Low-complexity LDPC coded BICM-ID with orthogonal modulations

A low-complexity low density parity check (LDPC) coded bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme with orthogonal modulations is proposed. With a novel mapping strategy of coded bits to symbols, the proposed scheme is equivalent to a generalised LDPC code with Hadamard constraints and thus orthogonal demodulation can be merged into the iterative LDPC decoding process, resulting in a simpler implementation and a lower computational complexity.     

Noncoherent iterative decoding of spectrally efficient coded modulations

In this paper, we consider possible solutions for noncoherent decoding of concatenated codes with spectrally efficient modulations. Two main classes of schemes are considered. A first class is obtained by concatenating parallel coding schemes with differential encoding. A second class considers serially concatenated coding structures and possible schemes derived from turbo trellis coded modulation (t-tcm), which do not employ differential encoding. In the first case, at the receiver side we consider separate detection and decoding, while in the second case we consider joint detection and decoding. The major problem connected with such an iterative decoding procedure is that taking into account an augmented channel memory leads to an intolerable trellis size, and hence to an impractical decoding complexity. Reduced-complexity techniques suited to iterative decoding become fundamental, and we consider a recently proposed state-reduction technique. This way, the performance of a coherent receiver is approached, by keeping the number of receiver states fixed.     

An iterative reliability-based decoding for LDPC coded modulation system

In this paper, A Belief Propagation concatenated Orderd-Statistic Decoder （BP-OSD） based on accumulated Log-Likelihood Ratio （LLR） is proposed for medium and short lengths Low Density Parity-Check （LDPC） codes coded Bit-Interleaved Coded Modulation （BICM） systems. The accumulated soft output values delivered by every BP iteration are used as reliability values of Soft-Input Soft-Output OSD （SISO-OSD） decoder and the soft output of SISO-OSD is used as a priori probabilities of the demodulator for the next iteration. Simulation results show that this improved algorithm achieves noticeable performance gain with only modest increase in computation complexity.     

LDPC coded MIMO multiple access with iterative joint decoding

An efficient scheme for the multiple-access multiple-input multiple-output (MIMO) channel is proposed, which operates well also in the single user regime, as well as in a direct-sequence spread-spectrum (DS-CDMA) setting. The design features scalability and is of limited complexity. The system employs optimized low-density parity-check (LDPC) codes and an efficient iterative (belief propagation-BP) detection which combines linear minimum mean-square error (LMMSE) detection and iterative interference cancellation (IC). This combination is found to be necessary for efficient operation in high system loads /spl alpha/>1. An asymptotic density evolution (DE) is used to optimize the degree polynomials of the underlining LDPC code, and thresholds as close as 0.77 dB to the channel capacity are evident for a system load of 2. Replacing the LMMSE with the complex individually optimal multiuser detector (IO-MUD) further improves the performance up to 0.14 dB from the capacity. Comparing the thresholds of a good single-user LDPC code to the multiuser optimized LDPC code, both over the above multiuser channel, reveals a surprising 8-dB difference, emphasizing thus the necessity of optimizing the code. The asymptotic analysis of the proposed scheme is verified by simulations of finite systems, which reveal meaningful differences between the performances of MIMO systems with single and multiple users and demonstrate performance similar to previously reported techniques, but with higher system loads, and significantly lower receiver complexity.     

用于 LDPC 码快速译码的改进多比特翻转算法简

为了提高RRWBF算法的译码速度,提出一种多比特翻转机制来加快RRWBF算法的收敛速度。但是,使用该多比特翻转机制的RRWBF算法时,译码过程中出现与单比特翻转类似的循环翻转现象,影响其译码性能。为此,进一步提出一种循环翻转消除机制来破坏多比特翻转译码过程中产生的循环翻转,进而提高其译码性能。仿真结果显示,与单比特翻转算法相比,提出的基于循环翻转消除的多比特RRWBF算法以较小的译码性能损失换来译码速度的较大提升。     

On multidimensional coded modulations having uniform error propertyfor generalized decoding and flat-fading channels

We consider the problem of uniform error property (UEP) for a coded modulation with constant energy multidimensional symbols, transmitted over the additive white Gaussian noise (AWGN) or fading channels and received by a broad class of decoders. This class includes coherent, partially coherent, double differential, and noncoherent decoders, decoders designed for fading channels, decoders using one or multiple-symbol observations, and many more. These decoders are described as special cases of a general decoder model. This decoder operates by maximizing an arbitrary likelihood function that its arguments are front-end correlator (matched-filter) outputs, A group code structure that guarantees UEP is developed by using the theory of geometrically uniform codes and applying it to the general decoder. These codes are defined over groups (commonly nonbinary) with isometric mapping to channel symbols. We show the code construction for the specific case of Lth-dimensional M-ary phase-shift keying (MPSK). An additional interesting property of these general uniform error codes is related to the case of noncoherent decoding. We show that when using codes of this family, if a code is noncoherently catastrophic, then it is also rotationally invariant. Then, the use of preceding of the input such that the code becomes rotationally transparent will also make it noncatastrophic     

LDPC调制系统中迭代解调解码信息的线性优化

在中短码长低密度奇偶校验（LDPC）码编码的比特交织编码调制系统（BICM）中,由二分图短圈导致的置信传播（BP）解码器输出外附信息之间的相关性是降低迭代解调/解码性能的主要原因,因此有必要对解码器输出外附对数似然比（LLR）信息进行优化。针对该问题,提出了一种简单有效的LLR线性优化算法。该算法首先基于匹配LLR值应满足的连续性条件,并结合BP解码器输出外附LLR信息的统计特性,对解码器输出LLR信息的条件概率密度函数（PDF）的计算进行简化,推导出了乘性优化因子,据此对解码器输出外附信息进行线性优化。仿真结果表明,与未优化方案相比,对于(504,252) LDPC 码编码的BICM系统,所提优化算法可获得0.6~0.8 dB 的信噪比增益;和推广互信息（GMI）优化方法相比,两者的误码性能接近,所提算法仅差0.1 dB,且具有更小的运算复杂度。     

一种改进的LDPC编码FSO-MIMO系统迭代检测解码算法

基于双伽玛(Gamma-Gamma)湍流信道,研究了低 密度奇偶校验码(LDPC)的自由空间光通信多输入多输出(FSO-MIMO)系统迭代检测解码(ID D)算法。针对最优最大后验概率(MAP)算法复杂度高和BP迭代过程 中比特节点后验对数似然比(LLR)震荡现象,结合概率数据辅助(PDA)算法在信号检测中 的良好性能, 提出了一种基于反馈均值的LDPC+PDA系统IDD码算法,采用BP解码方法,经迭代处理,求出 每次内 迭代中比特节点输出的后验信息均值,并将其作为解码器的输出反馈给检测器,从而提高了 解码器传递给 检测器的消息可靠性。仿真结果表明,当误码率(BER)为10－5左右 时,在弱湍流条件下,改进的IDD算法相 对传统的算法具有0.3dB的性能优势;在强湍流条件下,改进的IDD 算法比传统的算法提高了0.65dB 的性能增益。因而,改进的IDD算法能够进一步抑制湍流特别是强湍流的影响,提高了系统 性能。     

High coded data rate and multicodeword WiMAX LDPC decoding on Cell/BE

A novel, flexible and scalable parallel LDPC decoding approach for the WiMAX wireless broadband standard (IEEE 802.16e) in the multicore Cell broadband engine architecture is proposed. A multicodeword LDPC decoder performing the simultaneous decoding of 96 codewords is presented. The coded data rate achieved a range of 72? 80 Mbit/s, which compares well with VLSI-based decoders and is superior to the maximum coded data rate required by theWiMAX standard performing in worst case conditions. The 8-bit precision arithmetic adopted shows additional advantages over traditional 6-bit precision dedicated VLSI-based solutions, allowing better error floors and BER performance.     

Improved iterative joint detection and decoding of coded V-BLAST systems

Soft iterative detection and decoding techniques have been shown to achieve near-capacity performance in multiple antenna systems. In most cases, obtaining optimal soft information in a joint detection and decoding algorithm by marginalizing over the entire observation space is prohibitively complex. In this paper, an improved scheme adaptable to various list-type detectors providing superior performance is proposed.     

Two algorithms for soft-decision decoding of reed-solomon codes, with application to multilevel coded modulations

In this paper two symbol-level soft-decision decoding algorithms for Reed-Solomon codes, derived form the ordered statistics (OS) and from the generalized minimum-distance (GMD) decoding methods, are presented and analyzed. Both the OS and the GMD algorithms are based on the idea of producing a list of candidate code words, among which the one having the larger likelihood is selected as output. We propose variants of the mentioned algorithms that allow to finely tune the size of the list in order to obtain the desired decoding complexity. The method proposed by Agrawal and Vardy for computing the error probability of the GMD algorithm is extended to our decoding methods. Examples are presented where these algorithms are applied to singly-extended Reed-Solomon codes over GF(16) used as outer codes in a 128-dimensional coded modulation scheme that attains good performance, with manageable decoding complexity.     

一种改进的LDPC码低复杂度最小和算法

研究了低密度奇偶校验(Low-Density Parity-Check,LDPC)码的单最小值最小和(Single-Minimum Min-Sum,SMMS)算法,为了提高译码性能,在此基础上提出一种信道自适应可配置LDPC码最小和译码(Adaptive Configurable Min-Sum,ACMS)算法。ACMS算法在BP译码时的横向消息迭代更新过程中,LLR次小值用一个基于迭代次数的估算参数与最小值相加来取代,同时根据每次判决时的错误比特个数对不同信噪比下的估算参数进行动态修正。仿真结果表明,ACMS算法整体上提高了译码性能而仅增加少量复杂度。     

Low-complexity decoding of LDPC codes

The offset BP-based algorithm is a reduced-complexity derivative of the belief-propagation algorithm for decoding of low-density parity- check codes. It uses a constant offset term to simplify decoding, but at the cost of performance. A method to obtain a 'variable' offset parameter is presented here, to improve the performance of the algorithm.     

引入行重参数的改进不规则LDPC码译码算法

低密度奇偶校验(LDPC)码是一种逼近香农极限的线性分组码,而好的非规则LDPC码其性能优于同码率的规则码.在非规则LDPC码的对数似然比置信传播(LLR-BP)译码算法中,由于行重大小的不同,校验节点对伪后验判决贡献的外部信息不同,为此提出一种基于行重的改进LLR-BP译码算法,该算法引入行权重系数,用以调整不同行重...     

一种新的LDPC译码算法

由于LDPC码的优良性能,因此在信息可靠传输中有良好的应用前景。本文提出了一种将BP算法和基于列表的SIHO(软输入硬输出)算法相结合的译码算法,通过与BP、MLD算法的误码率性能和译码复杂度比较,本算法复杂度比MLD有明显降低,而在性能上优于BP算法并接近MLD译码算法。     

消息复用下的空间耦合LDPC码窗译码优化算法

空间耦合低密度奇偶校验（Spatially Coupled Low Density Parity Check,SC-LDPC）码由于其奇偶校验矩阵呈现对角带非零项的特点,采用窗译码可获得较低的时延及复杂度。针对SC-LDPC码窗译码性能损失、译码复杂度依然较高的问题,提出了消息复用（Message Reuse for Window Decoding,MR-WD）算法和动态多目标符号输出（Dynamic Multi-target-symbol Output for Window Decoding,DMO-WD）算法。消息复用算法以外部对数似然比值作为边信息传入窗口,与传统窗译码相比,译码性能得到了提升,译码复杂度降低。动态多目标符号输出算法在连续若干个窗口均满足奇偶校验方程判定为零时,增加目标符号的输出数量,反之减少目标符号的输出数量。该算法在误码率损失可忽略不计的情况下降低译码复杂度最大达20%,且在动态多目标符号窗译码中使用消息复用更新边信息时,相比于传统窗译码性能提升约0.2 dB,复杂度下降约35%。     

Memory-efficient sum-product decoding of LDPC codes

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.     

一种改进的LDPC码硬判决译码算法

LDPC码的硬判决译码通常是利用比特翻转算法(BF)以及在其基础上改进的加权比特翻转算法(WBF)来实现的,但是前者算法性能较差,而后者的复杂度较高,为了让译码算法能够兼顾其性能和复杂度,针对之前的BF以及WBF算法,提出了一种改进的LDPC码硬判决译码算法,该算法能够在前两次迭代中完成多个比特位的翻转.仿真结果表明,这种改进的算法可以在性能损失较小的条件下,大大降低算法的复杂度,从而提高译码的效率,减轻硬件的负担.     

Computationally efficient decoding of LDPC codes

A computationally efficient algorithm for the decoding of low-density parity check codes is introduced. Instead of updating all bit and check nodes at each decoding iteration, the developed algorithm only updates unreliable check and bit nodes. A simple reliability criteria is developed to determine the active bit and check nodes per decoding iteration. Based on the developed technique, significant computation reductions are achieved with very little or no loss in the BER performance of the LDPC codes. The proposed method can be implemented with a slight modification to the sum-product algorithm with negligible additional hardware complexity.