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 PDFInfo
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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
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
The expression message packets, subscript
Be the numbering of message packets,
, 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
The precoding bag that the expression message packets generates through LDPC coding back,
, use
The encoded packets that expression generates through LT Codes coding back,
2) Tanner according to the outer sign indicating number of Linear-Time PEG algorithm generation LDPC schemes,
Precoding obtains individual message packets through LDPC
Individual precoding bag, the Tanner of outer sign indicating number LDPC schemes the check matrix of corresponding LDPC sign indicating number
It is a upper triangular matrix;
3) the employing degree distributes
For encoded packets is selected the number of degrees
, wherein
Be the numbering of encoded packets,
, 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
Dimension two element field vector
,
The number of element " 1 " is in the dimension two element field vector
4)
Dimension two element field vector
In element
Value be " 0 " or " 1 ", element
Be corresponding being numbered of " 1 " expression
The precoding bag of LDPC Codes
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
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
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
, code check
Along with
Continuous growth and change;
7) the Seed reconstruct Tanner figure that the decoder basis is the same with transmitting terminal, basis receives then
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
2) the employing degree distributes
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) to newly-increased check-node
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)
,
And the annexation on limit between them, upgrade check-node
Arrive
Distance between the individual variable node is selected one and check-node
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
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;
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
Individual check-node
,
Individual variable node through the LDPC coding
, and the limit of link variable node and check-node;
2) distribute according to degree
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) to newly-increased check-node
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)
,
,
And the annexation on limit between them, upgrade check-node
Arrive
Distance between the individual variable node is selected one and check-node
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
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;
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
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
, 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
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
, signal to noise ratio
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
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
The expression message packets, subscript
Be the numbering of message packets,
, 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
The precoding bag that the expression message packets generates through LDPC coding back,
, use
The encoded packets that expression generates through LT Codes coding back,
2) Tanner according to the outer sign indicating number of Linear-Time PEG algorithm generation LDPC schemes,
Precoding obtains individual message packets through LDPC
Individual precoding bag, the Tanner of outer sign indicating number LDPC schemes the check matrix of corresponding LDPC sign indicating number
It is a upper triangular matrix;
3) the employing degree distributes
For encoded packets is selected the number of degrees
, wherein
Be the numbering of encoded packets,
, 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
Dimension two element field vector
,
The number of element " 1 " is in the dimension two element field vector
4)
Dimension two element field vector
In element
Value be " 0 " or " 1 ", element
Be corresponding being numbered of " 1 " expression
The precoding bag of LDPC Codes
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
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
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
, code check
Along with
Continuous growth and change;
7) the Seed reconstruct Tanner figure that the decoder basis is the same with transmitting terminal, basis receives then
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
2) the employing degree distributes
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) to newly-increased check-node
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)
,
And the annexation on limit between them, upgrade check-node
Arrive
Distance between the individual variable node is selected one and check-node
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
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;
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
Individual check-node
,
Individual variable node through the LDPC coding
, and the limit of link variable node and check-node;
2) distribute according to degree
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) to newly-increased check-node
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)
,
,
And the annexation on limit between them, upgrade check-node
Arrive
Distance between the individual variable node is selected one and check-node
The variable node that distance is maximum, and between them edged, when the choice variable node, if apart from check-node
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
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
The expression message packets, subscript
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
The precoding bag that the expression message packets generates through LDPC coding back,
, use
The encoded packets that expression generates through LT Codes coding back,
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,
Individual message packets is used
Expression, precoding obtains through LDPC
Individual precoding bag is used
Expression.This Tanner figure has
Individual variable node and
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
; Square frame represents check-node (c-node), is designated as
The LDPC Codes that generates with Linear-Time PEG algorithm is systematic code, so back 1900 nodes among its Tanner figure
Represent message packets
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
Be a upper triangular matrix:
Then the value of the encoded packets of LDPC Codes can be obtained by following formula:
3) distribute according to degree
For encoded packets is selected the number of degrees
, wherein
Be the numbering of encoded packets,
, 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
, the number of element " 1 " is in the 2000 dimension two element field vectors
4) 2000 dimension two element field vectors
In element
Value be " 0 " or " 1 ", element
Be corresponding being numbered of " 1 " expression
The precoding bag of LDPC Codes
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
Value:
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
Individual aliasing the Raptor Codes encoded packets of making an uproar living.
6) receiving terminal continues to receive
Individual encoded packets, the encoded packets sum that receive this moment becomes
, code check
Along with
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
During individual bag:
Therefore whenever new reception
During individual encoded packets, code check changes also can be used
Expression:
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
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
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
Individual, note is done
, corresponding to the precoding bag behind the LDPC Codes coding, also be the packets of information of LT Codes this moment
, and they are without channel, the initial information when the BP iteration is 0; Below a behavior coding nodes, be designated as
, the encoded packets of corresponding LT Codes
, these encoded packets are received termination through channel and receive.Box indicating check-node (c-node) is designated as among the figure
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
Encoded packets select
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
Individual variable node through the LDPC coding
2) distribute according to degree
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) be newly-increased check-node
Individual variable node
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)
,
And the annexation on limit between them, upgrade check-node
Arrive
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
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
, as shown in table 1:
Table 1
When code length more in short-term because
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
,
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
Do a little adjustment, the ratio of increase degree 1 reduces the big number of degrees, obtains
:
Table 2
Weigh the distribution situation of encircling among the Tanner figure of LT Codes with the shortest loop-length through each precoding bag, for
Individual precoding bag in the verification bag quantity that generates is
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
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
Raptor Codes and adopt Raptor Codes in the document " Rateless codes on noisy channels " in the message packets that adopts equal length
, identical signal to noise ratio
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
Individual check-node
,
Individual variable node through the LDPC coding
, and the limit of link variable node and check-node;
2) distribute according to degree
For encoded packets is selected the number of degrees
,
The numbering of corresponding encoded packets,
, increased check-node newly in the bigraph (bipartite graph) of LT sign indicating number
3) to newly-increased check-node
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)
,
,
And the annexation on limit between them, upgrade check-node
Arrive
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;
In the step 4) when the choice variable node, if the range coding node
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
As shown in table 4:
Table 4
Weigh the distribution situation of encircling among the Tanner figure of whole Raptor Codes with the shortest loop-length through each precoding bag, for
Individual precoding bag in the verification bag quantity that generates is
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
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
Raptor Codes and adopt Raptor Codes in the document " Rateless codes on noisy channels " in the message packets that adopts equal length
, identical signal to noise ratio
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
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
, the number of element " 1 " is d in the n dimension two element field vector
i
4) n dimension two element field vector
In element
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
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)
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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