0 " or " 1 ", element G LkPrecoding bag a for the corresponding LDPC Codes that is numbered l of " 1 " expression lSelected, the precoding bag that these are selected adopts the value that obtains behind the following formula operation to be the encoded packets t of LT Codes by bit iValue:
Transmitting terminal is encoded according to above formula, produces encoded packets continuously and sends into awgn channel, informs that up to receiving terminal it stops to send;
The step of interpretation method is as follows:
5) the receiving terminal Raptor Codes encoded packets of noise that at first received N=m aliasing;
6) receiving terminal continues to receive N encoded packets of Δ, and the encoded packets sum that receives becomes N=N+ Δ N, and code check R=m/N changes along with the continuous growth of N;
7) the Seed reconstruct Tanner figure that the decoder basis is the same with transmitting terminal obtains posterior probability according to N the encoded packets that receives then, posterior probability is sent into Tanner figure carry out the BP iterative decoding;
8) according to the correct decoding whether of the cyclic redundancy check (CRC) code judgment data bag in each bag, if decoding success then changes step 9) over to; Otherwise change step 6) over to;
9) decoding finishes, and receiving terminal sends signal by feedback channel and tells that transmitting terminal stops to send;
Describedly with the LT sign indicating number by the selection mode step of improved PEG algorithm edged be independently:
1.1) do not consider LDPC sign indicating number figure partly, to the independent composition of the LT improved PEG algorithm of foundation, the bigraph (bipartite graph) of initialization LT sign indicating number, the initial variable node V that only contains n process LDPC coding among the figure 1, V 2..., V n
2.1) employing degree distribution Ω (x) is that encoded packets selects number of degrees d i, the numbering of the corresponding encoded packets of i, i=1,2 ..., increased check-node C in the bigraph (bipartite graph) of LT sign indicating number newly i
3.1) to newly-increased check-node C iIn n variable node, select a variable node to be attached thereto randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4.1) according to existing node V in the bigraph (bipartite graph) 1, V 2..., V n, C 1, C 2..., C iAnd the annexation on limit between them, upgrade check-node C iTo the distance between n the variable node, select one and check-node C iThe variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node C iWhen variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5.1) repeating step 4.1) up to d iIndividual precoding bag is selected to finish;
Describedly with the LT sign indicating number in conjunction with the LDPC sign indicating number by the selection mode step of improved PEG algorithm edged be:
1.2) in conjunction with the sign indicating number figure that LDPC part has been constructed, the LT sign indicating number being carried out composition on the existing basis of LDPC sign indicating number, the bigraph (bipartite graph) of initialization Raptor Codes contains n-m check-node of LDPC coded portion among the figure
Figure FDA00003379171100021
N the variable node V through the LDPC coding 1, V 2..., V n, and the limit of link variable node and check-node;
2.2) select number of degrees d according to degree distribution Ω (x) for encoded packets i, the numbering of the corresponding encoded packets of i, i=1,2 ..., increased check-node C in the bigraph (bipartite graph) of LT sign indicating number newly k
3.2) to newly-increased check-node C kIn n variable node, select a variable node to be attached thereto randomly, and in the bigraph (bipartite graph) of LT sign indicating number, add this edge;
4.2) according to existing node in the bigraph (bipartite graph)
Figure FDA00003379171100022
V 1, V 2..., V n, C 1, C 2..., C iAnd the annexation on limit between them, upgrade check-node C iTo the distance between n the variable node, select one and check-node C iThe variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node C iWhen variable node farthest has several, then choose one randomly in them, the bigraph (bipartite graph) of LT sign indicating number upgrades the annexation on limit simultaneously;
5.2) repeating step 4.2) up to d iIndividual precoding bag is selected to finish.
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