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CN102970047B - BF decoding algorithm weighted gradient ldpc code based on the average amplitude decreases - Google Patents

BF decoding algorithm weighted gradient ldpc code based on the average amplitude decreases Download PDF

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CN102970047B
CN102970047B CN 201210505106 CN201210505106A CN102970047B CN 102970047 B CN102970047 B CN 102970047B CN 201210505106 CN201210505106 CN 201210505106 CN 201210505106 A CN201210505106 A CN 201210505106A CN 102970047 B CN102970047 B CN 102970047B
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CN102970047A (en )
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张高远
文红
周亮
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电子科技大学
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Abstract

本发明公开了一种基于平均幅度的LDPC码加权梯度下降比特翻转译码算法,包括单比特翻转译码步骤和多比特翻转译码步骤,均包括以下步骤:(1)初始化;(2)计算伴随式sk;(3)sk=0时停止迭代,译码输出为sk不为零时计算各个校验节点的权重ωm;(4)计算各个信息节点的翻转函数(5)判决和终止迭代检测。 The present invention discloses a method based on a weighted average amplitude of the LDPC code decoding algorithm gradient descent bit inversion, bit flipping decoding step including single and multiple-bit flip decoding step comprises the steps of: (1) Initialization; (2) Calculation syndrome sk; (3) sk = 0 stop iteration, the check node calculation each time the decode output is non-zero weights sk ωm; (5) terminating the iterative detection and judgment (4) calculating the roll function information of each node . 本发明将邻接校验节点的信息节点的平均幅度作为权重的组成部分,同时结合信息节点信道接收值与硬判决比特之间的相关性,构造出一种更为高效的比特翻转函数,相比于GDBF算法,在获得一定编码增益的同时,有更低的平均迭代次数;同时,本发明具有实现方式相对简单,硬件实现复杂度不高和译码性能优异等特点。 The present invention is the average amplitude of the information node adjacent check node as part of the weight, combined with the correlation values ​​between the received channel information and the hard-decision bit node constructs a bit flipping function more efficient, compared to in GDBF algorithm, while obtaining a certain coding gain, there is a lower average number of iterations; Meanwhile, the present invention has a relatively simple implementation, the hardware implementation complexity is not high and excellent decoding performance characteristics.

Description

基于平均幅度的LDPC码加权梯度下降比特翻转译码算法 BF decoding algorithm for the LDPC code decreases the magnitude of the weighted average based on the gradient

技术领域 FIELD

[0001] 本发明涉及一种低密度奇偶校验码加权比特翻转译码方法,特别是一种基于平均幅度的LDPC码加权梯度下降比特翻转译码算法。 [0001] The present invention relates to a low density parity check code weighting BF decoding method, LDPC codes based on a particular weighted average amplitude of the gradient drops BF decoding algorithm.

背景技术 Background technique

[0002] LDPC 码即低密度奇偶校验码(Low Density Parity Check Code,LDPC),最早在1963年由Gallager在他的博士论文中首次提出,是一种基于稀疏校验矩阵定义的线性分组码。 [0002] LDPC code that is LDPC (Low Density Parity Check Code, LDPC), was first put forward for the first time in his doctoral thesis by Gallager in 1963, is based on a linear block code defined by a sparse parity check matrix . 由于具有逼近shannon限的优异性能,且具有硬件可实现的编译码复杂度,结构设计、码参数选择灵活,目前,已经广泛应用于卫星通信、光线通信和深空通信等领域。 Due to superior performance approaching shannon limit, and having a codec hardware complexity can be achieved, design, code parameter selection flexible, currently, has been widely used in satellite communications, deep space communications and light communication. J. Thorpe等人提出的AR4JA码已经于2007年被空间通信系统咨询委员会正式批准成为深空通信信道编码的建议标准。 J. Thorpe, who made AR4JA code already in 2007 by the Space Communications System Advisory Committee formally approved as a proposed standard for deep space communication channel coding.

[0003] 鉴于LDPC码译码性能和复杂度之间不可调和的矛盾,基于二者之间的折中提出了众多不同的译码算法。 [0003] In view between the decoding performance and complexity of the LDPC code irreconcilable conflict, based on a compromise between the two proposed a number of different decoding algorithms. 其中,基于信息传播机制的软判决迭代译码算法占据主流,如置信传播(BP)算法、最小和算法以及它们的各种改进形式等。 Wherein the soft-decision iterative decoding algorithm information dissemination mechanism based on predominate, such as belief propagation (BP) algorithm, the minimum and algorithms and various modifications thereof and other forms. 软判决迭代译码算法具有出色的译码性能,但在处理中涉及较多的实数运算,硬件实现复杂度相对较高,不再适用于某些要求简单编译码装置的系统;基于BF (Bit Flipping,比特翻转)的硬判决迭代译码算法则是一个合适的选择,特别是基于WBF (Weighted Bit Flipping,加权比特翻转)的一类算法可以在硬件实现复杂度和性能之间获得一个较好的折中。 Soft-decision iterative decoding algorithm having superior decoding performance, but more real arithmetic, the hardware implementation complexity is relatively high in the process involves no longer applicable to certain codec system requiring a simple apparatus; based BF (Bit flipping, bit flipping) the hard-decision iterative decoding algorithm is an appropriate choice, in particular based WBF (weighted bit flipping, complexity and performance between the weighted bit-flipping) a class of algorithms may be implemented in hardware to get a better compromise.

[0004] Yu Kou等人在2001年提出的WBF算法将一种特殊的量(即校验节点邻接的信息节点的最小幅度)作为权重,并以此构造出每个信息节点的翻转函数。 [0004] WBF algorithm Yu Kou et al in 2001 to a particular amount (i.e., the minimum amplitude check nodes adjacent node information) as the weight, and thus reversing function constructed for each node information. 在该算法中,翻转比特的位置完全取决于信息节点邻接的校验式提供的加权信息,而与待翻转信息节点自身的可靠度基本无关。 In this algorithm, the bit inverted position depends entirely on the weighting information check node type provided adjacent to, and to be essentially independent of its inverting node reliability information. 此后,Juntan Zhang等人在2004年提出一种改进的WBF(MWBF,Modified Weighted Bit Flipping)算法,把校验式信息和信息节点的可靠度信息有效的融合起来, 使得翻转函数更加准确、有效。 Since then, Juntan Zhang et al 2004 an improved WBF (MWBF, Modified Weighted Bit Flipping) algorithm, to effectively integrate information check the reliability of the information and type information node, making the flip function is more accurate and effective. Tadashi Wadayama等人在2010年提出了一种⑶BF算法,其性能要优于Yu Kou和Juntan Zhang的算法。 Tadashi Wadayama, who in 2010 proposed a ⑶BF algorithm, its performance is superior to Juntan Zhang Yu Kou and algorithms. 然而,对于⑶BF算法而言,存在着编码增益较低、平均迭代次数较高等问题。 However, for ⑶BF algorithm, there is less coding gain, a higher average number of iterations other issues.

发明内容 SUMMARY

[0005] 本发明的目的在于克服现有技术的不足,提供一种基于平均幅度的LDPC码加权梯度下降比特翻转译码算法,该方法将邻接校验节点的信息节点的平均幅度作为权重的组成部分,同时结合信息节点信道接收值与硬判决比特之间的相关性,构造出一种更为高效的比特翻转函数,解决现有低密度奇偶校验码加权比特翻转译码方法算法编码增益偏低、 平均迭代次数偏高的问题。 [0005] The object of the present invention is to overcome the disadvantages of the prior art, there is provided a gradient of the weighted average amplitude of the LDPC code decreases BF decoding algorithm, which average amplitude information node adjacent check nodes as based on the weight composition part, combined channel correlation between the received value and the hard-decision bit information node, constructed a more efficient bit flipping function, to solve the conventional LDPC decoding method of bit-flipping weighted arithmetic coding gain bias low, the problem of high average number of iterations.

[0006] 本发明的目的是通过以下技术方案来实现的:基于平均幅度的LDPC码加权梯度下降比特翻转译码算法,二进制低密度奇偶校验码的校验矩阵为H MXN,Clm表示校验矩阵第m行中" 1"的数量,规则低密度奇偶校验码校验矩阵每行中" 1"的数量统一表示为A (m) 表示Hmxn第m行中为"1"的位置,B(n)表示Hmxn第η列中为"1"的位置;任意一个码字C=G1, C2,…,Cn,…,CN), Cn e (〇, 1)经过传输映射后得到 [0006] The object of the present invention is achieved by the following technical solutions: a weighted average amplitude of the LDPC code decoding algorithm gradient descent bit flipping, the binary low density parity check code based on the check matrix H MXN, CIm check represents number of m-th row in the matrix is ​​"1", the rule LDPC check matrix each row number "1" are collectively shown as a (m) represents the m-th row is Hmxn position "1", B (n) represents Hmxn column for the location of η "1"; and any codeword C = G1, C2, ..., Cn, ..., CN), Cn e (square, 1) after transmission map obtained

Figure CN102970047BD00061

其经过双相移相键控调制后加入加性高斯白噪声信道,接收端对其解调后,输出序列r=(ri,r2,~ ,rn,…,rN),并送至信道译码器,Z=Cz1, z2,…,zn,…,zN), zne (+1,-1)为硬判决输出序列, 判决规则为 After its binary phase shift keying modulation Houjiarujia white Gaussian noise channel, the receiving end demodulates the output sequence r = (ri, r2, ~, rn, ..., rN), and sent to the channel decoder is, Z = Cz1, z2, ..., zn, ..., zN), zne (+ 1, -1) as a hard decision output sequence, the decision rule is

Figure CN102970047BD00062

泽码输出戈 Ze code output Ge

Figure CN102970047BD00063

;所述的翻转译码方法包括一个单比特翻转译码步骤和一个多比特翻转译码步骤: ; Said decoding method comprising flipping a single bit flipping decoding step and a multi-bit flip decoding step:

[0007] 所述的单比特翻转译码步骤包括以下子步骤: [0007] The single-bit inverting decoding step comprises the substeps of:

[0008] SI 1 :初始化:初始化迭代次数k=l,设定最大迭代次数Kmax; [0008] SI 1: Initialization: Initialize the number of iterations k = l, Kmax of the set maximum number of iterations;

[0009] S12 :计算伴随式sk: [0009] S12: syndrome computing sk:

Figure CN102970047BD00064

[0011] S13 :sk=0时停止迭代,译码输出为 [0011] S13: sk = stop the iterative decoding output 0

Figure CN102970047BD00065

不为零时计算各个校验节点的权重ω Each check node calculation is not zero weights ω

Figure CN102970047BD00066

[0013] S14 :计算各个信息节点的翻转函数 [0013] S14: calculated for each node information flip function

Figure CN102970047BD00067

[0015] S15 :翻转函数巧满足以下条件的比特nk: [0015] S15: reversing functions satisfying the following conditions Qiao bits nk:

Figure CN102970047BD00068

[0017] S16 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S14 ; [0017] S16: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, proceeds to step S14;

[0018] 所述的多比特翻转译码步骤包括以下子步骤: [0018] The multi-bit flip decoding step comprises the substeps of:

[0019] S21 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax,目标函数初始化为 [0019] S21: Initialization: Initialize the number of iterations k = 1, set the maximum number of iterations Kmax, the objective function is initialized

Figure CN102970047BD00069

,翻转门限初始化为θ,Θ为一个负数; Flip initialized to the threshold θ, Θ is a negative number;

[0020] S22 :计算伴随式sk: [0020] S22: syndrome computing sk:

Figure CN102970047BD000610

[0022] S23 :sk=0时停止迭代,译码输出为t , Sk不为零时计算各个校验节点的权重ω [0022] S23: sk = 0 stop the iterative decoding output is t, each check node calculation is not zero when Sk weights ω

Figure CN102970047BD000611

[0024] S24 :计算各个信息节点的翻转函数<和目标函数fk(z): [0024] S24: calculated for each node information flip function <and the objective function fk (z):

Figure CN102970047BD000612

[0027] S25:当条件 [0027] S25: When the conditions

Figure CN102970047BD000613

同时满足,其中Φ表示空集,则翻转函数满足以下条件的比特nk: Meet, where Φ nk bits representing an empty set, the flip function satisfies the following conditions:

Figure CN102970047BD00071

[0029] 否则,翻转函数之满足以下条件的比特nk: [0029] Otherwise, the bit flipping function nk satisfy the following conditions:

Figure CN102970047BD00072

[0031] S26 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S24。 [0031] S26: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, jumps to step S24.

[0032] 对于规则的LDPC码,所述的译码方法包括以下步骤: [0032] For a regular LDPC code, the decoding method comprising the steps of:

[0033] 所述的单比特翻转译码步骤包括以下子步骤: [0033] The single-bit inverting decoding step comprises the substeps of:

[0034] S31 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax; [0034] S31: Initialization: Initialize the number of iterations k = 1, Kmax of setting the maximum number of iterations;

[0035] S32 :计算伴随式sk: [0035] S32: syndrome computing sk:

Figure CN102970047BD00073

[0037] S33 :sk=0时停止迭代,译码输出为f ,sk不为零时计算各个校验节点的权重ω [0037] S33: sk = 0 stop the iterative decoding output is f, is calculated for each check node is not zero when sk weights ω

Figure CN102970047BD00074

[0039] S34 :计算各个信息节点的翻转函数: [0039] S34: calculated for each node information flip function:

Figure CN102970047BD00075

[0041] S35 :翻转函数丨满足以下条件的比特nk: [0041] S35: Shu satisfies the following conditional inversion function bits nk:

Figure CN102970047BD00076

[0043] S36 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S34 ; [0043] S36: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, proceeds to step S34;

[0044] 所述的多比特翻转译码步骤包括以下子步骤: [0044] The multi-bit flip decoding step comprises the substeps of:

[0045] S41 :初始化:初始化迭代次数k=l,设定最大迭代次数Kmax,目标函数初始化为 [0045] S41: Initialization: Initialize the number of iterations k = l, the maximum number of iterations set to Kmax, the objective function is initialized

Figure CN102970047BD00077

,翻转门限初始化为θ,Θ为一个负数; Flip initialized to the threshold θ, Θ is a negative number;

[0046] S42 :计算伴随式sk: [0046] S42: syndrome computing sk:

Figure CN102970047BD00078

[0048] S43 :sk=0时停止迭代,译码输出为f 不为零时计算各个校验节点的权重ω [0048] S43: sk = 0 stop the iterative decoding output is calculated for each check node weight when f is not zero weight ω

Figure CN102970047BD00079

[0050] S44 :计算各个信息节点的翻转函数<和目标函数fk(z): [0050] S44: calculated for each node information flip function <and the objective function fk (z):

Figure CN102970047BD000710

[0053] S45:当条件 [0053] S45: When the conditions

Figure CN102970047BD000711

同时满足,其中Φ表示空集,则翻转函数式:满足以下条件的比特nk: Meet, where Φ represents the empty set, the flip function formula: nk bits satisfies the following conditions:

Figure CN102970047BD00081

[0055] 否则,翻转函数4满足以下条件的比特nk: [0055] Otherwise, the bit flipping function nk 4 satisfies the following conditions:

Figure CN102970047BD00082

[0057] S46 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S44。 [0057] S46: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, jumps to step S44.

[0058] 本发明将邻接校验节点的信息节点的平均幅度作为权重的组成部分,同时结合信息节点信道接收值与硬判决比特之间的相关性,构造出一种更为高效的比特翻转函数,相比于GDBF算法,在获得一定编码增益的同时,有更低的平均迭代次数;同时,本发明具有实现方式相对简单,硬件实现复杂度不高和译码性能优异等特点。 [0058] The present invention will be weight average amplitude of the information node adjacent check node as a right part of the combined channel correlation between the received value and the hard-decision bit information node, constructed a more efficient bit-flipping function compared to GDBF algorithm, while obtaining a certain coding gain, there is a lower average number of iterations; Meanwhile, the present invention has a relatively simple implementation, hardware implementation complexity is not high and is excellent decoding performance characteristics.

附图说明 BRIEF DESCRIPTION

[0059] 图1为列重为3的(1008,504)PEGLDPC码在MffBF、单比特翻转⑶BF-single、多比特翻转GDBF-mu 11 i、单比特翻转AMffGDBF-s i ng I e及多比特翻转AMffGDBF-mu 11 i算法下的误比特率曲线图; [0059] FIG. 1 is a column weight (1008,504) PEGLDPC code 3 in MffBF, single bit flipping ⑶BF-single, multi-bit flip GDBF-mu 11 i, a single bit flipping AMffGDBF-s i ng I e and the multi-bit flip BER graph algorithm at 11 i AMffGDBF-mu;

[0060] 图2为列重为3的(1008,504)PEGLDPC码在MffBF、单比特翻转⑶BF-single、多比特翻转GDBF-mu 11 i、单比特翻转AMffGDBF-s i ng I e及多比特翻转AMffGDBF-mu 11 i算法下的平均迭代次数取值曲线图; [0060] FIG. 2 is a column weight (1008,504) PEGLDPC code 3 in MffBF, single bit flipping ⑶BF-single, multi-bit flip GDBF-mu 11 i, a single bit flipping AMffGDBF-s i ng I e and the multi-bit the average number of iterations in the inversion 11 i algorithm AMffGDBF-mu graph values;

[0061] 图3为列重为3的(504,252)PEGLDPC码在MWBF、单比特翻转⑶BF-single、多比特翻转GDBF-mu 11 i、单比特翻转AMffGDBF-s i ng I e及多比特翻转AMffGDBF-mu 11 i算法下的误比特率曲线图; [0061] FIG. 3 is a column weight (504,252) PEGLDPC code 3 in MWBF, single bit flipping ⑶BF-single, multi-bit flip GDBF-mu 11 i, a single bit flipping AMffGDBF-s i ng I e and the multi-bit flip AMffGDBF BER graph algorithm in -mu 11 i;

[0062] 图4为列重为3的(504,252)PEGLDPC码在MWBF、单比特翻转⑶BF-single、多比特翻转GDBF-mu 11 i、单比特翻转AMffGDBF-s i ng I e及多比特翻转AMffGDBF-mu 11 i算法下的平均迭代次数曲线图。 [0062] FIG. 4 is a column weight (504,252) PEGLDPC code 3 in MWBF, single bit flipping ⑶BF-single, multi-bit flip GDBF-mu 11 i, a single bit flipping AMffGDBF-s i ng I e and the multi-bit flip AMffGDBF -mu graph showing the average number of iterations of the algorithm 11 i.

具体实施方式 detailed description

[0063] 下面结合附图进一步详细描述本发明的技术方案,但本发明的保护范围不局限于以下所述。 [0063] The following aspect of the present invention are described in further detail in conjunction with the accompanying drawings, but the scope of the present invention is not limited to the below.

[0064] 基于平均幅度的LDPC码加权梯度下降比特翻转译码算法,二进制低密度奇偶校验码的校验矩阵为HMXN,cL表示校验矩阵第m行中" 1"的数量,规则低密度奇偶校验码校验矩阵每行中"1"的数量统一表示为A(m)表示Hmxn第m行中为"1"的位置,B(n) 表不H mxn第η列中为"1"的位置;任意一个码字c=(c η c2,…,cn,…,cN), cne (〇, 1)经过传输映射后得到 [0064] LDPC codes based on a weighted average amplitude of the gradient descent BF decoding algorithm, the binary low density parity check code check matrix HMXN, cL represents the number of m-th row in the check matrix of "1", the irregular low density each row number "1" of the parity check matrix collectively as a (m) represents the m-th row is Hmxn position "1", B (n) η table does H mxn first column is "1 "position; any codeword c = (c η c2, ..., cn, ..., cN), cne (square, 1) after transmission map obtained

Figure CN102970047BD00083

其经过双相移相键控调制后加入加性高斯白噪声信道,接收端对其解调后,输出序列r=(ri,r2,…,rn,…,r N),并送至信道译码器, Z= (Z1, Z2,…,Zn,…,ZN), Zn e (+1,-1)为硬判决输出序列,判决规则为 After its binary phase shift keying modulation Houjiarujia white Gaussian noise channel, the receiving end demodulates the output sequence r = (ri, r2, ..., rn, ..., r N), and sent to the translation channel decoder, Z = (Z1, Z2, ..., Zn, ..., ZN), Zn e (+ 1, -1) as a hard decision output sequence, the decision rule is

Figure CN102970047BD00084

,译码输出戈 , Ge decode output

Figure CN102970047BD00085

所述的翻转译码方法包括一个单比特翻转译码步骤和一个多比特翻转译码步骤: Said decoding method comprising inverting a single bit flipping decoding step and a multi-bit flip decoding step:

[0065] 所述的单比特翻转译码步骤包括以下子步骤: [0065] The single-bit inverting decoding step comprises the substeps of:

[0066] Sll :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax; [0066] Sll: Initialization: Initialize the number of iterations k = 1, Kmax of setting the maximum number of iterations;

[0067] S12 :计算伴随式sk: [0067] S12: syndrome computing sk:

Figure CN102970047BD00091

[0069] S13 :sk=0时停止迭代,译码输出为f ,sk不为零时计算各个校验节点的权重ω [0069] S13: sk = 0 stop the iterative decoding output is f, is calculated for each check node is not zero when sk weights ω

Figure CN102970047BD00092

[0071] S14 :计算各个信息节点的翻转函数 [0071] S14: calculated for each node information flip function

Figure CN102970047BD00093

[0073] S15 :翻转函数式:满足以下条件的比特nk: [0073] S15: Flip functional: NK bits meet the following criteria:

Figure CN102970047BD00094

[0075] S16 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S14 ; [0075] S16: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, proceeds to step S14;

[0076] 所述的多比特翻转译码步骤包括以下子步骤: [0076] The multi-bit flip decoding step comprises the substeps of:

[0077] S21 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax,目标函数初始化为 [0077] S21: Initialization: Initialize the number of iterations k = 1, set the maximum number of iterations Kmax, the objective function is initialized

Figure CN102970047BD00095

翻转门限初始化为θ,Θ为一个负数; Flip initialized threshold θ, Θ is a negative number;

[0078] S22 :计算伴随式sk: [0078] S22: syndrome computing sk:

Figure CN102970047BD00096

[0080] S23 :sk=0时停止迭代,译码输出为f , Sk不为零时计算各个校验节点的权重ω [0080] S23: sk = 0 stop the iterative decoding output is f, is calculated for each check node is not zero when Sk weights ω

Figure CN102970047BD00097

[0082] S24 :计算各个信息节点的翻转函数皮和目标函数fk (ζ): [0082] S24: calculating respective information nodes and skin flip function objective function fk (ζ):

Figure CN102970047BD00098

[0085] S25:当条件 [0085] S25: When the conditions

Figure CN102970047BD00099

同时满足,其中Φ表示空集,则翻转函数』ί満足以下条件的比特nk: Meet, where Φ represents the empty set, then the bit flipping function nk "ί the Man under conditions sufficient to:

Figure CN102970047BD000910

[0087] 否则,翻转函数式满足以下条件的比特nk: [0087] Otherwise, the following conditional formula flip function bits nk:

Figure CN102970047BD000911

[0089] S26 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S24。 [0089] S26: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, jumps to step S24.

[0090] 对于规则的LDPC码,所述的译码方法包括以下步骤: [0090] For a regular LDPC code, the decoding method comprising the steps of:

[0091] 所述的单比特翻转译码步骤包括以下子步骤: [0091] The single-bit inverting decoding step comprises the substeps of:

[0092] S31 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax; [0092] S31: Initialization: Initialize the number of iterations k = 1, Kmax of setting the maximum number of iterations;

[0093] S32 :计算伴随式sk: [0093] S32: syndrome computing sk:

Figure CN102970047BD00101

[0095] S33 :sk=0时停止迭代,译码输出为f , Sk不为零时计算各个校验节点的权重ω [0095] S33: sk = 0 stop the iterative decoding output is f, is calculated for each check node is not zero when Sk weights ω

Figure CN102970047BD00102

[0097] S34 :计算各个信息节点的翻转函数式:: [0097] S34: calculated for each node information flip function formula ::

Figure CN102970047BD00103

[0099] S35 :翻转函数满足以下条件的比特nk: [0099] S35: function of the following conditions are inverted bits nk:

Figure CN102970047BD00104

[0101] S36 :判决和终止迭代检测:重新计算伴随式sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S34 ; [0101] S36: terminating the iterative detection and judgment: recalculated syndrome SK, terminate the iteration when Sk = O time, when the syndrome is not completely met and the maximum number of iterations reaches limit, terminate the iterative decoding fails, otherwise proceed an iterative process, k from a plus, proceeds to step S34;

[0102] 所述的多比特翻转译码步骤包括以下子步骤: [0102] The multi-bit flip decoding step comprises the substeps of:

[0103] S41 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kniax,目标函数初始化为 [0103] S41: Initialization: Initialize the number of iterations k = 1, set the maximum number of iterations Kniax, the objective function is initialized

Figure CN102970047BD00105

,翻转门限初始化为θ,Θ为一个负数; Flip initialized to the threshold θ, Θ is a negative number;

[0104] S42:计算伴随式sk: [0104] S42: syndrome computing sk:

Figure CN102970047BD00106

[0106] S43 :sk=0时停止迭代,译码输出为,,Sk不为零时计算各个校验节点的权重ω [0106] S43: sk = 0 stop the iterative decoding output is calculated for each check node ,, Sk when the non-zero weights ω

Figure CN102970047BD00107

[0108] S44 :计算各个信息节点的翻转函数<和目标函数fk(ζ): [0108] S44: calculated for each node information flip function <objective function and fk (ζ):

Figure CN102970047BD00108

[0111] S45:当条件 [0111] S45: When the conditions

Figure CN102970047BD00109

同时满足,其中Φ表示空集,则翻转函数,满足以下条件的比特nk: Meet, where Φ nk bits representing an empty set, the flip function, satisfying the following conditions:

Figure CN102970047BD001010

[0113] 否则,翻转函数满足以下条件的比特nk: [0113] Otherwise, the function satisfies the following conditions inverting bits nk:

Figure CN102970047BD001011

[0115] S46 :判决和终止迭代检测:重新计算伴随式Sk,当Sk=O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k 自加一,跳转到步骤S44。 [0115] S46: terminating the iterative detection and judgment: recalculated syndrome of Sk, Sk = O when the iteration termination time, when the syndrome is not completely met and limit the number of iterations reaches the maximum number, terminating the iterative decoding fails, otherwise proceed an iterative process, k from a plus, jumps to step S44.

[0116] 列重为3的(1008,504)PEGLDPC码在MffBF、单比特翻转⑶BF-single、多比特翻转⑶BF-multi、单比特翻转AMWGDBF-single及多比特翻转AMffGDBFmulti算法下的误比特率如图1所示。 [0116] Column weight (1008,504) PEGLDPC code 3 in MffBF, single bit flipping ⑶BF-single, multi-bit flip ⑶BF-multi, flipping a single bit at the bit error rate AMWGDBF-single and multi-bit flipping algorithm as AMffGDBFmulti 1 shown in FIG. 最大迭代次数设置为100次,MffBF的最优的加权系数α设定为〇. 2,多比特翻转⑶BF算法的翻转门限Θ =-〇. 6,多比特翻转AMffGDBF算法翻转门限Θ =-〇. 4,在SNR=3. 5dB到6dB的范围内,AMWGDBF-multi的性能都要好于⑶BF-multi算法,在误比特率为10 5时,⑶BF-multi算法可获得0. 075dB的编码增益。 Maximum number of iterations is set to 100, the optimum weighting coefficient α is set to MffBF billion. 2, the multi-bit flip flipping algorithm ⑶BF threshold Θ = -〇. 6, the multi-bit flip flipping algorithm AMffGDBF threshold Θ = -〇. 4, in the range of SNR 3. 5dB to 6dB of =, AMWGDBF-multi properties are better than ⑶BF-multi algorithm, the bit error rate is 5 10, ⑶BF-multi 0. 075dB algorithm of coding gain can be obtained.

[0117] 列重为3的(1008,504)PEGLDPC码在MWBF、单比特翻转⑶BF-single、多比特翻转⑶BF-multi、单比特翻转AMWGDBF-single及多比特翻转AMWGDBF-multi算法下的平均迭代次数如图2所示。 [0117] Column weight (1008,504) PEGLDPC code 3 in MWBF, single bit flipping ⑶BF-single, multi-bit flip ⑶BF-multi, single bit flipping AMWGDBF-single and multi-bit flip average number of iterations in AMWGDBF-multi Algorithm the number 2. 在SNR=3. IdB到6dB的范围内,AMWGDBF-multi算法的平均迭代次数要比⑶BFiulti 算法小3. 2-9. 3%。 In SNR = 3. IdB to 6dB in the range of the average number of iterations AMWGDBF-multi algorithm 3. Algorithm smaller than ⑶BFiulti 2-9. 3%.

[0118] 列重为3的(504,252)PEGLDPC码在MWBF、单比特翻转⑶BF-single、多比特翻转⑶BF-multi、单比特翻转AMWGDBF-single及多比特翻转AMWGDBF-multi算法下的误比特率如图3所示。 [0118] Column weight (504,252) PEGLDPC code 3 in MWBF, single bit flipping ⑶BF-single, multi-bit flip ⑶BF-multi, single bit flipping AMWGDBF-single and bit error rate under AMWGDBF-multi algorithm is a multi-bit flip as 3 shown in FIG. 最大迭代次数设置为50次,MffBF的最优的加权系数α设定为0. 2,多比特比特翻转⑶BF算法的翻转门限Θ =-〇. 6,多比特翻转AMffGDBF算法翻转门限Θ =-〇. 5,在SNR=2. 5dB到6dB的范围内,AMWGDBF-multi的性能都要好于⑶BF-multi算法,在误比特率为10 5时,⑶BF-multi算法可获得0. 075dB的编码增益。 Maximum number of iterations is set to 50, MffBF optimum weighting coefficient α is set to 0.2, the inversion algorithm 多比特比特 flip ⑶BF threshold Θ = -〇. 6, the multi-bit flip flipping algorithm AMffGDBF threshold Θ = -〇 5, in the range of SNR = 2. 5dB to a 6dB, AMWGDBF-multi properties are better than ⑶BF-multi algorithm, the bit error rate at 5 10, ⑶BF-multi 0. 075dB algorithm of coding gain can be obtained.

[0119] 列重为3的(504,252)PEGLDPC码在在MWBF、单比特翻转⑶BF-single、多比特翻转⑶BF-multi、单比特翻转AMWGDBF-single及多比特翻转AMWGDBF-multi算法下的平均迭代次数如图4所示。 [0119] the column weight is 3 (504,252) PEGLDPC code in MWBF, single bit flipping ⑶BF-single, multi-bit flip ⑶BF-multi, single bit flipping AMWGDBF-single and multi-bit flip average number of iterations in AMWGDBF-multi Algorithm As shown in Figure 4. 在SNR=2. 5dB到6dB的范围内,AMWGDBF-multi算法的平均迭代次数要比⑶BFiulti算法小3. 3-9. 4%。 In the range of SNR = 2. 5dB to 6dB, the average number of iterations AMWGDBF-multi ⑶BFiulti smaller than the algorithm Algorithm 3. 3-9. 4%.

Claims (2)

  1. 1.基于平均幅度的LDPC码加权梯度下降比特翻转译码方法,二进制低密度奇偶校验码的校验矩阵为HMXN,Clm表示校验矩阵第m行中" 1"的数量,规则低密度奇偶校验码校验矩阵每行中"1"的数量统一表示为A (m)表示Hmxn第m行中为"1"的位置,B (η)表示Hmxn第η列中为"1"的位置;任意一个码字c = (c C2,…,cn,…,cN),cne {〇, 1}经过传输映射后得到 1. The weighted average amplitude of the gradient descent LDPC code decoding method based on inversion bit binary LDPC parity check matrix represents a parity check matrix of m row number "1", the low density parity rule is HMXN, Clm code parity check matrix each row number "1" are collectively shown as a (m) represents the m-th row is Hmxn position "1", B (η) of [eta] Hmxn column indicates the position "1" ; any one codeword c = (c C2, ..., cn, ..., cN), cne {square, 1} after the transmission map obtained
    Figure CN102970047BC00021
    其经过双相移相键控调制后加入加性高斯白噪声信道,接收端对其解调后,输出序列r = (Γι,r2,…,rn,…,rN),并送至信道译码器,z = (Z1, Z2,…,Zn,…,Zn),Zne {+1,-1}为硬判决输出序列,判决规则为 After its binary phase shift keying modulation Houjiarujia white Gaussian noise channel, the receiving end demodulates the output sequence r = (Γι, r2, ..., rn, ..., rN), and sent to the channel decoder is, z = (Z1, Z2, ..., Zn, ..., Zn), Zne {+ 1, -1} to output the hard decision sequence, the decision rule is
    Figure CN102970047BC00022
    译码输出为 Decode output is
    Figure CN102970047BC00023
    其特征在于:所述的翻转译码方法包括一个单比特翻转译码步骤和一个多比特翻转译码步骤: 所述的单比特翻转译码步骤包括以下子步骤: 511 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax; 512 :计算伴随式sk: Characterized in that: said decoding method comprising flip bit flipping a single decoding step and a multi-bit flip decoding step: the single-bit flip decoding step comprises the substeps of: 511: Initialization: Initialize the number of iterations k = 1, setting the maximum number of iterations Kmax; 512: syndrome computing sk:
    Figure CN102970047BC00024
    513 :sk= 〇时停止迭代,译码输出为f , J不为零时计算各个校验节点的权重ω n: 513: sk = 0:00 stop the iterative decoding output is f, is calculated for each check node J is not zero when the weight ω n:
    Figure CN102970047BC00025
    514 :计算各个信息节点的翻转函数尾% 514: calculating the respective inverting nodes function information tail%
    Figure CN102970047BC00026
    515 :翻转函数<满足以下条件的比特nk: 515: Flip Function <nk bits satisfies the following conditions:
    Figure CN102970047BC00027
    516 :判决和终止迭代检测:重新计算伴随式sk,当Sk= O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k自加一,跳转到步骤S14 ; 所述的多比特翻转译码步骤包括以下子步骤: 521 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax,目标函数初始化为 516: Iterative detection and termination decision: recalculated syndrome SK, terminate the iteration when Sk = O, the syndrome when the number of iterations and can not fully meet the limit reaches the maximum number, terminating the iterative decoding fails, otherwise the iterative process continues, since k is incremented by one jumps to step S14; inverting the multi-bit decoding step comprises the substeps of: 521: initialization: initialize the number of iterations k = 1, Kmax of setting the maximum number of iterations, the objective function is initialized
    Figure CN102970047BC00028
    、翻转门限初始化为θ,Θ为一个负数; 522 :计算伴随式sk: Flip initialized to the threshold θ, Θ is a negative number; 522: SK syndrome calculating:
    Figure CN102970047BC00029
    523 :sk= O时停止迭代,译码输出为f,Sk不为零时计算各个校验节点的权重ω 523: sk = stop the iterative decoding when output O is f, is calculated for each check node is not zero when Sk weights ω
    Figure CN102970047BC00031
    524 :计算各个信息节点的翻转函数ϋί和目标函数fk(z): 524: calculating the respective node information and the flip function ϋί objective function fk (z):
    Figure CN102970047BC00032
    525 :当条件 525: When the condition
    Figure CN102970047BC00033
    同时满足,其中Φ表示空集,则翻转函数纪满足以下条件的比特nk: Meet, where Φ represents an empty set of bits nk, Ji rollover function satisfies the following conditions:
    Figure CN102970047BC00034
    否则,翻转函数贫满足以下条件的比特nk: Otherwise, the following conditions are met flip function lean a bit nk:
    Figure CN102970047BC00035
    526 :判决和终止迭代检测:重新计算伴随式sk,当Sk= O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k自加一,跳转到步骤S24。 526: judgment and terminate the iterative detection: Recalculate syndrome sk, Sk = O is terminated when the iteration time, when the syndrome can not be fully met and the number of iterations reaches the maximum number limit, terminate the iterative decoding failure, or continue to iterate, since k plus a jump to step S24.
  2. 2.根据权利要求1所述的基于平均幅度的LDPC码加权梯度下降比特翻转译码方法,其特征在于:对于规则的LDPC码,所述的译码方法包括以下步骤: 所述的单比特翻转译码步骤包括以下子步骤: 531 :初始化:初始化迭代次数k = 1,设定最大迭代次数1(_; 532 :计算伴随式sk: According to claim 1 LDPC code based on the weighted average of the amplitude of the gradient drops BF decoding method, wherein: for a regular LDPC code, the decoding method comprising the steps of: said single bit flipping decoding step comprises the substeps of: 531: initialization: initialize the number of iterations k = 1, setting a maximum number of iterations (_; 532: SK syndrome calculating:
    Figure CN102970047BC00036
    533 :sk= O时停止迭代,译码输出为f , Sk不为零时计算各个校验节点的权重ω m: 533: sk = O iteration is stopped, the decode output is f, is calculated for each check node is not zero when Sk weights ω m:
    Figure CN102970047BC00037
    534 :计算各个信息节点的翻转函数.£f:.: 534: calculating the respective inverting nodes information function £ f.:.:
    Figure CN102970047BC00038
    535 :翻转函数圮满足以下条件的比特nk: 535: Flip destroyed function NK bits meet the following criteria:
    Figure CN102970047BC00039
    536 :判决和终止迭代检测:重新计算伴随式sk,当Sk= O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k自加一,跳转到步骤S34 ; 所述的多比特翻转译码步骤包括以下子步骤: 541 :初始化:初始化迭代次数k = 1,设定最大迭代次数Kmax,目标函数初始化为 536: judgment and terminate the iterative detection: Recalculate syndrome sk, Sk = O is terminated when the iteration time, when the syndrome can not be fully met and the number of iterations reaches the maximum number limit, terminate the iterative decoding failure, or continue to iterate, since k is incremented by one jumps to step S34; inverting the multi-bit decoding step comprises the substeps of: 541: initialization: initialize the number of iterations k = 1, Kmax of setting the maximum number of iterations, the objective function is initialized
    Figure CN102970047BC00041
    翻转门限初始化为θ,Θ为一个负数; 542 :计算伴随式sk: Flip initialized threshold θ, Θ is a negative number; 542: SK syndrome calculating:
    Figure CN102970047BC00042
    543 :sk= O时停止迭代,译码输出为f , Sk不为零时计算各个校验节点的权重ω m: 543: sk = O iteration is stopped, the decode output is f, is calculated for each check node is not zero when Sk weights ω m:
    Figure CN102970047BC00043
    544 :计算各个信息节点的翻转函数纪和目标函数&⑴: 544: calculating the respective inverting nodes of information and functions the objective function Ji & ⑴:
    Figure CN102970047BC00044
    545 :当条件 545: When the condition
    Figure CN102970047BC00045
    同时满足,其中Φ表示空集,则翻转函数g满足以下条件的比特nk: Meet, where Φ nk bits representing an empty set, the flip function g satisfies the following conditions:
    Figure CN102970047BC00046
    否则,翻转函数忠满足以下条件的比特nk: Otherwise, the bit flipping function loyal nk meet the following criteria:
    Figure CN102970047BC00047
    546 :判决和终止迭代检测:重新计算伴随式sk,当Sk= O时终止迭代,当伴随式不能完全满足且迭代次数达到最大次数限制时,终止迭代,译码失败,否则继续进行迭代处理,k自加一,跳转到步骤S44。 546: judgment and terminate the iterative detection: Recalculate syndrome sk, Sk = O is terminated when the iteration time, when the syndrome can not be fully met and the number of iterations reaches the maximum number limit, terminate the iterative decoding failure, or continue to iterate, since k plus a jump to step S44.
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