CN103580699A - Rate-code-free fixed window long side eliminating belief propagation decoding method - Google Patents

Abstract

The invention discloses a rate-code-free fixed window long side eliminating belief propagation decoding method. A rate-code-free encoding mode is adopted by a sending end to send information to a receiving end, and the receiving end selects variable nodes with a fixed number (window length) to carry out decoding according to the confidence coefficient of a received encoding pack. After a plurality of turns of 'side elimination' belief propagation decoding are tried in a decoder with a fixed window length, if the decoding fails, new variable nodes with the number equal to that of the variable nodes currently removed through the side elimination operation are supplemented in the decoder, and decoding is tried again until the decoding succeeds or the side elimination operation cannot remove the variable nodes any more. The operating complexity and scale of the decoding cannot be increased along with the decoding, uncertain changes cannot be carried out continuously, and hardware processing is convenient to achieve.

Description

Belief propagation interpretation method is eliminated on the long limit of fixed window of no-rate codes

Technical field

The present invention relates to wireless communication field, belief propagation interpretation method is eliminated on the long limit of fixed window that is specifically related to a kind of no-rate codes.

Background technology

Conventional no-rate codes coded system is that Raptor Code(is shown in " Raptor Codes ", IEEE Transactions on Information Theory, Vol.52, No.6, pp.2551-2567, June2006).Its application scenarios is generally divided into two kinds.When the first is passed through erasure channel (BEC) when the coded identification of no-rate codes, due to receiving terminal acquisition is 0,1 bit sequence, first we can translate the number of degrees is 1 the corresponding input variable node of output variable node (symbol) (symbol), and then eliminate these incoming symbols that translate to the impact of other output symbols and simplify Tanner figure by " limit elimination ", this process is called iteration one time, finally by iteration repeatedly to translate all incoming symbols.Another kind is when passing through binary white Gauss noise channel (BI-AWGNC) without rate coding symbol, due to receiving terminal acquisition is the sequence of real numbers that mapping symbols is superimposed with white Gauss noise, we now use " belief propagation Belief Propagation (BP) " decoding algorithm, by on the limit in Tanner figure back and forth iteration upgrade and transmit LLR information, make uncertainty along with iteration reduces gradually, finally reach the object that translates all incoming symbols.

These two kinds of methods are all the interpretation method of message propagation in essence, different is, and what on " limit elimination " method limit in Tanner figure, to transmit is all deterministic 0,1 message, and after this certainty message transmission, by the limit that disappears, simplify Tanner and scheme, make annexation in Tanner figure along with the carrying out of decoding more and more simpler (number on limit is fewer and feweri), finally by constantly subduing with the renewal of corresponding information of limit, complete decoding; What on the limit of BP decoding algorithm in Tanner figure, transmit is LLR information, by iteration, make LLR information constantly restrain (constantly deflection+∞ or-direction of ∞), finally by probabilistic, constantly reduced decoding, yet the scale of decoding complexity and Tanner figure is constant all the time.If the thought of two kinds of interpretation methods is combined, be applied in situation about transmitting by noisy communication channel without rate coding symbol, when so just can carry out the renewal of LLR information iteration on one side, eliminate those confidence levels limit that sufficiently high node has connected (simultaneously eliminating their impacts on the follow-up decoding of other nodes) on one side, make the uncertain ever-reduced while, the annexation of Tanner figure is also constantly simplified, thereby can when assurance is successfully decoded, reduce decoding computational complexity.According to " information of whether utilizing the iterative decoding of completed subgraph to preserve ", interpretation method can be divided into non-progressive BP algorithm and progressive BP algorithm.

The interpretation method feature of " non-progressive " is: while adopting " limit elimination " BP decoding algorithm to fail decoding in a little figure, trial and error decoding in the large figure of continuation after an expansion, acquired LLR information, limit elimination information etc. when again not retaining little figure decoding during trial and error decoding and finishing, therefore along with the carrying out of decoding, the node number that enters decoder is more and more, and the scale of Tanner figure is increasing.The interpretation method feature of " progressive " is: while adopting " limit elimination " BP decoding algorithm to fail decoding in a little figure, in the large figure of continuation after an expansion, trial and error decoding again on the basis of acquired LLR information, limit elimination information etc. when retaining little figure decoding and finish, until successfully decoded.The decoding meeting of " progressive " mode causes the scale of Tanner figure along with the carrying out of decoding, expansion due to figure increases on the one hand, owing to having retained the existing side information that disappears, reduce again on the other hand, therefore the node number that participates in computing in every Tanner figure during decoding in decoder is unfixed (the node number being at every turn removed is fixing, and the node number at every turn entering is fixed as decoding stepping Δ N).As can be seen here, in decode procedure, the memory space that decoder is required, computation complexities etc. are all constantly changing, and this makes troubles to the realization of hardware circuit.Therefore,, if can guarantee that the computational complexity of decoder and the scale of Tanner figure can constantly not increase or do uncertain variation along with the carrying out of decoding, that realizes the processing that is more conducive to hardware.

Summary of the invention

The object of the invention is to eliminate decoder required memory space when hardware is realized, the uncertainty of computation complexity etc., provides a kind of long limit of fixed window of no-rate codes to eliminate belief propagation interpretation method.

The object of the invention is to be achieved through the following technical solutions.

The long limit of fixed window of no-rate codes is eliminated belief propagation interpretation method and is: transmitting terminal adopts no-rate codes to encode to the information of needs transmission, and receiving terminal adopts belief propagation decoding; The number of the variable node of storing in decoder when " window is long " is defined as each decoding, namely participate in the number of the variable node of computing, on the limit that fixed window is long, eliminate in belief propagation interpretation method, the number of the variable node of storing in decoder is fixed all the time; Receiving terminal filters out by setting a threshold value output variable node that confidence level surpasses the LT code of this threshold value, and selection and long equal-sized several variable nodes after screening of window are sent into decoder and started decoding; After attempting the decoding of number wheel limit elimination belief propagation, if fail successfully decoded, by the limit operation that disappears, how many variable nodes have been removed at present, the output variable node that supplements how many new LT codes enters decoder, and trial and error decoding again, until the successfully decoded or limit operation that disappears cannot remove variable node again;

If: the check-node of LDPC code and the number of variable node are respectively m and n, and the check-node of LT code and the number of variable node that participate in first round decoded operation are respectively N and N+n, and window is long is W=n+N, and variable node is designated as v _i, i=1,2 ..., n+N, check-node is designated as c _j, j=1,2 ..., m+N, N (v _i) c _jexpression is except c _joutside other and v _iconnected check-node, N (c _j) v _iexpression is except v _ioutside other and c _jconnected variable node, e _i,jrepresent to connect v _iand c _jlimit, E _lDPC={ e _i,j| i=1,2 ..., n, j=1,2 ..., m} represents the limit corresponding to LDPC code check matrix, $E_{\mathrm{LT}}^{\left(l\right)}=\left\{e_{i,j}\right|i=\mathrm{1,2},...,n,j=m+1,m+2,...,m+N\}$ While being illustrated in the decoded operation of l wheel corresponding to the limit of LT code generator matrix,

the limit that has connected LT code check node and output variable node while being illustrated in the decoded operation of l wheel,

v while being illustrated in the decoded operation of l wheel _ipass to c _jlog-likelihood ratio,

c while being illustrated in the decoded operation of l wheel _jpass to v _ilog-likelihood ratio, the input log-likelihood ratio of self-channel while being illustrated in the decoded operation of l wheel, because the output variable node of LDPC code does not pass through transmission, so

l ^(l)(v _i) while being illustrated in the decoded operation of l wheel corresponding to v _i, i=1,2 ..., the log-likelihood ratio value that is used for doing hard decision of n+N, ξ and T represent respectively to adjudicate L ^(l)(v _i), i=1,2 ..., the threshold value that need to reach when n confidence level is enough high and the number of times that reaches this threshold value, for

f ^(l)(e _i,je when)=0 is illustrated in the decoded operation of l wheel _i,jconnected a variable node v who is eliminated _i, f ^(l)(e _i,jwhen)=1 is illustrated in the decoded operation of l wheel

and it has connected a variable node v who is eliminated _i, f ^(l)(e _i,je when)=2 are illustrated in the decoded operation of l wheel _i,j∈ E _lDPCand it has connected a variable node v who is eliminated _i; For

due to do not participate in the disappearing limit operation of these limits, so f ^(l)(e _{j-m+n, j})=0; Output variable node v for LDPC code _i, i=1,2 ..., n, F ^(l)(v _iwhen)=0 is illustrated in the decoded operation of l wheel, this node not yet completes the limit operation that disappears, F ^(l)(v _iwhen)=1 item is illustrated in the decoded operation of l wheel, this node has completed the limit operation that disappears;

all while being illustrated in the decoded operation of l wheel

the set of information,

all while being illustrated in the decoded operation of l wheel

the combination of information,

and num ^(l)(v _i) v that stores while being illustrated respectively in the decoded operation of l wheel _ibe used for do the log-likelihood ratio value of hard decision and this value has reached the number of times of thresholding ξ, the check-node c to each LDPC code continuously _j, j=1,2 ..., m arranges two arrays

with

and initialization value is 0, N _rthe coded-bit number that represents the LT code of the actual reception of receiving terminal when decoding finishes;

Concrete steps are as follows:

1) initialization: make l=1, select after screening

the coded-bit of individual LT code enters decoder, by window length, is decoder fill completely, now have order

input variable node v to LT code _i, i=1,2 ..., n arranges F ⁽¹⁾(v _i)=0,

num ⁽¹⁾(v _i)=0; Right $\∀e_{i,j}\∈E_{\mathrm{LDPC}}\∪E_{\mathrm{LT}}^{\left(1\right)}\∪E_O^{\left(1\right)},$ Flag is set ⁽¹⁾(e _i,j)=0;

2) if l=1 enters step 3); Otherwise long for W when front window, comprised

the input variable node of individual LT code and

in the decoder of the output variable node of individual LT code, carry out decoding, the input variable node v to LT code _if is set ^(l)(v _i)=F ^(l-1)(v _i),

num ^(l)(v _i)=0; Right $\∀e_{i,j}\∈E_{\mathrm{LDPC}}\∪E_{\mathrm{LT}}^{(l-1)}\∪E_O^{(l-1)}$ Flag is set ^(l)(e _i,j)=flag ^(l-1)(e _i,j); Right $\∀e_{j-m+n,j}\∈(E_O^{\left(l\right)}-E_O^{(l-1)})$ Flag is set ^(l)(e _{j-m+n, j})=0; Right

if F ^(l)(v _i)=0 item arranges flag ^(l)(e _i,j)=0, if F ^(l)(v _i)=1 item arranges flag ^(l)(e _i,j)=1 is also upgraded

its update rule is as follows:

$L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right)=\left\{\begin{array}{cc}{L}_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)\&GreaterEqual;0\\ -L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)<0\end{array}\right.;$

3) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, and the output variable node of all LT codes in decoder

utilize following formula to upgrade the information that it transmits to adjacent check-node:

$q_{v_i,c_j}^{\left(l\right)}=\underset{c_{j^{\&prime;}}\&Element;N\left(v_i\right)\backslash c_j}{\mathrm{\&Sigma;}}{r}_{c_{j^{\&prime;}},v_i}^{(l-1)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

4) for each check-node in decoder

limit { e to its all connections _i,j| v _i∈ N (c _j) adjudicate, if flag ^(l)(e _i,j)=0, utilizes following formula to upgrade the information that it transmits to adjacent variable node:

$r_{c_j,v_i}^{\left(l\right)}=2{\tanh }^{-1}\left(\underset{{\mathrm{flag}}^{\left(l\right)}\left(e_{i^{\&prime;},j}\right)\&NotEqual;1}{\underset{v_{i^{\&prime;}}\&Element;N\left(c_j\right)\backslash v_i}{\mathrm{\&Pi;}}}\tanh \left(\frac{1}{2}{q}_{v_{i^{\&prime;}},c_j}^{(l-1)}\right)\right);$

5) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, utilizes following formula to upgrade the log-likelihood ratio information that it is used for doing hard decision:

$L^{\left(l\right)}\left(v_i\right)=\underset{c_j\&Element;N\left(v_i\right)}{\mathrm{\&Sigma;}}{r}_{c_j,v_i}^{\left(l\right)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

6) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, estimates the coded-bit w that it is corresponding _ivalue:

$w_i=\left\{\begin{array}{cc}0,& L^{\left(l\right)}\left(v_i\right)\&GreaterEqual;0\\ 1,& L^{\left(l\right)}\left(v_i\right)<0\end{array}\right.,$

If now met the verification relation that the check-node of LDPC code limits, entered step 9); If do not meet verification relation and do not reach the maximum iteration time I setting _max, enter step 7), otherwise enter step 8);

7) its L of output variable node of judgement LDPC code ^(l)(v _i) whether continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, concrete determination methods is as follows: each is met to F ^(l)(v _iThe variable node v of)=0 _i, i=1,2 ..., n proceeds as follows, when Time, if | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1; Otherwise, do not carry out any operation; When

Time, can be divided into again following five kinds of situations,When And | L ^(l)(v _i) |>=ξ and

Order And num ^(l)(v _i)=num ^(l)(v _i)+1, if num ^(l)(v _i)>=T, operation is upgraded on the limit that disappears, even F ^(l)(v _i)=1 and right F is set ^(l)(e _i,j)=1, to e _I,j∈ E _LDPCF is set ^(l)(e _i,j)=2, if

And | L ^(l)(v _i) |>=ξ and

Order

And num ^(l)(v _i)=1, if And | L ^(l)(v _i) | < ξ,Order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) | < ξ, order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1, if find some L ^(l)(v _i) continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, the output variable node of these LDPC codes of cancellation and the limit connecting thereof complete the limit that disappears and upgrade operation, even F ^(l)(v _i)=1 and right

F is set ^(l)(e _i,j)=1, to e _i,j∈ E _LDPCF is set ^(l)(e _i,j)=2; In order to eliminate these impact of operation on other node successive iterations decodings, to meeting flag ^(l)(e _i,jThe limit of)=2, will be later by v _iTo c _jThe L when information of transmitting is made as this node and is eliminated ^(l)(v _i),An i.e. definite value

And no longer calculate by c _jTo v _iThe information of transmitting

l _i=l+1, l+2 ...; Once there be new limit to be set to flag ^(l)(e _i,j)=2, by its current L ^(l)(v _i) deposit in

In, and by the node v of cancellation _iThe bit w translating _iValue deposit in

In, upgrade by c afterwards at every turn _jIn the time of the log-likelihood ratio information of the variable node output not being eliminated to other,

In each element only transmit L separately ^(l)(v _i); Meanwhile, when each judgement translates bit and whether meets the verification relational expression of LDPC code afterwards,

In each w _iAlso participate in XOR, return to step 3), start the iterative decoding of a new round;

8) record

f ^(l)(v _i) (i=1,2 ..., n), flag ^(l)(e _i,j)

value; If do not have the input variable node of LT code to be moved out of decoder in the l time decoding is attempted, enter step 9); If have N in the l time decoding is attempted ^(l)the input variable node of individual LT code is moved out of decoder, selects N again ^(l)the coded-bit of individual LT code after screening enters decoder, even

after the long decoder for W of window is filled, make l=l+1, and enter step 2), the decoding that starts a new round is attempted;

9) stop decoding.

The coded-bit of described step 1) and the selection in the step 8) LT code after screening enters decoder and is: set a threshold value and filter out the coded-bit that confidence level surpasses the LT code of this threshold value, and the coded-bit after screening is sent into decoder by these; Suppose to be superimposed upon the noise n in receiving sequence _ifor additive white Gaussian noise, its variance is σ ², i coded-bit of LT code is x _i, receive code word y _i=1-2x _i+ n _i, set a decoder and enter thresholding ζ, only have when receiving the initial log-likelihood ratio absolute value of code word and surpass this thresholding, that is:

$\left|L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right)\right|=\left|\frac{2y_{i-n}}{{\mathrm{\&sigma;}}^2}\right|\&GreaterEqual;\mathrm{\&zeta;}(i\&GreaterEqual;n+1);$

Just this is received to code word, the output variable node of LT code is sent into decoder and is carried out decoding processing.

The present invention can guarantee that the number of the variable node stored in decoder fixes all the time, although receiving terminal is received new coded-bit (the output variable node of LT code) continuously, but the actual variable node operating (window of decoder is long) is always a definite value, the scale of computational complexity and Tanner figure can constantly not increase along with the carrying out of decoding (as the BP algorithm of " non-progressive "), also can do uncertain variation (as the BP algorithm of " progressive "), the processing of being convenient to hardware realizes disconnectedly.

Accompanying drawing explanation

Fig. 1 is the schematic diagram that belief propagation interpretation method is eliminated on the long limit of the fixed window of no-rate codes;

Fig. 2 is the long W=24250 of given window, and during 25200,26150,27,100 four kinds of situations, bit error rate is with the long simulation curve figure changing of window, and has marked under each window elongate member the R reciprocal of average bit rate when decoding stops ^-1=N _r/ (n-m) and the average decoding number of times l that attempts while stopping of decoding _ave.

Embodiment

The long limit of fixed window of no-rate codes is eliminated belief propagation interpretation method and is: transmitting terminal adopts no-rate codes to encode to the information of needs transmission, and receiving terminal adopts belief propagation decoding; Without rate coding mode, can adopt Raptor Code(to see " Raptor Codes ", IEEE Transactions on Information Theory, Vol.52, No.6, pp.2551-2567, June2006); The number of the variable node of storing in decoder when " window is long " is defined as each decoding, namely participate in the number of the variable node of computing, on the limit that fixed window is long, eliminate in belief propagation interpretation method, the number of the variable node of storing in decoder is fixed all the time; Receiving terminal filters out by setting a threshold value output variable node that confidence level surpasses the LT code of this threshold value, and selection and long equal-sized several variable nodes after screening of window are sent into decoder and started decoding; On trial number wheel limit, eliminate belief propagation decoding and (see " Belief Propagation with Gradual Edge Removal for Raptor Codes over AWGN Channel ", accepted by PIMRC2013) afterwards, if fail successfully decoded, by the limit operation that disappears, how many variable nodes have been removed at present, the output variable node that supplements how many new LT codes enters decoder, and trial and error decoding again, until the successfully decoded or limit operation that disappears cannot remove variable node again;

If: LDPC(low-density checksum) check-node of code and the number of variable node are respectively m=500 and n=10000, the check-node of LT code and the number of variable node that participate in first round decoded operation are respectively N=1.5 * 9500=14250 and N+n=14250+10000=24250, window is long is W=n+N=24250, and variable node is designated as v _i, i=1,2 ..., n+N, check-node is designated as c _j, j=1,2 ..., m+N, N (v _i) c _jexpression is except c _joutside other and v _iconnected check-node, N (c _j) v _iexpression is except v _ioutside other and c _jconnected variable node, e _i,jrepresent to connect v _iand c _jlimit, E _lDPC={ e _i,j| i=1,2 ..., n, j=1,2 ..., m} represents the limit corresponding to LDPC code check matrix, $E_{\mathrm{LT}}^{\left(l\right)}=\left\{e_{i,j}\right|i=\mathrm{1,2},...,n,j=m+1,m+2,...,m+N\}$ While being illustrated in the decoded operation of l wheel corresponding to the limit of LT code generator matrix, the limit that has connected LT code check node and output variable node while being illustrated in the decoded operation of l wheel,

v while being illustrated in the decoded operation of l wheel _ipass to c _jlog-likelihood ratio,

c while being illustrated in the decoded operation of l wheel _jpass to v _ilog-likelihood ratio,

the input log-likelihood ratio of self-channel while being illustrated in the decoded operation of l wheel, because the output variable node of LDPC code does not pass through transmission, so

l ^(l)(v _i) while being illustrated in the decoded operation of l wheel corresponding to v _i, i=1,2 ..., the log-likelihood ratio value that is used for doing hard decision of n+N, ξ=18 and T=2 represent respectively to adjudicate L ^(l)(v _i), i=1,2 ..., the threshold value that need to reach when n confidence level is enough high and the number of times that reaches this threshold value, for

e while being illustrated in the decoded operation of l wheel _i,jconnected a variable node v who is eliminated _i, f ^(l)(e _i,jwhen)=1 is illustrated in the decoded operation of l wheel

and it has connected a variable node v who is eliminated _i, f ^(l)(e _i,je when)=2 are illustrated in the decoded operation of l wheel _i,j∈ E _lDPCand it has connected a variable node v who is eliminated _i; For

due to do not participate in the disappearing limit operation of these limits, so f ^(l)(e _{j-m+n, j})=0; Output variable node v for LDPC code _i, i=1,2 ..., n, F ^(l)(v _iwhen)=0 is illustrated in the decoded operation of l wheel, this node not yet completes the limit operation that disappears, F ^(l)(v _iwhen)=1 item is illustrated in the decoded operation of l wheel, this node has completed the limit operation that disappears;

all while being illustrated in the decoded operation of l wheel

the set of information,

all while being illustrated in the decoded operation of l wheel

the combination of information,

and num ^(l)(v _i) v that stores while being illustrated respectively in the decoded operation of l wheel _ibe used for do the log-likelihood ratio value of hard decision and this value has reached the number of times of thresholding ξ, the check-node c to each LDPC code continuously _j, j=1,2 ..., m arranges two arrays

with

and initialization value is 0, N _rthe coded-bit number that represents the LT code of the actual reception of receiving terminal when decoding finishes;

As shown in Figure 1, concrete steps are as follows for the schematic diagram of the long limit elimination of the fixed window belief propagation interpretation method of no-rate codes:

1) initialization: make l=1, select after screening

the coded-bit of individual LT code enters decoder, by window length, is

decoder fill completely, now have

order

input variable node v to LT code _i, i=1,2 ..., n arranges F ⁽¹⁾(v _i)=0,

num ⁽¹⁾(v _i)=0; Right

flag is set ⁽¹⁾(e _i,j)=0;

2) if l=1 enters step 3); Otherwise long for W when front window, comprised

the input variable node of individual LT code and in the decoder of the output variable node of individual LT code, carry out decoding, the input variable node v to LT code _if is set ^(l)(v _i)=F ^(l-1)(v _i),

num ^(l)(v _i)=0; Right $\&ForAll;e_{i,j}\&Element;E_{\mathrm{LDPC}}\&cup;E_{\mathrm{LT}}^{(l-1)}\&cup;E_O^{(l-1)}$ Flag is set ^(l)(e _i,j)=flag ^(l-1)(e _i,j); Right $\&ForAll;e_{j-m+n,j}\&Element;(E_O^{\left(l\right)}-E_O^{(l-1)})$ Flag is set ^(l)(e _{j-m+n, j})=0; Right

if F ^(l)(v _i)=0 item arranges flag ^(l)(e _i,j)=0, if F ^(l)(v _i)=1 item arranges flag ^(l)(e _i,j)=1 is also upgraded its update rule is as follows:

$L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right)=\left\{\begin{array}{cc}{L}_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)\&GreaterEqual;0\\ -L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)<0\end{array}\right.;$

3) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, and the output variable node of all LT codes in decoder

utilize following formula to upgrade the information that it transmits to adjacent check-node:

$q_{v_i,c_j}^{\left(l\right)}=\underset{c_{j^{\&prime;}}\&Element;N\left(v_i\right)\backslash c_j}{\mathrm{\&Sigma;}}{r}_{c_{j^{\&prime;}},v_i}^{(l-1)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

4) for each check-node in decoder

limit { e to its all connections _i,j| v _i∈ N (c _j) adjudicate, if flag ^(l)(e _i,j)=0, utilizes following formula to upgrade the information that it transmits to adjacent variable node:

$r_{c_j,v_i}^{\left(l\right)}=2{\tanh }^{-1}\left(\underset{{\mathrm{flag}}^{\left(l\right)}\left(e_{i^{\&prime;},j}\right)\&NotEqual;1}{\underset{v_{i^{\&prime;}}\&Element;N\left(c_j\right)\backslash v_i}{\mathrm{\&Pi;}}}\tanh \left(\frac{1}{2}{q}_{v_{i^{\&prime;}},c_j}^{(l-1)}\right)\right);$

5) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, utilizes following formula to upgrade the log-likelihood ratio information that it is used for doing hard decision:

$L^{\left(l\right)}\left(v_i\right)=\underset{c_j\&Element;N\left(v_i\right)}{\mathrm{\&Sigma;}}{r}_{c_j,v_i}^{\left(l\right)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

6) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, estimates the coded-bit w that it is corresponding _ivalue:

$w_i=\left\{\begin{array}{cc}0,& L^{\left(l\right)}\left(v_i\right)\&GreaterEqual;0\\ 1,& L^{\left(l\right)}\left(v_i\right)<0\end{array}\right.,$

If now met the verification relation that the check-node of LDPC code limits, entered step 9); If do not meet verification relation and do not reach the maximum iteration time I setting _max=50, enter step 7), otherwise enter step 8);

7) its L of output variable node of judgement LDPC code ^(l)(v _i) whether continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, concrete determination methods is as follows: each is met to F ^(l)(v _iThe variable node v of)=0 _i, i=1,2 ..., n proceeds as follows, when

Time, if | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1; Otherwise, do not carry out any operation; When

Time, can be divided into again following five kinds of situations,When

And | L ^(l)(v _i) |>=ξ and

Order

And num ^(l)(v _i)=num ^(l)(v _i)+1, if num ^(l)(v _i)>=T, operation is upgraded on the limit that disappears, even F ^(l)(v _i)=1 and right

F is set ^(l)(e _i,j)=1, to e _I,j∈ E _LDPCF is set ^(l)(e _i,j)=2, if

And | L ^(l)(v _i) |>=ξ and Order

And num ^(l)(v _i)=1, if

And | L ^(l)(v _i) | < ξ,Order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) | < ξ, order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1, if find some L ^(l)(v _i) continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, the output variable node of these LDPC codes of cancellation and the limit connecting thereof complete the limit that disappears and upgrade operation, even F ^(l)(v _i)=1 and right

F is set ^(l)(e _i,j)=1, to e _i,j∈ E _LDPCF is set ^(l)(e _i,j)=2; In order to eliminate these impact of operation on other node successive iterations decodings, to meeting flag ^(l)(e _i,jThe limit of)=2, will be later by v _iTo c _jThe L when information of transmitting is made as this node and is eliminated ^(l)(v _i),An i.e. definite value

And no longer calculate by c _jTo v _iThe information of transmitting

l _i=l+1, l+2 ...; Once there be new limit to be set to flag ^(l)(e _i,j)=2, by its current L ^(l)(v _i) deposit in

In, and by the node v of cancellation _iThe bit w translating _iValue deposit in

In, upgrade by c afterwards at every turn _jIn the time of the log-likelihood ratio information of the variable node output not being eliminated to other,

In each element only transmit L separately ^(l)(v _i); Meanwhile, when each judgement translates bit and whether meets the verification relational expression of LDPC code afterwards,

In each w _iAlso participate in XOR, return to step 3), start the iterative decoding of a new round;

8) record

f ^(l)(v _i) (i=1,2 ..., n), flag ^(l)(e _i,j)

value; If do not have the input variable node of LT code to be moved out of decoder in the l time decoding is attempted, enter step 9); If have N in the l time decoding is attempted ^(l)the input variable node of individual LT code is moved out of decoder, selects N again ^(l)the coded-bit of individual LT code after screening enters decoder, even

after the long decoder for W of window is filled, make l=l+1, and enter step 2), the decoding that starts a new round is attempted;

9) stop decoding.

The coded-bit of described step 1) and the selection in the step 8) LT code after screening enters decoder and is: set a threshold value and filter out the coded-bit that confidence level surpasses the LT code of this threshold value, and the coded-bit after screening is sent into decoder by these; Suppose to be superimposed upon the noise n in receiving sequence _ifor additive white Gaussian noise, its variance is σ ²i coded-bit of=0.9577, LT code is x _i, receive code word y _i=1-2x _i+ n _i, set a decoder and enter thresholding ζ=1, only have when receiving the initial log-likelihood ratio absolute value of code word and surpass this thresholding, that is:

$\left|L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right)\right|=\left|\frac{2y_{i-n}}{{\mathrm{\&sigma;}}^2}\right|\&GreaterEqual;\mathrm{\&zeta;}(i\&GreaterEqual;n+1);$

Namely | y _i-n|>=0.478829 o'clock, just this is received to code word, the output variable node of LT code is sent into decoder and is carried out decoding processing.

Fig. 2 emulation the long W=24250 of window, 25250,26150 and 27,100 four kinds of situations, the number of repetition of emulation is set to NUM=1000.In figure, each point of transverse axis represents that a window is long, and the longitudinal axis is the average error bit rate (BER) of corresponding decoding while stopping.While also having marked in addition under each window is long decoding in figure, the average decoding number of times of attempting when decoding stops, being respectively l _ave=1.009,2.002,3.776,1.097, and the R reciprocal of the average bit rate of decoding while stopping ^-1=N _r/ (n-m), be respectively R ^-1=1.95253,2.08347,2.41263,2.38674.Can see, along with the long increase of window, the amount of information that in decode procedure, decoder obtains is larger, so BER declines thereupon.When window length is very little (as W=24250), the information that when each decoding is attempted, decoder obtains very little, after attempting, a decoding substantially do not have the input variable node of LT code to reach the condition of removing to be moved out of decoder completing, therefore have new node to supplement, do not enter decoder, decoding cannot go on, and decoding stops (l _ave=1.009).Long when not enough large (as W=25200,26150) when window, the information that when each decoding is attempted, decoder obtains is not abundant, at (l after the trial of decoding several times _avebe respectively 2.002 and 3.776), just do not have the input variable node of LT code to reach the condition of removing and be moved out of decoder, therefore decoding stops.When window is considerable, enough when large (as W=27100), the information that when each decoding is attempted, decoder obtains is abundant, and what add its utilization is the good received code symbol of initial information after screening, thus only need decoding seldom attempt (1 time to 2 times, l _ave=1.097) with regard to energy decoding success, BER is down to 10 ^-7below.Code check when finally, decoding stops is the coded-bit sum N being received by receiving terminal _r(comprise and send into two parts decoder and that screened out) determined, thus received code total number of bits during W=27100 decoding success during than W=26150 the decoding of number wheel attempt after the coded-bit sum that receives while stopping of decoding few, i.e. R ^-1smaller on the contrary.

Claims (2)

1. a belief propagation interpretation method is eliminated on the long limit of the fixed window of no-rate codes, it is characterized in that, transmitting terminal adopts no-rate codes to encode to the information of needs transmission, and receiving terminal adopts belief propagation decoding; The number of the variable node of storing in decoder when " window is long " is defined as each decoding, namely participate in the number of the variable node of computing, on the limit that fixed window is long, eliminate in belief propagation interpretation method, the number of the variable node of storing in decoder is fixed all the time; Receiving terminal filters out by setting a threshold value output variable node that confidence level surpasses the LT code of this threshold value, and selection and long equal-sized several variable nodes after screening of window are sent into decoder and started decoding; After attempting the decoding of number wheel limit elimination belief propagation, if fail successfully decoded, by the limit operation that disappears, how many variable nodes have been removed at present, the output variable node that supplements how many new LT codes enters decoder, and trial and error decoding again, until the successfully decoded or limit operation that disappears cannot remove variable node again;

If: the check-node of LDPC code and the number of variable node are respectively m and n, and the check-node of LT code and the number of variable node that participate in first round decoded operation are respectively N and N+n, and window is long is W=n+N, and variable node is designated as v _i, i=1,2 ..., n+N, check-node is designated as c _j, j=1,2 ..., m+N, N (v _i) c _jexpression is except c _joutside other and v _iconnected check-node, N (c _j) v _iexpression is except v _ioutside other and c _jconnected variable node, e _i,jrepresent to connect v _iand c _jlimit, E _lDPC={ e _i,j| i=1,2 ..., n, j=1,2 ..., m} represents the limit corresponding to LDPC code check matrix, $E_{\mathrm{LT}}^{\left(l\right)}=\left\{e_{i,j}\right|i=\mathrm{1,2},...,n,j=m+1,m+2,...,m+N\}$ While being illustrated in the decoded operation of l wheel corresponding to the limit of LT code generator matrix,

the limit that has connected LT code check node and output variable node while being illustrated in the decoded operation of l wheel, v while being illustrated in the decoded operation of l wheel _ipass to c _jlog-likelihood ratio,

c while being illustrated in the decoded operation of l wheel _jpass to v _ilog-likelihood ratio,

the input log-likelihood ratio of self-channel while being illustrated in the decoded operation of l wheel, because the output variable node of LDPC code does not pass through transmission, so

l ^(l)(v _i) while being illustrated in the decoded operation of l wheel corresponding to v _i, i=1,2 ..., the log-likelihood ratio value that is used for doing hard decision of n+N, ξ and T represent respectively to adjudicate L ^(l)(v _i), i=1,2 ..., the threshold value that need to reach when n confidence level is enough high and the number of times that reaches this threshold value, for

f ^(l)(e _i,je when)=0 is illustrated in the decoded operation of l wheel _i,jconnected a variable node v who is eliminated _i, f ^(l)(e _i,jwhen)=1 is illustrated in the decoded operation of l wheel

and it has connected a variable node v who is eliminated _i, f ^(l)(e _i,je when)=2 are illustrated in the decoded operation of l wheel _i,j∈ E _lDPCand it has connected a variable node v who is eliminated _i; For

due to do not participate in the disappearing limit operation of these limits, so f ^(l)(e _{j-m+n, j})=0; Output variable node v for LDPC code _i, i=1,2 ..., n, F ^(l)(v _iwhen)=0 is illustrated in the decoded operation of l wheel, this node not yet completes the limit operation that disappears, F ^(l)(v _iwhen)=1 item is illustrated in the decoded operation of l wheel, this node has completed the limit operation that disappears;

all while being illustrated in the decoded operation of l wheel the set of information,

all while being illustrated in the decoded operation of l wheel

the combination of information,

and num ^(l)(v _i) v that stores while being illustrated respectively in the decoded operation of l wheel _ibe used for do the log-likelihood ratio value of hard decision and this value has reached the number of times of thresholding ξ, the check-node c to each LDPC code continuously _j, j=1,2 ..., m arranges two arrays

with and initialization value is 0, N _rthe coded-bit number that represents the LT code of the actual reception of receiving terminal when decoding finishes;

Concrete steps are as follows:

1) initialization: make l=1, select after screening

the coded-bit of individual LT code enters decoder, by window length, is

decoder fill completely, now have

order

input variable node v to LT code _i, i=1,2 ..., n arranges F ⁽¹⁾(v _i)=0,

num ⁽¹⁾(v _i)=0; Right $\&ForAll;e_{i,j}\&Element;E_{\mathrm{LDPC}}\&cup;E_{\mathrm{LT}}^{\left(1\right)}\&cup;E_O^{\left(1\right)},$ Flag is set ⁽¹⁾(e _i,j)=0;

2) if l=1 enters step 3); Otherwise long for W when front window, comprised

the input variable node of individual LT code and

in the decoder of the output variable node of individual LT code, carry out decoding, the input variable node v to LT code _if is set ^(l)(v _i)=F ^(l-1)(v _i),

num ^(l)(v _i)=0; Right $\&ForAll;e_{i,j}\&Element;E_{\mathrm{LDPC}}\&cup;E_{\mathrm{LT}}^{(l-1)}\&cup;E_O^{(l-1)}$ Flag is set ^(l)(e _i,j)=flag ^(l-1)(e _i,j); Right $\&ForAll;e_{j-m+n,j}\&Element;(E_O^{\left(l\right)}-E_O^{(l-1)})$ Flag is set ^(l)(e _{j-m+n, j})=0; Right if F ^(l)(v _i)=0 item arranges flag ^(l)(e _i,j)=0,

if F ^(l)(v _i)=1 item arranges flag ^(l)(e _i,j)=1 is also upgraded its update rule is as follows:

$L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right)=\left\{\begin{array}{cc}{L}_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)\&GreaterEqual;0\\ -L_{\mathrm{ch}}^{\left(l\right)}\left(v_{j-m+n}\right),& L^{(l-1)}\left(v_i\right)<0\end{array}\right.;$

3) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, and the output variable node of all LT codes in decoder

utilize following formula to upgrade the information that it transmits to adjacent check-node:

$q_{v_i,c_j}^{\left(l\right)}=\underset{c_{j^{\&prime;}}\&Element;N\left(v_i\right)\backslash c_j}{\mathrm{\&Sigma;}}{r}_{c_{j^{\&prime;}},v_i}^{(l-1)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

4) for each check-node in decoder

limit { e to its all connections _i,j| v _i∈ N (c _j) adjudicate, if flag ^(l)(e _i,j)=0, utilizes following formula to upgrade the information that it transmits to adjacent variable node:

$r_{c_j,v_i}^{\left(l\right)}=2{\tanh }^{-1}\left(\underset{{\mathrm{flag}}^{\left(l\right)}\left(e_{i^{\&prime;},j}\right)\&NotEqual;1}{\underset{v_{i^{\&prime;}}\&Element;N\left(c_j\right)\backslash v_i}{\mathrm{\&Pi;}}}\tanh \left(\frac{1}{2}{q}_{v_{i^{\&prime;}},c_j}^{(l-1)}\right)\right);$

5) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, utilizes following formula to upgrade the log-likelihood ratio information that it is used for doing hard decision:

$L^{\left(l\right)}\left(v_i\right)=\underset{c_j\&Element;N\left(v_i\right)}{\mathrm{\&Sigma;}}{r}_{c_j,v_i}^{\left(l\right)}+L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right);$

6) for meeting F ^(l)(v _ithe input variable node v of the LT code of)=0 _i, i=1,2 ..., n, estimates the coded-bit w that it is corresponding _ivalue:

$w_i=\left\{\begin{array}{cc}0,& L^{\left(l\right)}\left(v_i\right)\&GreaterEqual;0\\ 1,& L^{\left(l\right)}\left(v_i\right)<0\end{array}\right.,$

If now met the verification relation that the check-node of LDPC code limits, entered step 9); If do not meet verification relation and do not reach the maximum iteration time I setting _max, enter step 7), otherwise enter step 8);

7) its L of output variable node of judgement LDPC code ^(l)(v _i) whether continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, concrete determination methods is as follows:

Each is met to F ^(l)(v _iThe variable node v of)=0 _i, i=1,2 ..., n proceeds as follows, when

Time, if | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1; Otherwise, do not carry out any operation; When Time, can be divided into again following five kinds of situations, when And | L ^(l)(v _i) |>=ξ and

Order

And num ^(l)(v _i)=num ^(l)(v _i)+1, if num ^(l)(v _i)>=T, operation is upgraded on the limit that disappears, even F ^(l)(v _i)=1 and right F is set ^(l)(e _i,j)=1, to e _i,j∈ E _LDPCF is set ^(l)(e _i,j)=2,If

And | L ^(l)(v _i) |>=ξ and

Order And num ^(l)(v _i)=1, if And | L ^(l)(v _i) | < ξ, order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) | < ξ, order

And num ^(l)(v _i)=0, if

And | L ^(l)(v _i) |>=ξ, order

And num ^(l)(v _i)=1, if find some L ^(l)(v _i) continuous T time reach threshold value ξ and | L ^(l)(v _i) | increase gradually, the output variable node of these LDPC codes of cancellation and the limit connecting thereof complete the limit that disappears and upgrade operation, even F ^(l)(v _i)=1 and right F is set ^(l)(e _i,j)=1, to e _i,j∈ E _LDPCF is set ^(l)(e _i,j)=2; In order to eliminate these impact of operation on other node successive iterations decodings, to meeting flag ^(l)(e _i,jThe limit of)=2, will be later by v _iTo c _jThe L when information of transmitting is made as this node and is eliminated ^(l)(v _i), i.e. a definite value

And no longer calculate by c _jTo v _iThe information of transmitting

l _i=l+1, l+2 ...; Once there be new limit to be set to flag ^(l)(e _i,j)=2, by its current L ^(l)(v _i) deposit in

In, and by the node v of cancellation _iThe bit w translating _iValue deposit in

In, upgrade by c afterwards at every turn _jIn the time of the log-likelihood ratio information of the variable node output not being eliminated to other,

In each element only transmit L separately ^(l)(v _i); Meanwhile, when each judgement translates bit and whether meets the verification relational expression of LDPC code afterwards,

In each w _iAlso participate in XOR, return to step 3), start the iterative decoding of a new round;

8) record

f ^(l)(v _i) (i=1,2 ..., n), flag ^(l)(e _i,j) value; If do not have the input variable node of LT code to be moved out of decoder in the l time decoding is attempted, enter step 9); If have N in the l time decoding is attempted ^(l)the input variable node of individual LT code is moved out of decoder, selects N again ^(l)the coded-bit of individual LT code after screening enters decoder, even

after the long decoder for W of window is filled, make l=l+1, and enter step 2), the decoding that starts a new round is attempted;

9) stop decoding.

2. belief propagation interpretation method is eliminated on the long limit of the fixed window of a kind of no-rate codes according to claim 1, the coded-bit of the step 1) described in it is characterized in that and the selection in the step 8) LT code after screening enters decoder and is: set a threshold value and filter out the coded-bit that confidence level surpasses the LT code of this threshold value, and the coded-bit after screening is sent into decoder by these; Suppose to be superimposed upon the noise n in receiving sequence _ifor additive white Gaussian noise, its variance is σ ², i coded-bit of LT code is x _i, receive code word y _i=1-2x _i+ n _i, set a decoder and enter thresholding ζ, only have when receiving the initial log-likelihood ratio absolute value of code word and surpass this thresholding, that is:

$\left|L_{\mathrm{ch}}^{\left(l\right)}\left(v_i\right)\right|=\left|\frac{2y_{i-n}}{{\mathrm{\&sigma;}}^2}\right|\&GreaterEqual;\mathrm{\&zeta;}(i\&GreaterEqual;n+1);$

Just this is received to code word, the output variable node of LT code is sent into decoder and is carried out decoding processing.

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