乘积码迭代译码算法研究

介绍了在分组码的软输入软输出译码基础上以扩展BCH码为子码的乘积码的迭代译码算法,提出了在高带宽利用率调制方式下的算法应用方式,并给出了仿真结果。最后与传统的并联卷级码代译码方案比较,发现在高编码效率时,乘积码迭代译码方案有着较好的应用性。     

Non-sequential decoding algorithm for hard iterative turbo product codes - [transactions letters]

In this letter, we propose a new decoding algorithm to improve the bit error rate performance of the hard-input hard-output (HIHO) turbo product codes (TPC) with hard iterative decoding. The proposed algorithm iteratively, but not sequentially, decodes the received TPC blocks based on the reliability of the constituent codes. Simulation results confirm a noticeable coding gain improvement using the proposed decoding process with respect to standard HIHO TPC decoding. An efficient implementation of the new technique offers a negligible additional complexity when the channel-bit error probability is less than 10^?2.     

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.     

Serial concatenated TCM with an inner accumulate code - part II: density-evolution analysis

In a companion paper, we showed the existence of decoding thresholds for maximum-likelihood (ML) decoding of a serial concatenated trellis-coded modulation (SCTCM) system with one or more inner accumulate codes. In this paper, we compute the decoding thresholds for an iterative, non-ML decoder by density evolution (DE), assuming infinite blocklengths. We also derive a stability condition for the particular case of an outer parity-check code and a single inner accumulate code. We show that, for equiprobable signaling, the bit-wise log-likelihood ratio densities for higher order constellations are symmetric. Furthermore, when used in DE, these densities can be averaged without significantly affecting the resulting threshold values. For an outer single parity-check code, the lowest decoding thresholds are achieved with two inner accumulate codes. For an outer repeat code, a single inner accumulate code gives the lowest thresholds. At code rates r/sub c/>2/3, the decoding thresholds for the SCTCM system are within 1 dB of the constellation-constrained channel capacity for additive white Gaussian noise channels, and within 1.5 dB for independent, identically distributed Rayleigh channels. Simulation results verify the computed thresholds.     

Iterative maximum-likelihood trellis decoding for block codes

An iterative trellis search technique is described for the maximum-likelihood (ML) soft decision decoding of block codes. The proposed technique derives its motivation from the fact that a given block code may be a subcode for a parent code whose associated trellis has substantially fewer edges. Through the use of list-Viterbi (1967) decoding and an iterative algorithm, the proposed technique allows for the use of a trellis for the parent code in the ML decoding of the desired subcode. Complexity and performance analyses, as well as details of potential implementations, indicate a substantial reduction in decoding complexity for linear block codes of practical length while achieving ML or near-ML soft decision performance     

DIFFERENTIAL AMPLITUDE PHASE SHIFT KEYING：A NEW MODULATION METHOD FOR TURBO CODE IN DIGITAL RADIO BROADCASTING

The multilevel modulation techniques of M-Differential Amplitude Phase Shift Keying(DAPSK)have been proposed in combination with Turbo code scheme for digital radio broad-casting bands below 30 MHz radio channel.Comparison of this modulation method with channel coding in an Additive White Gaussian Noise(AWGN)and mulit-path fading channels has been presented.The analysis provides an iterative decoding of the Turbo code.     

基于VHDL的TPC译码器设计

Turbo乘积码是一种性能卓越的前向纠错码,具有译码复杂度低,且在低信噪比时可以获得近似最优的性能。介绍基于Chase算法的Turbo乘积码软入软出（SISO）迭代译码算法,提出基于VHDL硬件描述语言的TPC译码器设计方案,并在FPGA芯片上进行了仿真和验证。仿真结果证明该译码器有很大的实用性和灵活性。     

Accumulate-Repeat-Accumulate Codes

In this paper, we propose an innovative channel coding scheme called accumulate-repeat-accumulate (ARA) codes. This class of codes can be viewed as serial turbo-like codes or as a subclass of low-density parity check (LDPC) codes, and they have a projected graph or protograph representation; this allows for high-speed iterative decoding implementation using belief propagation. An ARA code can be viewed as precoded repeat accumulate (RA) code with puncturing or as precoded irregular repeat accumulate (IRA) code, where simply an accumulator is chosen as the precoder. The amount of performance improvement due to the precoder will be called precoding gain. Using density evolution on their associated protographs, we find some rate-1/2 ARA codes, with a maximum variable node degree of 5 for which a minimum bit SNR as low as 0.08 dB from channel capacity threshold is achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA, IRA, or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore, by puncturing the inner accumulator, we can construct families of higher rate ARA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results are provided and compared with turbo codes. In addition to iterative decoding analysis, we analyzed the performance of ARA codes with maximum-likelihood (ML) decoding. By obtaining the weight distribution of these codes and through existing tightest bounds we have shown that the ML SNR threshold of ARA codes also approaches very closely to that of random codes. These codes have better interleaving gain than turbo codes     

基于校验子的Turbo乘积码仿真研究

针对Turbo乘积码译码延时的问题,提出一种基于校验子的Turbo乘积码译码算法(S-TPC),该算法根据校验子的值采取不同方式对每行(列)进行译码,节省了一部分校验子为0的码字的硬判决译码运算量。仿真结果表明,S-TPC(32,26)在迭代4次时,能在不降低译码性能的情况下,减少近50%的计算量。     

移动衰落信道中设计多级编码(MLC)方案的一种非欧度量

本文提出了在移动衰落信道中设计多级编码(MLC)方案的一种非欧度量:"信道容量规则"+"映射规则".在AWGN信道中为:"信道容量规则"+"UP(Ungerboeck Partitioning) 规则";在Rayleigh衰落信道中为:"信道容量规则"+"BP(Block Partitioning)规则".并在此理论指导下,选用不同码长的BCH码作为MLC系统中各级分量码,通过计算机模拟,比较了在AWGN和Rayleigh衰落信道中,采用8ASK调制方式、多级译码(MSD)、三种不同映射方法下的三级MLC方案的性能.     

Multilevel trellis coded modulations for the Rayleigh fadingchannel

The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel. The schemes are based on multilevel trellis-coded-modulation constructions and utilize maximum free Hamming distance binary convolutional codes as building blocks. A suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated. Examples are constructed to show that the proposed schemes outperform the best modified codes of the Ungerboeck type due to significantly higher implicit time diversity, yielding seven branches of built-in time diversity, whereas the Ungerboeck code yields four branches of time diversity for a 64-state system. The transmission delay is higher, however. The new schemes can provide three levels of unequal error protection when 8-PSK or 8-differential-phase-shift-keying (8-DPSK) modulations are used. They provide 10-14-dB channel signal-to-noise ratio gain over uncoded 4-DPSK at a bit error rate of 10^-3 for a modest decoding complexity     

基于Cyclic-2伪最大似然算法的Turbo乘积码在高速移动通信系统中的译码方法

采用扩展汉明码作为Turbo乘积码 (TPC)的子码时,与传统的Chase算法相比,Cyclic-2PML(循环 2伪最大似然)算法复杂度低。本文研究了基于该算法的TPC在高速移动通信系统中的译码方法,仿真比较了采用不同子码组合的TPC结合不同的调制方式在高斯信道和多径衰落信道中的性能。结果表明,以(32, 26, 4)扩展汉明码为子码的TPC,不仅具有较高的码率,同时可以获得更好的误比特率性能。     

Bit-interleaved space-time coded modulation with iterative decoding

Bit-interleaved space-time coded modulation (BI-STC), which combines serial concatenation of bit-interleaved coded modulation (BICM) with space-time block codes, can effectively exploit the available diversity in space and time under various fading conditions. In this letter, we propose to use iterative decoding to further improve the performance of BI-STC by exploiting the concatenating structure of the codes. The decoding metric is therefore modified to fit for the iterative process, and the derived error bounds suggest that set-partition labeling instead of gray labeling should be used when considering iterative decoding.     

Near-capacity coding in multicarrier modulation systems

We apply irregular low-density parity-check (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequency-selective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray-labeled bits are protected using an irregular LDPC code with iterative soft-decision decoding, while other bits are protected using a high-rate Reed-Solomon code with hard-decision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Gray-labeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bit-loading algorithm, we apply this coding scheme to an ensemble of frequency-selective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a bit-error rate of 10/sup -7/ and a block length of approximately 10/sup 5/ b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8-1.2 dB using constellation shaping.     

Bounds on the bit error probability of a linear cyclic code overGF(2l) and its extended code

An upper bound on the bit-error probability (BEP) of a linear cyclic code over GF(2^l) with hard-decision (HD) maximum-likelihood (ML) decoding on memoryless symmetric channels is derived. Performance results are presented for Reed-Solomon codes on GF(32), GF(64), and GF(128). Also, a union upper bound on the BEP of a linear cyclic code with either hard- or soft-decision ML decoding is developed, as well as the corresponding bounds for the extended code of a linear cyclic code. Using these bounds, which are tight at low bit error rate, the performance advantage of soft-decision (SD) ML and HD ML over bounded-distance (BD) decoding is established     

Graph-based iterative decoding algorithms for parity-concatenatedtrellis codes

We construct parity-concatenated trellis codes in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. From the Tanner-Wiberg-Loeliger (1981, 1996) graph representation, several iterative decoding algorithms can be derived. However, since the graph of the parity-concatenated code contains many short cycles, the conventional min-sum and sum-product algorithms cannot achieve near-optimal decoding. After some simple modifications, we obtain near-optimal iterative decoders. The modifications include either (a) introducing a normalization operation in the min-sum and sum-product algorithms or (b) cutting the short cycles which arise in the iterative Viterbi algorithm (IVA). After modification, all three algorithms can achieve near-optimal performance, but the IVA has the least average complexity. We also show that asymptotically maximum-likelihood (ML) decoding and a posteriori probability (APP) decoding can be achieved using iterative decoders with only two iterations. Unfortunately, this asymptotic behavior is only exhibited when the bit-energy-to-noise ratio is above the cutoff rate. Simulation results show that with trellis shaping, iterative decoding can perform within 1.2 dB of the Shannon limit at a bit error rate (BER) of 4×10^-5 for a block size of 20000 symbols. For a block size of 200 symbols, iterative decoding can perform within 2.1 dB of the Shannon limit     

三维TPC译码器的设计及FPGA实现

Turbo乘积码（TPC）是一种性能优秀的纠错编码方法,它具有译码复杂度低、译码延时小等优点,且在低信噪比下可以获得近似最优的性能。介绍了基于Chase算法的三维TPC软输入软输出（SISO）迭代译码算法,提出了三维TPC译码器硬件设计方案并在FPGA芯片上进行了仿真和验证。测试结果表明,该译码器具有较高的纠错能力,满足移动通信误码率的要求。     

Performance of joint multilevel/AES‐LDPCC‐CPFSK schemes over wireless sensor networks

In wireless sensor networks, data encryption and channel coding are considered together for ensuring secure and robust communication. In order to achieve this purpose, we introduce a new joint scheme, namely ‘Multilevel/Advanced Encryption Standard‐Low Density Parity Check Coded‐Continuous Phase Frequency Shift Keying (ML/AES‐LDPCC‐CPFSK)’. AES algorithm is the most powerful and widely used symmetric key cryptography in providing secure data transmission. LDPC codes have very large Euclidean distance and use iterative decoding algorithms. In this study, we have increased error performance employing multilevel structure to AES and LDPC. In all communications systems, phase discontinuities of modulated signals result in extra bandwidth requirements. CPFSK, which is a special type of continuous phase modulation, is a powerful solution for this problem. In this paper, we simulate error performance of ML/AES‐LDPCC‐CPFSK for regular LDPC codes. Simulation results are drawn for 4CPFSK, 8CPFSK and 16CPFSK over wireless cooperative sensor networks. Using this scheme, we are able to improve bit error performance, channel throughput, security level of communication and reduction in complexity compared with related schemes such as various turbo code structures. Copyright © 2009 John Wiley & Sons, Ltd.     

宽带移动通信中Turbo乘积码的仿真研究

推出了一种新型的纠错码——Turbo乘积码(TPC),描述了Turbo乘积码的编译码基本思想,详细地分析了TPC的Turbo软迭代译码的核心思想,并对AWGN信道和瑞利衰落信道下的TPC的译码性能做了仿真分析,从仿真结果可以看出,在高编码效率时,TPC不仅具有更高的码率,而且可以获得很好的误码率性能,所以乘积码的软迭代译码方案有很好的应用性,在未来的宽带移动通信中具有广阔的应用前景。