CN1973440A - LDPC encoders, decoders, systems and methods - Google Patents

Abstract

An LDPC encoder with a complexity that increases linearly as a function of block size is provided. They are implementable with simple logic consisting of a repeater with an irregular repeat pattern, an interleaver, and an accumulator that performs irregular accumulations.

Description

LDPC encoder, decoder, system and method

Technical field

The present invention relates to LDPC encoder, decoder, system and method.

Background technology

The performance that has proved LDPC (low-density checksum) sign indicating number by many research work has surpassed Turbo code, and even can only be lower than shannon limit 0.045dB.This algorithm that is used for the message transmission allows parallel computation, and compares storage resources and the computing cost that only needs seldom with the Turbo decoding algorithm.

This message pass-algorithm is based on the characteristic of the parity check matrix H of linear block coding, and comprising: parity matrix multiply by any effective code word will obtain null vector.Another key property of check matrix is that it is sparse, and the number of unit is the linear function of codeword size in the matrix.Therefore, decoding complexity is the linear function of the length of code word.

The validity of decoding algorithm can not guarantee the validity of encryption algorithm efficiently efficiently.By the theory of linear block coding as can be known, generator matrix G is commonly used to message is encoded.The pass of generator matrix G and check matrix H is: HG ^T=0mod2.The complexity of coding and encoding block are pressed quadratic power and are increased.In order to be～10 to length ³Code word encode, the required number of times of computing is～10 ⁶, thereby will be difficult for the application of reality.A kind of method that addresses this problem is utilize to use the sign indicating number thought RA-IRA of linear time code (repeat to add up-irregular the repetition add up).

Summary of the invention

According to an aspect widely, the invention provides a kind of LDPC encoder that the output of generation system and parity check are exported that is suitable for linear complexity, this encoder comprises: duplicator, realize irregular duplication code; Interleaver is carried out the output of duplicator and to be interweaved; Accumulator is carried out the output of interleaver and to be added up and export parity check output.

In certain embodiments, interleaver be S at random or the congruence interleaver.

In certain embodiments, accumulator is carried out irregular adding up.

In certain embodiments, the accumulator executing rule adds up.

In certain embodiments, the LDPC encoder also contains the parallel-to-serial function between duplicator and interleaver.

In certain embodiments, the LDPC encoder is by the repeat pattern of duplicator, and the sequence of interleaver changes and comes parametrization.

In certain embodiments, the change of repeat pattern and sequence is best.

In certain embodiments, the s random interleaver is half random algorithm with refusal, and interweaving in advance continuous to s provides the back interleaved distance that is not less than s, $s\&le;\sqrt{\frac{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">N</figure-callout>}}{2}}.$

In certain embodiments, the LDPC sign indicating number can be represented by the parity matrix with double diagonal line structure:

In certain embodiments, whole sign indicating number is expressed as follows with matrix form:

$H=[\left.\begin{array}{cccccc}{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,1}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{0,2}}& ...& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,m_b-2}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,m_b-1}\\ {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}& ...& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,m_b-2}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,m_b-1}\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,0}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}& <figure-callout\; id="2"\; label="...\; p"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">.</figure-callout>..& p_{}{}_{2,m_b-2}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{2,m_{b-1}}\\ .& .& .& ...& .& .\\ .& .& .& ...& .& .\\ .& .& .& ...& .& .\\ P_{m_b-\mathrm{1,0}}& P_{m_b-\mathrm{1,1}}& P_{m_b-\mathrm{1,2}}& ...& P_{m_b-1,m_b-2}& p_{m_b-1,m_b-1}\end{array}\right]=P^{H_b}$

Wherein H is the matrix of big or small m * n, and n is that the length and the m of sign indicating number is the number of the parity check bit in the sign indicating number, wherein P _{I, j}Be move to right in unit matrix or the z * z null matrix one of one group of z * z; Matrix H is to be m by size _b* n _bThe binary radix matrix H _bExpand, wherein n=zn _bAnd m=zm _b, and z is positive integer, this basic matrix is by the unit matrix that moves to right with each the 1 usefulness z * z in the basic matrix, and the null matrix of each 0 usefulness z * z replaces expanding; With H _bSeparated into two parts, wherein H _B1Corresponding with system bits, and H _B2Corresponding with parity check bit; Again with H _B2Separated into two parts, wherein vectorial h _bHave strange weight, and H ' _B2Matrix element with the capable j row of its i equals 1 at i=j during i=j+1, all the other are 0 double diagonal line structure:

H wherein _b(0)=1, h _b(m-1)=1, and the 3rd the value h _b(j) equal 1,0＜j＜(m _b-1).

In certain embodiments, the LDPC encoder also is suitable for allowing based on the conventional coders/decoder with rate-compatible check node processor structural feature to the structure of one group of different code check and the structure based on the speed of compression to being complementary with the check-node cascade.

According to the aspect of another wide model, the invention provides a kind of LDPC encoder with basic matrix structure, it has avoided having a plurality of weights in the matrix of expansion is 1 row.

According to the aspect of another wide model, the invention provides a kind of LDPC encoder, realized the LDPC sign indicating number that can represent by parity matrix with following double diagonal line structure:

In certain embodiments, whole sign indicating number is expressed as follows with matrix form:

$H=\left[\begin{array}{cccccc}{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,1}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{0,2}}& ...& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,n_b-2}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,n_b-1}\\ {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}& ...& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,n_b-2}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,n_b-1}\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,0}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}& ...& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{2,n_b-2}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{2,n_b-1}\\ .& .& .& & .& .\\ .& .& .& ...& .& .\\ .& .& .& & .& .\\ P_{m_b-\mathrm{1,0}}& P_{m_b-\mathrm{1,1}}& P_{m_b-\mathrm{1,2}}& ...& P_{m_b-1,n_b-2}& P_{m_b-1,n_b-1}\end{array}\right]\text{=}{P}^{H_b}$

According to the aspect of another wide model, the invention provides a kind of given information sequence s, carry out the LDPC coding to determine the method for parity sequences P, it contains following steps: the k that information sequence s is divided into the z position _b=n _b-m _bGroup makes this grouping s be represented as u,

u＝[u(0)u(1)…u(k _b-1)]，

Wherein each element of u is following column vector

u(i)＝[s _izs _iz+1…s _(i+1)z-1] ^T

Matrix H uses a model _b, determine that in the group of z the parity sequences p of parity sequences p-order grouping represents with v,

v＝[v(0)v(1)…v(m _b-1)]

Wherein each element of v is following column vector

v(i)＝[p _izp _iz+1…p _(i+1)z-1] ^T

Carry out initialization step to determine v (0);

Carry out recurrence to determine v (i+1), 0≤i≤m according to v (i) _b-2;

In certain embodiments, the expression formula of v (0) can be passed through H _bRow summation obtain to obtain

$P_{P(x,k_b)}v\left(0\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m_b-1}{\mathrm{\&Sigma;}}}{P}_{p(i,j)}u\left(j\right)---\left(1\right)$

Wherein x is non-negative and azygous h for its clauses and subclauses _bLine index, 1≤x≤m _b-2,, and p _iRepresent ring shift right z * z unit matrix of i by size.Equation (1) is by taking advantage of P _{P (x, kb)} ^-1Find the solution v (0), and $P_{P(x,k_b)}^{-1}=p_{z-p(x,k_b)},$ Because p is (x, k _b) the expression cyclic shift.

In certain embodiments, recurrence is stipulated according to following formula:

$v\left(1\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{P(i,j)}u\left(j\right)+P_{P(i,k_b)}v\left(0\right),i=0,---\left(2\right)$

$v(i+1)=v\left(i\right)+\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{p(i,j)}u\left(j\right)+P_{p(i,k_b)}v\left(0\right),i=1,...,m_b-2---\left(3\right)$

Wherein

P _-1≡0 _z×z

In certain embodiments, the LDPC encoder contains: parallel node processing structure, the code check and the interleaver that are suitable for any selection are selected, and are used for the sign indicating number of realizing according to any aforesaid method is decoded.

Description of drawings

Fig. 1 is the schematic diagram of RA code structure;

Fig. 2 is the schematic diagram of RA coder structure;

Fig. 3 is the schematic diagram of decoding algorithm;

Fig. 4 is the schematic diagram of the improvement interleaver of this decoder;

Fig. 5 is the schematic diagram that message is calculated;

Fig. 6 is the schematic diagram of check node calculation;

Fig. 7 is the schematic diagram of group fully of incident;

Fig. 8 is the curve chart of function ln ((exp (x)-1)/(exp (x)+1));

Fig. 9 is the figure that repeats to show of irregular variable node;

Figure 10 is the curve chart of BER to Eb/No;

Figure 11 is the curve chart of BER to Eb/No variable speed decoder structure;

Figure 12 is the structural representation of variable speed decoder;

Figure 13 is the curve chart at the number of the system message of check node;

Figure 14 is the curve chart of " frame error rate of variable speed decoder: IRA-7 and 3GPP turbo, frame sign are 1000 ";

Figure 15 is the schematic diagram of basic IRA decoder architecture;

Figure 16 is the schematic diagram of parallel node processing;

Figure 17 is the schematic diagram of the repetition factor in the interleaver;

Figure 18 is the schematic diagram of interleaver structure;

Figure 19 is the schematic diagram of even-odd interleaver;

Figure 20 is the schematic diagram of the strange-even interleaver of expansion;

Figure 21 is the schematic diagram of basic check node processor;

Figure 22 is the schematic diagram of the check node processor of 1/2 speed;

Figure 23 is the schematic diagram of the check node processor of 1/2 rate variable;

Figure 24 is the schematic diagram of rate-compatible check node processor 1/4,1/3,1/2;

Figure 25 is the schematic diagram of speed set constructor;

Figure 26 is the schematic diagram of check node processor 2/3;

Figure 27 is the schematic diagram of check node processor 4/5;

Figure 28 is the schematic diagram of the modal processor based structures (variable and verification) determined of tape symbol not;

Figure 29 is the complete check node processor structure 2+2LUT schematic diagram except that parity check symbol;

Figure 30 is the initialized schematic diagram of parity check node;

Figure 31 is the schematic diagram of handling by parity check variable node processor (need not to calculate);

Figure 32 is the schematic diagram of check node processor with cascade of umbral symbol compression;

Figure 33 is the schematic diagram of variable node processor 3;

Figure 34 is the schematic diagram of variable node processor 3-3-3-5;

Figure 35 is the schematic diagram of variable node processor 7;

Figure 36 is the curve chart of the comparison FER of IRA-7 and 3GPP2 turbo sign indicating number;

Figure 37 is the curve chart of the comparison BER of IRA-7 and 3GPP2 turbo sign indicating number;

Figure 38 is the curve chart of simple compression loss FER;

Figure 39 is the curve chart of simple compression loss BER;

Figure 40 repeats to add up the curve chart of yard FER;

Figure 41 repeats to add up the curve chart of yard BER;

Figure 42 is the FER curve chart that repetition factor reduces;

Figure 43 is the FER curve chart by RA-3 sign indicating number simple compression;

Figure 44 is the FER curve chart according to the performance of iterations; And

Figure 45 is the BER curve chart according to the performance of iterations.

Embodiment

Fig. 1 shows the example of symmetrical RA code structure, and wherein Bian Ma complexity is along with the length of code block increases linearly.Illustrated example is got 4 system bits and is produced 5 check digit.These 4 system bits inputs are shown in 10,12,14,16 places.A plurality of copies of each system bits are imported into interleaver 18.Interleaver output through selecting is fed to 5 check- nodes 18,20,22,24,26 that produce parity check bit.LDPC message pass-algorithm is applicable to the structure of this sign indicating number.In other words this sign indicating number allows to decode by Tanner figure.The actual performance that obtains is unlike other yards difference of LDPC class.

The encoder that is provided by embodiments of the invention is provided form with block diagram in Fig. 2.This encoder has the input 50 that is used to receive the system bits that will be encoded.Encoder output contains system bits 68 and parity check bit 66.System bits input 50 is imported into duplicator 52, and it produces the also line output 53 that is fed to parallel to serial converter 54.Serial output 55 is imported into interleaver 56.Interleaver output 57 is imported into accumulator.Accumulator contains distance function 60 and state element 62 in this illustrated examples, but other designs also are possible.The output of distance function 60 is fed back to second input of distance function 60 by state element.Every now and then, be preferably in the irregular accumulation period, be taken as one of them of parity check bit 66 in the position of the output of accumulator 58 (the distance function 60 in the illustrated examples).It uses schematically explanation of switch 64.The number of times that parity check bit is got in output place of distance function 60 is the function of coder structure.

In order to strengthen error correcting capability, the irregular repetition of best system symbol is with the same being used of irregular summation after the interleaver.Therefore, three forms below can be used to the sign indicating number in the structure of Fig. 2 is provided with:

1, the form of components of system as directed repetition;

2, interleaver;

3, the summation form after interweaving;

Contain that components of system as directed repeats and the example of the form of the both information of suing for peace illustrates hereinafter.How input produces according to system bits to repeat the output of grid column identification duplicator.In illustrated examples, there is system's input of 8.This repeats row indications except this position is repeated, and has how many times to be repeated, and how much output of summation grid column indication interleaver has summed export to produce each parity check bit.The summation form will be in the generation of output distance function 60 places of the example of Fig. 2 control parity check bit 66.In illustrated examples, exist for per 8 system bits and 5 parity check bits of total of producing.

We have 8 system bits, and we are 8 and use the left column circulation to repeat so that expand to:

The 11222333=17 position

These are interleaved and the right then summation form that is listed as is used to summation to produce parity check bit:

3 → 14 → 15 → 13 → 12 → 1 we the code check that amounts to 5 these examples of parity check bit is arranged is 8/ (8+5)=8/13

Form 1 coding form (example)

Repeat form	The summation form
		0	3
0	4
		1	5
1	3
		1	2
2
		2
2

By last form as seen, first and second are once involved, and the the 3rd, the 4th and the 5th involved twice, and the the 6th, the 7th and the 8th is comprised three times.By last form as seen, in order to obtain first check digit, nonequivalence operation must sequentially be carried out by 3 at the interleaver output.Next check digit with following 4 positions of interleaver output and first check digit etc., uses the number of such position of appointment in form to obtain by exclusive-OR operation.Be used to refer to use that each system bits is repeated the form of how many times and be the simple examples of the structure that can be used to realize this function.Each the number of times of repetition of (course) can be the function of concrete sign indicating number design in the study course, as the number of the system bits used, i.e. block size.Similarly, the parity check bit of generation can be the function of specific code design, and is used for producing separately that the number of the carry-out bit of the interleaver of parity check bit is the specific parameter of sign indicating number.The example that coding form provides in the form 1 only is extremely specific example.

In example, Fig. 9 shows irregular repetition factor and based on different code checks, has listed the summation factor in form 4.

In a preferred embodiment, interleaver is " s at random " interleaver.Selected algorithm is half random algorithm with refusal, and interweaving continuously in advance to s, the position provides the back interleaved distance that is not less than s.As verified, if $s\&le;\sqrt{\frac{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">N</figure-callout>}}{2}},$ Then such interleaving process convergence.This interweaving method allows to get rid of the short period in the matrix that obtains.

Direct coding

Usually, each LDPC sign indicating number all is the system linearity block code.Each LDPC sign indicating number in this group LDPC sign indicating number is stipulated that by the matrix H of big or small m * n wherein n is that the length and the m of sign indicating number are the number of parity check bit in the sign indicating number.The number of system bits is k=n-m.

Matrix H is defined as the expansion of basic matrix and can be expressed as:

$H=\left[\begin{array}{cccccc}{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{0,1}}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{0,2}}& ...& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,n_b-2}& {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{0,n_b-1}\\ {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}& ...& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,n_b-2}& {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="A20058001744200331.png,A20058001744200351.png"\; state="\{\{state\}\}">P</figure-callout>}}_{1,n_b-1}\\ {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,0}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>\; </figure-callout>}}_{\mathrm{2,2}}& ...& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{2,n_b-2}& {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">P</figure-callout>}}_{2,n_b-1}\\ .& .& .& & .& .\\ .& .& .& ...& .& .\\ .& .& .& & .& .\\ P_{m_b-\mathrm{1,0}}& P_{m_b-\mathrm{1,1}}& P_{m_b-\mathrm{1,2}}& ...& P_{m_b-\mathrm{1,}{n}_b-2}& P_{m_b-1,n_b-1}\end{array}\right]=P^{H_b}$

P wherein _{L, j}Be move to right one of unit matrix or z * z null matrix of one group of z * z.Matrix H is by big or small m _b* n _bThe binary radix matrix H _bExpansion, wherein n=zn _bAnd m=zm _b, and z is a positive integer.This basic matrix is by unit matrix that each the 1 usefulness z * z in the basic matrix is moved to right, and the null matrix of each 0 usefulness z * z replaces expanding.Therefore this design adapts to different bag sizes by the big or small z that changes submatrix.

Known such H _bCan be divided into two parts, wherein H _B1Corresponding with system bits, and H _B2Corresponding with parity check bit.

According to an aspect of the present invention, H _B2Part is divided into two parts, wherein h again _bHave strange weight, and H ' _B2Have matrix element at the capable j row of i place at i=j, equal 1 during i=j+1, all the other are 0 double diagonal line structure:

This basic matrix has h _b(0)=1, h _b(m-1)=1, and the 3rd the value h _b(j), 0＜j＜(m _b-1) equals 1.The structure of basic matrix avoids that a plurality of weights are arranged in the matrix of expansion be 1 row, and this can realize by the optimization of interleaver.

More particularly, non-zero submatrices is come ring shift right by concrete cyclic shift value.H ' _B2In each 1 distributed 0 shift size, and when expanding to H, replace with z * z unit matrix.This has allowed to have the realization of the double diagonal line structure of simple recurrence circuit.Be positioned at h _bTop and two 1 of bottom distributed the shift size that equates, and to h _bMiddle the 3rd 1 given azygous shift size.This azygous shift size is 0.

Coding is to provide the process that information sequence s determines parity sequences p.For encoding, block of information s is divided into the k of z position _b=n _b-m _bGroup.Make this group s represent with u,

u＝[u(0)u(1)…u(k _b-1)]，

Wherein each element of u is following column vector:

u(i)＝[s _izs _iz+1…s _(i+1)z＝1] ^T

Matrix H uses a model _b, parity sequences p determines in the group of z.Make this group parity sequences p represent with v,

v＝[v(0)v(1)…v(m _b-1)]，

Wherein each element of v is following column vector:

v(i)＝[p _izp _iz+1…p _(i+1)z+1] ^T

Coding divides two steps to carry out, and v (O) is wherein determined in (a) initialization, and (b) recurrence, wherein determines v (i+1), 0≤i≤m according to v (i) _b-2.

The form of v (0) reaches formula to be passed through H _bRow sue for peace and obtain so that obtain:

$P_{p\left(x_1{k}_b\right)}v\left(0\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m_b-1}{\mathrm{\&Sigma;}}}{P}_{p(1,j)}u\left(j\right)---\left(1\right)$

Wherein x is h _bRow coefficient, 1≤x≤m _b-2, wherein clauses and subclauses are non-negative and azygous, and p _iRepresent the z of i ring shift right * z unit matrix by size.Equation (1) is by taking advantage of P _{P (x, kb)} ^-1Find the solution v (0), and $P_{p(x,k_b)}^{-1}=P_{z-p(x,k_b),}$ Because p is (x, k _b) the expression cyclic shift.

Consider H ' _B2Structure, recurrence can followingly obtain,

$v\left(1\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{p(1,j)}u\left(j\right)+P_{p(1,k_b)}v\left(0\right),i=0,---\left(2\right)$

$v(i+1)=v\left(i\right)+\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{p(1,j)}u\left(j\right)+P_{p(1,k_b)}v\left(0\right),i=1,...,m_b-2---\left(3\right)$

Wherein

P _-1≡0 _z×s。

Therefore all parity check bits in v (0) do not pass through equation (2) at 0≤i≤m _bEstimated in-2 o'clock to determine.

Encryption algorithm has intactly been described in equation (1) and (2).These equations also have the direct decipher according to the standard digital logic architecture.More particularly, they can be easy to use the coding scheme structure of describing with reference to top Fig. 2 to realize.

The basic decoder structure

The following improvement of decoding algorithm is possible:

1, minimum and (Min-sum) algorithm (simulation of maximum Log MAP)

2 and long-pending (sum-product) (simulation of Log-MAP)

A, E show in (E-presentation) and long-pending

B, probabilistic decoding (tanh () rule).

With known graphic decoder notion, decoding is carried out repeatedly, and promptly the purpose of iteration is that parity information is supplied with next iteration.Therefore, the search of immediate legal-code is carried out by continuous approach method.The result who has shown this method is near maximum likelihood decision.

Fig. 3 shows the example of message pass-algorithm block diagram.Two numbers that are called as message of edge coupling of each figure: the message from the variable node to the check-node, and the message from the check-node to the variable node.Each message is the number of picture soft-decision.They are initialized to zero before decoding.Size and interleaver that the size of message array equals the inner interleaver of decoder are used for they are carried out the sequence change.

For the RA sign indicating number, the inner interleaver of decoder is distinguished according to the parity check bit that is included in the interleaving process according to the inner interleaver of encoder.Referring to Fig. 4.

The form that repeats and sue for peace changes according to interleaver.When decoding, system node and parity check node are not distinguished, but the both is considered variable node.

The computing of the output message of calculating from the variable node to the check-node comprises sues for peace from all message that other check-nodes receive to variable node, except supposing one that receives this message, adds the soft-decision that receives from demodulator.Referring to Fig. 5.

In the computing interval of the output message from the check-node to the variable node, schedule to last the calculated input message of output message and be left in the basket from variable node.

The computing that message from the check-node to the variable node is calculated has two parts:

● the regulation of information symbol, and

● the regulation of the mould of message.

Symbol of message by verification and zero equate that condition stipulates.Therefore, calculated from the input message of variable node and, and the symbol that obtains is assigned to output message.Calculating is from the straightforward procedure of the output message of check-node (minimum and).

The output message mould is calculated by the function among Fig. 5.This function is decision function or log-likelihood ratio.Function f has tradable feature:

f(a，b，c，d)＝f(a，f(b，f(c，f(d))))

f(d)＝d

There are several methods that function f is set:

1. the simplest method is usually said minimum-sum algorithm.The absolute value of output message

Equal the minimum modulus of the input message considered:

f(|Q _m′n|，except_|Q _m′n′|)＝min _m′n′(|Q _m′n|)

1. other method is similar to the calculating of the function E in the LOG MAP algorithm.This function f is provided by following formula:

f(a，b)＝mmin(a，b)+δ，

δ＝log(1-exp(-|a+b|))-log(1-exp(-|a-b|))

Function E (x)=log (1-exp (| x|)), extensively be used in the turbo coding, can be set to form.

1. method 2 has a kind of improvement, wherein:

$\mathrm{\&delta;}=\left\{\begin{array}{c}1,|a-b|\&le;1,|a+b|>1\\ -1,|a-b|>1,|a+b|\&le;1\\ 0,\mathrm{else}\end{array}\right\}$

This method does not need function E form.Yet the method causes the reduction of performance.

Because carry the check-node message calculating that instant symbol is considered, the number of times of the computing of method 2 can reduce.This technology that realizes this is below described.

The log-likelihood ratio algorithm computation of the check-node during E shows

Consider the tradable feature of function f, let us is considered basic " case summation " (" the box-sum ") computing or the calculating of log-likelihood ratio.

$\mathrm{\&lambda;}=\ln \left(\frac{P_{i=1}}{P_{i=p}}\right)=\ln \left(\frac{P}{1-P}\right)=\frac{2x}{{\mathrm{\&sigma;}}^2}\&prime;\begin{array}{c}{p}_{i=1}=p\\ p_{i=v}=1-p\end{array}---\left(1\right)$

Wherein p is the posterior probability of transmission 1, equals under the condition of x at the signal that receives, and signal is BPSK:+1 ,-1; And noise is for having deviation σ ²AWGN.

Respectively, λ is decision function or log-likelihood ratio logarithm.

$e^{\mathrm{\&lambda;}}=\frac{P}{1-p}\&prime;$ (1-p)c ^λ＝p′ $P=\frac{e^{\mathrm{\&lambda;}}}{1+e^{\mathrm{\&lambda;}}}\&prime;$ $1-P=\frac{1}{e^{\mathrm{\&lambda;}}+1}$

Problem statement: if posterior probability p ₁And p ₂(log-likelihood ratio logarithm λ ₁, λ ₂) be known, the posterior probability p among Fig. 6 then ₃(log-likelihood ratio logarithm λ ₃) what are? the computing of carrying out at the check node of encoder is that mould 2 adds.

As shown in Figure 7, in order to solve the problem that proposes above, made up the group fully of incident.So,

${\mathrm{\&lambda;}}_3=\ln \left(\frac{p_1(1-p_2)+p_2(1-p_1)}{p_1{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20058001744200381.png,A20058001744200471.png"\; state="\{\{state\}\}">p</figure-callout>}}_2+(1-p_1)(1-p_2)}\right)---\left(3\right)$

${\mathrm{\&lambda;}}_3=\ln \left(\frac{\frac{e^{{\mathrm{\&lambda;}}_1}}{(e^{{\mathrm{\&lambda;}}_1}+1)}\frac{1}{(e^{{\mathrm{\&lambda;}}_2}+1)}+\frac{e^{{\mathrm{\&lambda;}}_2}}{(e^{{\mathrm{\&lambda;}}_2}+1)}\frac{1}{(e^{{\mathrm{\&lambda;}}_1}+1)}}{\frac{e^{{\mathrm{\&lambda;}}_1}}{(e^{{\mathrm{\&lambda;}}_1}+1)}\frac{e^{{\mathrm{\&lambda;}}_1}}{(e^{{\mathrm{\&lambda;}}_1}+1)}+\frac{1}{(e^{{\mathrm{\&lambda;}}_1}+1)}\frac{1}{(e^{{\mathrm{\&lambda;}}_2}+1)}}\right)---\left(4\right)$

Or

${\mathrm{\&lambda;}}_3=\ln \left(\frac{e^{{\mathrm{\&lambda;}}_1}+e^{{\mathrm{\&lambda;}}_2}}{e^{{\mathrm{\&lambda;}}_1+{\mathrm{\&lambda;}}_2}+1}\right)---\left(5\right)$

At e ^{λ 1}+ 1 ≠ 0, e ^{λ 2}Under+1 ≠ 0 the condition,

λ ₃＝ln(e ^λ1+e ^λ2)-ln(e ^λ1+λ2+1)＝E(λ ₁，λ ₂)-E(0，λ ₁+λ ₂) (6)

Wherein turbo sign indicating number function E uses widely

E(a，b)＝ln(e ^a+e ^b)＝max(a，b)+ln(1+e ^-|a-b|) (7)

Therefore, the message with correct symbol can be calculated immediately.Except two of function E call, only need to carry out a sub-addition and a subtraction.

The other method of calculating log-likelihood ratio (probabilistic decoding-tanh () rule) is in the Probability p shown in (3) ₃Can be expressed as:

p ₁＝p ₁(1-p ₂)+p ₂(1-p ₁)＝p ₁+p ₂-2p ₁p ₂ (8)

Both sides all take advantage of 2 and deduct 1, can get:

2p ₃-1＝2p ₁+2p ₂-4p ₁p ₂-1 (9)

Factor is resolved on the right:

(2p ₁-1)(2p ₂-1)＝4p ₁p ₂-2p ₁-2p ₂+1 (10)

The substitution loss result, we obtain:

(2p ₃-1)＝-(2p ₁-1)(2p ₂-1) (11)

Or, remove 2p ₁Outside the situation of-1=0, take the logarithm in both sides:

[ln(2p ₃-1)]＝-[ln(2p ₁-1)]-[ln(2p ₂-1)]2p ₁≠0.5 (12)

Wherein this logarithm is expressed as follows with λ:

$\ln (2p-1)=\ln (\frac{{2e}^{\mathrm{\&lambda;}}}{1+e^{\mathrm{\&lambda;}}}-1)=\ln \left(\frac{e^{\mathrm{\&lambda;}}-1}{e^{\mathrm{\&lambda;}}+1}\right)---\left(13\right)$

Let us is considered function $f\left(\mathrm{\&lambda;}\right)=\ln \left(\frac{e^{\mathrm{\&lambda;}}-1}{e^{\mathrm{\&lambda;}}+1}\right)$ Character,

This function has following character:

1. even function f (λ)=f (λ)

2. this function is drawn in Figure 10

3. this function not definition at 0 place

This function is self-converse (self-inverse) function f (f (x))=x

Order of operation in the calculating of check node is provided by following steps:

1. if do not have zero in input message, then the output message symbol calculates by standard mode by the input symbol of message is carried out XOR except that this, otherwise output message also is zero;

To all input message with form f (x)=-((exp (x)-1)/(exp (x)+1) directly changes ln, and wherein x is for importing message (drawing) in Fig. 8;

According to (12) calculate conversion message and.

4. be obtain and conversion that calculate inverse function f.(？)

Summary

Two kinds of algorithms of check-node operation are provided: " E displaying " and " tanh () rule ".The both does not lose and has provided the ML judgement.These methods will partly continue in the design of H/W architecture to consider.Next part will provide comparison with the turbo sign indicating number having simulator that E shows.

The comparison of emulation and Turbo code

First simulation objectives is to carry out comparison by fixed rate 1/2.Introduced the coder structure that adds up that repeats then based on the LDPC sign indicating number of rate-compatible.Next simulation objectives be with following form 4 in the 3GPP2 turbo decoder of compression of appointment compare.

Input signal quantizes

If use E function form, then input signal must the unit's of being converted into deviation and is expressed as Or

R wherein ₁And r ₂Be distance to constellation point.Then with $\mathrm{\&Delta;}=\frac{{\mathrm{\&sigma;}}^2}{32}$ Step-length carry out 8 quantifications.E function form is by same step initialization.

Coding parameter and simulation result

Carry out relatively at speed 1/2 place, the size of block of information is 1000.To LDPC IRA sign indicating number, selected irregular repetition form (Fig. 9).The size of inner interleaver is 7000 in the case.This is the s random interleaver of s=32.After interweaving, to speed 1/2 at check-node to equal the merging of 7 interval executing rule.

For relatively, selected 3GPP turbo sign indicating number.

Structure based on the RA encoder of the LDPC decoder of rate-compatible obtains by the cascade check-node that the compression parity check symbol is decomposed by multichannel.If the component node have zero verification and, then force to equal zero at the parity check sum of the check-node of cascade.Figure 12 has illustrated the derivation from the possible speed of institute of RA encoder by the size that changes check-node.The RA coder structure guarantees that parity check sum equals zero.

In coder side, rate-compatible code produced by the cycle that changes locking key " parity character end ".At decoder-side, the number of the message that changes to the sequence of check-node is corresponding with the parity character generation cycle.The comparison of simulation result and 3GPP2 turbo decoder provides in Figure 13.

The number of the system message of table 2 check node

Speed	The message that the sequence of the variable number in the generation of parity check symbol cycle-from system node to each check-node changes
		1/2	?7
1/3	?3-4
		1/4	?2-2-3
3/4	?14
		4/5	?28
1/8	?1

Last table has been selected repetition factor α=7, and the best irregular structure of repetition form is shown in Figure 9, and the number of times of repetition proves the function of the bits number in the transmission.

The LDPC IRA sign indicating number of rate-compatible is compared the not loss except utmost point low rate 1/4 and high speed (4/5) of turbo sign indicating number.It is best so that obtaining optimum performance on main speed (1/2,1/3,2/3,3/4) repeating to show.In the case, speed 1/8 specific speed 1/4 is poorer, and promptly speed is 1/4 o'clock, and data should be repeated twice, rather than are 1/8 o'clock coding in speed.In addition, compare with the turbo sign indicating number, (error floor) is much lower for the lowest limit of makeing mistakes of IRA sign indicating number.

Average repetition factor 7 is based on that maximal rate 1/8 selects.

Should notice that equally above-mentioned sign indicating number is rate-compatible code, promptly it has formed variable bit rate sign indicating number series, has allowed the realization of HARQ-II.

Following table is the speed group, and has provided the simulation result from the bipolar big demodulator of SNR of having that is used for modulation symbol.

The MCS index	Code check	QAM	Payload (bits/TTI (2ms))	User rate (Mbits/s)
					1	0.125	2	2428	1.21
2	0.200	2	3863	1.93
					3	0.250	2	4856	2.43
4	0.333	2	6512	3.26
					5	0.500	2	9824	4.91
6	0.667	2	13135	6.57
					7	0.800	2	15785	7.89
8	0.500	4	19759	9.88
					9	0.667	4	26382	13.19
10	0.800	4	31681	15.84
					11	0.667	6	39629	19.81
12	0.750	6	44596	22.30
					13	0.800	6	47577	23.79

Form 3 speed groups

The performance conclusion of IRA-7 sign indicating number

Existence is according to BER, the FER curve of modulation symbol energy to noise ratio.All MCS of form 4 have been provided.Remaining problem is that the sign indicating number matrix of each speed is different.Sign indicating number according to the exploitation of this project goal in this project is (1/8-4/5) of rate-compatible.This means that two-forty obtains by compressing female sign indicating number.The components of system as directed of coding must be identical and stable.Yet the result who obtains has relatively provided good benchmark test for coding.

H/W architecture Design and complexity analyzing

Basic LDPC decoder architecture

Figure 15 shows the example decoder structure.

The main problem of implementation of this architecture is the FPGA restriction of RAM access.More particularly, Virtex 812EM has realized the dual-port access to the 4k memory block.That is to say that two numbers can be read from such district in a clock, perhaps a number can be read and another can be written into.Therefore, the realization that concurrent messages is handled need be arranged the message from variable node in accessible memory bank, so that read the message of being handled by check node processor from different memory banks, and writes different memory banks to avoid access conflict.

Figure 16 illustrates the structure of parallel check node processor based on " decoder-first yard design " rule.Let us is considered the arithmetic speed estimation of this decoder:

$T=\frac{F_d*Z*R}{\mathrm{\&alpha;}*I}$

Wherein Fd is the FPGA clock rate, the parallel factor of z for calculating, and R is a code check, and α is code sign repetition factor (average), and I is an iterations.

Z equals the number of parallel computation message.Number in the corresponding data position that a FPGA clock is handled is by iterations calculating and separately so that obtain throughput and decoder arithmetic speed.Following formula is applied to parallel LDPC decoder to calculate its arithmetic speed.

Interleaver designs

The approach that has two kinds of interleaver designs.

● algebraically

● at random

Investigated of the performance loss of algebraically interleaver for speed R＞1/2 (promptly 2/3,3/4,4/5).The rate-compatible decoder is the scope of 1/8-4/5 and is not suitable in speed.

Random interleaver with RA coder structure concentrates in this work.

Demand to interleaver can be expressed as:

● the maximum parallel factor

● the given parallel factor there is not performance loss (not having low weight codewords)

Consider the RA code structure, can make to draw a conclusion:

● parity check symbol need not interleaver, only needs to repeat by the factor 2.

● system symbol need by be at least 3 the factor repeat with before interweaving

Tanner figure (Figure 17) goes up each edge of expression.

The random interleaver number needs storage.Need have size for 1000 pieces by the realization of repetition factor 7 is 7000 interleaver.It gets 7000 * 14.The generation of idle number is bad idea, because it takies the FPGA clock.It is solution that interleaver is divided into little interleaver (its number equals the parallel factor).Each little interleaver uploads in the FGPA RAM piece.Therefore, each number from interleaver needs 8 (referring to Figure 18).

The size of the RAM piece on the high FPGA plate is very big (18k at least).This piece is that can not expire and as broad as long for storage 8 or 16.

Good interleaver can be found by random search.

By using 2 kinds of following technology, the needs of interleaver memory also can further reduce:

● even odd symmetry

● the interleaver of expansion

The strange interleaver of idol is symmetrical interleaver, and it allows each even place-exchange in strange position, and vice versa.This interleaver structure satisfies following two restrictions:

● strange conversion: imod2 ≠ π (i) mod2,  i to idol

● symmetry: π (i)=j  π (j)=i

Suppose in the interleaver vector, only to have stored strange position.All address stored are even number then, mean the LSB always zero in the binary representation of each address.Therefore provide extra memory to save.The computing of odd-even device is illustrated among Figure 19.

In order to keep the odd even symmetric property, though expanded the length of interleaver, we need insert two undefined elements after per second in former interleaver.This improvement has guaranteed that locational each element of the idol in former interleaver still remains on even position after expansion, and vice versa.

The rate-compatible check node processor

Investigate the architecture of rate-compatible check node processor.Obtain two-forty by the basic check-node that compresses parity check symbol and divide (demaroated) by these symbols by cascade.Basic check node processor structure in Figure 21 with E illustrate, wherein: computing+mean " case summation " device, octagon is a parity check node message, square is the system variable node messages.The parallel application of these processors makes can realize speed 1/8,1/4,1/3.

Below distortion may be from speed 1/2.

The distortion of being considered has the time-delay of 8 " case summation " clocks, and needs 7 " case summation " modules simultaneously at the 8th clock, and needs 2 modules at every other clock.The distortion that the another kind of this processor check-node is realized also is possible.

Need four modules at first clock, 6 on second clock, 8 on the 3rd clock, and 7 on last clock.The peak value of module is increased to 8, and the decreased number of required clock is 4.In addition, this processor can be used in two speed: 1/3 (near 1/3) and 1/2.The result of check-node 3 is ready at the 3rd clock.

Yet for speed is adjusted to 1/3, being incorporated in the variable cycle in check-node carried out: 3-4, and the architecture of being considered produces check-node by 3.This just causes the following distortion of check-node realization for speed 1/4,1/3,1/2, shown in Figure 21,24.

There is the unit of " 1 " to come initialization with maximum number for selected quantification corresponding to logical block (1).

Clock:

● first clock → 6 " case summation " module

● second clock → 4+4+3=11 " case summation " module-peak load

● the 3rd clock → 6 " case summation " module

● the 4th clock → 7 " case summation " module

Therefore, for the processor check-node of rate-compatible, 11 " case summation " modules (maximum) and 7 " case summation " modules (minimum) are essential.Calculate " case summation " module (minimum) that time-delay takies 4 clocks, and " case summation " module (maximum) of 7 clocks.

The speed set constructor is shown in Figure 25.

Therefore, speed 2/3,4/5 is left from the speed group that realizes quite easily.

Figure 26 is the example of check node processor 2/3.

Figure 27 is the example of check node processor 4/5.

Ln ((exp (x)-1)/(exp (x)+the 1)) function (based on the architecture of tanh () rule) of the modal processor that reduces based on complexity.

Another architecture that complexity reduces is shown in Figure 28.

(represent by the Direct Transform of (exp (x)-1)/(exp (x)+1) with type-ln for LUT (form 4).Because this function property, identical form also is used in forward and the reciprocal transformation.

Table 4 LUT-6 position f (x)=and ln ((exp (x/16)-1)/(exp (x/16)+1) } * 16

x	f(x)	x	f(x)	x	f(x)	x	f(x)
								1 2 3 4 5 6 7 8	55 44 38 33 30 27 25 23	17 18 19 20 21 22 23 24	12 11 10 9 9 8 8 7	33 34 35 36 37 38 39 40	4 4 4 3 3 3 3 3	49 50 51 52 53 54 55 56	1 1 1 1 1 1 1 1

9 10 11 12 13 14 15 16

21 19 18 16 15 14 13 12

25 26 27 28 29 30 31 32

7 6 6 6 5 5 5 4

41 42 43 44 45 46 47 48

2 2 2 2 2 2 2 2

57 58 59 60 61 62 63 64

1 1 1 1 1 1 1 1

It is not problem that bit width increases above 6.In this case, this input value quantizes by 7 when zero not having.The 6th is the soft-decision module, and the 7th is sign bit.LUT can add zero f (0)=0 in this case.This is zero without any physical significance, and can be used in the merging of the different modal processors of variable speed decoder.

Adder Figure 28 is traditional integer adder.Figure 28 shows the principle of output message detection module, and it should be finished by output message symbol definition principle.Compute classes at the symbol processor place is similar to the calculating of module definition principle, replaces addition to distinguish by distance.Same variable node structure must be finished by the conversion from the sign form to the complement of two's two's complement, and the form as symbol addition (carrying out at the variable node place) is pressed more expediently is carried out.The complete structure of check node processor 2+2 is shown in Figure 29.Notice that the LUT conversion need not parity check symbol in the IRA sign indicating number, as consider simple transposition (Figure 31) in their processing at parity check node place.The LUT conversion is at initialized carry out simultaneously (Figure 30).Figure 32 illustrates the configuration node processor of the structure that contains the composite node processor that is used for variable speed decoder.Two modal processors are used in the supposition of this structure, and wherein with zero amplitude initialization, and this symbol is comprised in two formation processors Ya Suo parity check symbol by logical block (1).The distance of the corresponding configuration node processor information symbol of the output symbol of the symbol of message that obtains at composite node processor place by having the second configuration node processor obtains.The message amplitude that obtains at configuration node processor place is by having the amplitude addition generation that the second corresponding configuration node processor that constitutes the output amplitude of processor obtains.The structure of variable node processor is shown in Figure 33.Input message amplitude is not having to come conversion with same form under the prerequisite of figure shift by LUT.Resulting value is transformed to the complement of two's two's complement.After summation, output message is that signed integer produces by these message transformations.

The structure of variable node processor, the message of processing greater number is similar to shown in Figure 33.In the result, the input message of all conversion have a symbol and be written to " output " unit, adjudicate as the soft data position, output message is obtained by the subtraction from the LUT conversion of the corresponding input message of " output ".

Problem of implementation and arithmetic speed are estimated

Repeat to add up coding principle selection because following reason make:

● encode as far as possible simply

● sign indicating number contains system and parity check part

● the common interleaver of parity check symbol

● reduce to minimum parity check symbol and repeat (twice of 2-).

Arithmetic speed estimation formulas not tape code rate is write as:

$T=\frac{Z*F_d}{I*\mathrm{\&alpha;}}---\left(15\right)$

Wherein z is the parallel factor of interleaver, and α is the repetition factor of system bits.Fd is a FPGA plate clock rate, and I is an iterations.

Following problem is considered in next part: how parallel data stream is uploaded on the interleaver with irregular repetition.It is possible that the symbol that repeats is in various degree merged to the piece with fixed rate, and its length equals the parallel factor of interleaver.

Irregular code

Be reduced to except that calculating in variable node processor place computation purpose for the relevant message sum of all nodes the calculated message of its response message.

For the variable parity check node, under two situations, such computing is simple: the position 2 times that exchanges them.Such computing directly is performed after the processor check-node becomes the simulation that system node interweaves.In order to simplify the processing of variable node, selected irregular repetition form to be several times as much as the number that is used in the memory bank in the message stores with the number of the symbol of keeping repetition.In this case, this number equals 28, and it also is can be by the maximum number of the message of check node processor parallel processing.The number of obviously, parallel processing message can not be greater than this number.

Irregular repetition form can be organized in the following manner:

The permissible sequence of the symbol that exist to repeat, thus the number of the symbol that repeats is 7 a multiple and under 28.

3335-4 information symbol all repeated Figure 34 14 times

The message of any number of 7-can be repeated 7 times, Figure 35

First of 113-is repeated 11 times, and next bit is repeated 3 times

The 1315-data bit is all repeated 28 times

The maximum number of the repetition of a position of 28-

Except calculating from the output message of variable node, the output soft-decision is that decoder produces by processor.This soft-decision can be used directly in uploaded data during the iteration.Computing herein "+" is the tape symbol summation.

On Figure 36 and Figure 37, show the sign indicating number allowable loss of hardware constraints (interleaver and repeat table).As can be seen, there is not big piece error code loss, though observed with respect to this loss of IRA sign indicating number at random with respect to the turbo sign indicating number.

Arithmetic speed is estimated as

T＝(z*Fd)/(I*Alpha)＝(28*Fd)/(I*7)。Modern number iteration is I=24, and Fd=100MHz (28*100MHz)/(24*7)=100MHz/6=15MBps.Maximum 32 parity check symbols need be uploaded concurrently, therefore need minimum 16 to store them.Memory distribution 7000/250+16=28+16=44RAM piece minimum.

Simple compression or check-node cascade

Simple compression work, but compare with the check-node cascade, the loss of 1dB is arranged when FER=0.01.Yet the algorithm of check-node cascade (Figure 32, Figure 26, Figure 27) needs more logic FPGA plate.Simulation result provides in Figure 38 and Figure 39.

Regular code

For increasing throughput and arithmetic speed, realized that rule repeats the sign indicating number that adds up.Repetition factor is reduced to 3.This just means that each system bits only is repeated 3 times.The parallel factor 72 realizes by reducing interleaver diversity (the S factor).Interleaver size be 9000 and the components of system as directed size be 3000.Code check is 1/2.

The performance loss of regular code is left in the basket.In the uploading of parallel data stream, do not have problems.

Referring to Figure 40 and 41.

Arithmetic speed is estimated as

T＝(z*Fd)/(I*Alpha)＝(28*Fd)/(I*7)。Make that number of iterations is I=24, and Fd=100MHz (72*100MHz)/(24*3)=100MHz=100Mbit/s.Maximum 48 parity check symbols need be uploaded concurrently, and 24 of therefore minimum needs are stored them.Memory distribution 9000/125+48=72+48=120RAM piece minimum

Reduce the influence of repetition factor

Following emulation has provided the answer of this problem.Use identical interleaver and had data repetition factor 3,2,1.First sign indicating number is with speed 3000/ (3000+3000)=1/2 computing, and next with speed 4500/ (4500+3000)=3/5 computing, last is with speed 9000/ (9000+3000)=3/4 computing.

Repetition factor is reduced to 2 losses that 3dB arranged by 3.Repetition factor is reduced to 1 at BER=10 by 3 ^-6There is the loss of 7dB at the place.Referring to Figure 42.

The influence of simple compression

Simple compression work (2/3,3/4,4/5) but the loss of 1db is arranged for the algorithm of the check-node cascade of describing herein.Referring to Figure 43.

The influence of iterations reduces to decode

Among Figure 43,44 and 45 example has been shown.Iterations is reduced to 24 losses that 0.3dB arranged by 100.Iterations is reduced to 10 at BER=10 by 100 ^-6There is the loss of 1dB at the place.

According to top instruction, a large amount of improvement of the present invention and variation all are possible.Therefore will appreciate that in the scope of appending claims the present invention can be implemented by being different from this paper with specifically describing.

Claims (18)

1. one kind is suitable for the LDPC encoder with linear complexity that the generation system exports and parity check is exported, and described encoder comprises:

Duplicator is realized irregular duplication code;

Interleaver interweaves to described duplicator output execution;

Accumulator is carried out the output of described interleaver and to be added up and export described parity check output.

2. LDPC encoder as claimed in claim 1, wherein said interleaver be S at random or the congruence interleaver.

3. LDPC encoder as claimed in claim 1, wherein said accumulator is carried out irregular adding up.

4. LDPC encoder as claimed in claim 1, wherein said accumulator executing rule adds up.

5. LDPC encoder as claimed in claim 1 also is included in the parallel-to-serial function between described duplicator and the described interleaver.

6. LDPC encoder as claimed in claim 1 changes to come by parametrization by the repeat pattern of described duplicator and the sequence of described interleaver.

7. LDPC encoder as claimed in claim 1, it is best that wherein said repeat pattern and sequence change.

8. LDPC encoder as claimed in claim 1, wherein said S random interleaver are half random algorithm with refusal, and interweaving in advance continuous to s provides the back interleaved distance that is not less than s, $s\&le;\sqrt{\underset{2}{\overset{N}{\&OverBar;}}}.$

9. LDPC encoder as claimed in claim 1, wherein said LDPC sign indicating number can be represented by following parity matrix with double diagonal line structure:

$H_{b2}=\left[h_b\right|H_{b2}^{\&prime;}]$

10. LDPC encoder as claimed in claim 1, wherein whole sign indicating number is expressed as follows by matrix form:

$H=\left[\begin{array}{cccccc}{P}_{\mathrm{0,0}}& P_{\mathrm{0,1}}& P_{\mathrm{0,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{0,n_b-2}& P_{0,n_b-1}\\ P_{\mathrm{1,0}}& P_{\mathrm{1,1}}& P_{\mathrm{1,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{1,n_b-2}& P_{1,n_b-1}\\ P_{\mathrm{2,0}}& P_{\mathrm{2,1}}& P_{\mathrm{2,2}}& \&CenterDot;\&CenterDot;\&CenterDot;& P_{2,n_b-2}& P_{2,n_b-1}\\ .& .& .& & .& .\\ .& .& .& ...& .& .\\ .& .& .& & .& .\\ P_{m_b-\mathrm{1,0}}& P_{m_b-\mathrm{1,1}}\mathrm{}& P_{m_b-\mathrm{1,2}}& ...& P_{m_b-1,n_b-2}& P_{m_b-1,n_b-1}\end{array}\right]=P^{H_b}$

Wherein H is the matrix of big or small m * n, and n is that the length and the m of described sign indicating number is the number of parity check bit in the described sign indicating number, P _{1, j}Be move to right in unit matrix or the z * z null matrix one of one group of z * z;

Described matrix H is m according to size _b* n _bThe binary radix matrix H _bExpansion, wherein n=zn _bAnd m=zm _b, and z is positive integer, described basic matrix is by unit matrix that each the 1 usefulness z * z in the described basic matrix is moved to right, and each 0 usefulness z * z null matrix is replaced expanding;

With H _bBe divided into two parts, wherein H _B1Corresponding with system bits, and H _B2Corresponding with parity check bit;

With H _B2The part separated into two parts, wherein vectorial h _bHave strange weight, and H ' _B2Equal 1 when having matrix element at the capable j row of i place at i=j, i=j+1, all the other are 0 double diagonal line structure:

$H_{b2}=\left[h_b\right|H_{b2}^{\&prime;}]$

H wherein _b(0)=1, h _b(m-1)=1, and the 3rd the value h _b(j), 0＜j＜(m _b-1) equals 1.

11. LDPC encoder as claimed in claim 1 also is suitable for allowing based on the conventional coders/decoder with rate-compatible check node processor structural feature to the structure of one group of different code check and the structure based on the speed of compression to being complementary with the check-node cascade.

12. one kind has, and to avoid a plurality of weights in the matrix of having expanded be the LDPC encoder of the basic matrix structure of 1 row.

13. a LDPC encoder of realizing the LDPC sign indicating number, described LDPC sign indicating number can be represented by following parity matrix with double diagonal line structure:

$H_{b2}=\left[h_b\right|H_{b2}^{\&prime;}]$

14. LDPC encoder as claimed in claim 13, wherein whole sign indicating number is expressed as follows by matrix form:

$H=\left[\begin{array}{cccccc}{P}_{\mathrm{0,0}}& P_{\mathrm{0,1}}& P_{\mathrm{0,2}}& ...& P_{0,n_b-2}& P_{0,n_b-1}\\ P_{\mathrm{1,0}}& P_{1.1}& P_{\mathrm{1,2}}& ...& P_{1,n_b-2}& P_{1,n_b-1}\\ P_{\mathrm{2,0}}& P_{\mathrm{2,1}}& P_{\mathrm{2,2}}& ...& P_{2,n_b-2}& P_{2,n_b-1}\\ .& .& .& & .& .\\ .& .& .& ...& .& .\\ .& .& .& & .& .\\ P_{m_b-\mathrm{1,0}}& P_{m_b\text{-1,1}}& P_{m_b-\mathrm{1,2}}& ...& P_{m_b-1,n_b-2}& P_{m_b-1,n_b-1}\end{array}\right]=P^{H_b}$

15. a given information sequence s carries out the LDPC coding to determine the method for parity sequences p, said method comprising the steps of:

The k that described information sequence s is divided into the z position _b=n _b-m _bGroup makes this grouping s represent with u,

u＝[u(0)u(1)…u(k _b-1)]

Wherein each element of u is following column vector:

u(i)＝[s _ks _k+1…s _(i+1)＝-1] ^r

Matrix H uses a model _b, in the group of z, determine described parity sequences p, make the parity sequences p that is grouped represent with v,

v＝[v(0)v(1)…v(m _b-1)]，

Wherein each element of v is following column vector

v(i)＝[p _kp _k+1…p _(i+1)＝-1] ^T

Carry out initialization step to determine v (0);

Carry out recurrence with according to v (i), 0≤i≤m _b-2 determine v (i+1).

16. method as claimed in claim 15, wherein:

The form of v (0) reaches formula to be passed through H _bRow summation derive to obtain

$P_{p\left(x_{,}{k}_n\right)}v\left(0\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{m_p-1}{\mathrm{\&Sigma;}}}{P}_{p(i,j)}u\left(j\right)---\left(1\right)$

Wherein x is non-negative and azygous h for its clauses and subclauses _bLine index 1≤x≤m _b-2, and P _iRepresent the z of i ring shift right * z unit matrix by size, equation (1) is by multiply by P ^-1 _{P (x, kb)}Come v (0) is found the solution, and $P_{p(x,k_n)}^{-1}=P_{2-p(x,k_b),}$ Because p is (x, k _b) the expression cyclic shift.

17. method as claimed in claim 16, wherein said recurrence are according to following regulation:

$v\left(1\right)=\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{p(i,j)}u\left(j\right)+P_{p(i,k_b)}v\left(0\right),i=0,---\left(2\right)$

$v(i+1)=Y\left(i\right)+\underset{j=0}{\overset{k_b-1}{\mathrm{\&Sigma;}}}{P}_{p(i,j)}u\left(j\right)+P_{p(i,k_n)}v\left(0\right),i=1,...,m_b-2---\left(3\right)$

Wherein

P _-1≡0 _z×z。

18. a LDPC decoder comprises:

Parallel node processing structure, the code check and the interleaver that are suitable for any selection are selected, and are used for the sign indicating number according to any one realization of claim 1 to 17 is decoded.

Images