CRC-assisted error correction in a convolutionally coded system

In communication systems employing a serially concatenated cyclic redundancy check (CRC) code along with a convolutional code (CC), erroneous packets after CC decoding are usually discarded. The list Viterbi algorithm (LVA) and the iterative Viterbi algorithm (IVA) are two existing approaches capable of recovering erroneously decoded packets. We here employ a soft decoding algorithm for CC decoding, and introduce several schemes to identify error patterns using the posterior information from the CC soft decoding module. The resultant iterative decoding-detecting (IDD) algorithm improves error performance by iteratively updating the extrinsic information based on the CRC parity check matrix. Assuming errors only happen in unreliable bits characterized by small absolute values of the log-likelihood ratio (LLR), we also develop a partial IDD (P-IDD) alternative which exhibits comparable performance to IDD by updating only a subset of unreliable bits. We further derive a soft-decision syndrome decoding (SDSD) algorithm, which identifies error patterns from a set of binary linear equations derived from CRC syndrome equations. Being noniterative, SDSD is able to estimate error patterns directly from the decoder output. The packet error rate (PER) performance of SDSD is analyzed following the union bound approach on pairwise errors. Simulations indicate that both IDD and IVA are better tailored for single parity check (PC) codes than for CRC codes. SDSD outperforms both IDD and LVA with weak CC and strong CRC. Applicable to AWGN and flat fading channels, our algorithms can also be extended to turbo coded systems.     

Energy-efficient node position identification through payoff matrix and variability analysis

This paper investigates the use of punctured recursive systematic convolutional codes for turbo coding in a 2-user binary adder channel (2-BAC) in the presence of additive white Gaussian noise, aiming to achieve a higher transmission sum rate with reduced decoding complexity. The encoders for the 2-BAC are assumed to be block synchronized and to employ identical puncturing patterns. Iterative decoding combining the Bahl Cocke Jelinek Raviv algorithm and a two-user punctured trellis is employed. For each user and for a fixed puncturing pattern, random interleavers of length 256 bits or 1024 bits, respectively, are simulated and corresponding curves relating bit error rate versus signal to noise ratio are presented for performance comparison purposes. Computer simulation indicates that the loss in performance of a punctured turbo code can be negligible when longer interleavers are used for both users, similarly to the single user case.     

Bandwidth-efficient turbo trellis-coded modulation using puncturedcomponent codes

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used     

RS级联编码在超短波通信与卫星通信信道的仿真分析

超短波波段数据通信与卫星通信已被广泛应用。在这些信道中都存在较强的多径衰落,并且为克服两个波段中的多种干扰,纠正随机错误和突发错误,RS编码被普遍选为信道编码方案。RS码是线性分组码中纠突发错误能力最强,效率最高的编码,Turbo码是可以接近香农限的编码方案。文章提出RS编码与Turbo码的级联码编码方案和解码算法,适当选择参数,并通过仿真验证了方案的正确性与可行性。     

Turbo码概率-代数联合解码算法

Turbo码采用修正的BAHL et al.算法实现解码.这是一种基于软值的概率迭代解码算法.本文在保持Turbo码迭代软解码算法优点的基础上,充分利用Turbo码编码器结构这一确知条件,结合代数解码原理,提出了一种Turbo码概率-代数联合解码算法.该算法结合了概率解码和代数解码的优点,又有效避免了误差传播的发生,使Turbo码的纠错性能在原经典算法的基础上得到进一步的提高.该算法不仅为降低Turbo码的比特误码率和误差地板值提供了一种新的研究途径,而且因其更好的纠错性能而具有十分明显的实用价值.仿真实验结果显示,在比特误码率(BER)为10^-3~10^-4时,与经典Turbo码解码算法相比,采用该算法能获得0.1dB左右的编码增益.     

Iterative decoding for partial response (PR), equalized,magneto-optical (MO) data storage channels

Turbo codes and low-density parity check (LDPC) codes with iterative decoding have received significant research attention because of their remarkable near-capacity performance for additive white Gaussian noise (AWGN) channels. Previously, turbo code and LDPC code variants are being investigated as potential candidates for high-density magnetic recording channels suffering from low signal-to-noise ratios (SNR). We address the application of turbo codes and LDPC codes to magneto-optical (MO) recording channels. Our results focus on a variety of practical MO storage channel aspects, including storage density, partial response targets, the type of precoder used, and mark edge jitter. Instead of focusing just on bit error rates (BER), we also study the block error statistics. Our results for MO storage channels indicate that turbo codes of rate 16/17 can achieve coding gains of 3-5 dB over partial response maximum likelihood (PRML) methods for a 10^-4 target BER. Simulations also show that the performance of LDPC codes for MO channels is comparable to that of turbo codes, while requiring less computational complexity. Both LDPC codes and turbo codes with iterative decoding are seen to be robust to mark edge jitter     

Huffman code based error screening and channel code optimization for error concealment in perceptual audio coding (PAC) algorithms

The class of perceptual audio coding (PAC) algorithms yields efficient and high-quality stereo digital audio bitstreams at bit rates from 16 kb/sec to 128 kb/sec (and higher). To avoid "pops and clicks" in the decoded audio signals, channel error detection combined with source error concealment, or source error mitigation, techniques are preferred to pure channel error correction. One method of channel error detection is to use a high-rate block code, for example, a cyclic redundancy check (CRC) code. Several joint source-channel coding issues arise in this framework because PAC contains a fixed-to-variable source coding component in the form of Huffman codes, so that the output audio packets are of varying length. We explore two such issues. First, we develop methods for screening for undetected channel errors in the audio decoder by looking for inconsistencies between the number of bits decoded by the Huffman decoder and the number of bits in the packet as specified by control information in the bitstream. We evaluate this scheme by means of simulations of Bernoulli sources and real audio data encoded by PAC. Considerable reduction in undetected errors is obtained. Second, we consider several configurations for the channel error detection codes, in particular CRC codes. The preferred set of formats employs variable-block length, variable-rate outer codes matched to the individual audio packets, with one or more codewords used per audio packet. To maintain a constant bit rate into the channel, PAC and CRC encoding must be performed jointly, e.g., by incorporating the CRC into the bit allocation loop in the audio coder.     

A new high rate code scheme with highly parallel and low complexity decoding algorithm

A new high rate code scheme is proposed in this paper. It consists of serial concatenated recursive systematic ordinary (nonpunctured) convolutional codes with only 8 states in the trellis of the corresponding reciprocal dual codes. With a low complexity and highly parallel decoding algorithm, over additive white Gaussian noise channels, the proposed codes can achieve good bit error rate (BER) performance comparable to that of turbo codes and low density parity check (LDPC) codes. At code rate R=16/17, the overall decoding complexity of the proposed code scheme is almost half that of the LDPC codes.     

Turbo-SPC codes

This letter is concerned with a family of modified turbo-type codes, referred to as turbo-SPC (single parity check) codes. A technique based on the SPC code is introduced to replace puncturing for rate adjustment. A noticeable feature of the proposed scheme is the significantly reduced decoding complexity compared with the standard punctured turbo code. The cost reduction factor becomes more noticeable as rate increases (over ten times for rate →1). The error-rate floor problem known to turbo codes can also be improved using the proposed scheme. For moderate to high rates, performances of about 0.5 dB from the theoretical limits at BER=10^-5 have been observed for turbo-SPC codes     

On the Performance and Implementation Issues of Interleaved Single Parity Check Turbo Product Codes

In this paper, both performance and complexity aspects of two-dimensional single parity check turbo product codes (I-SPC-TPC) are investigated. Based on the proposed I-SPC-TPC coding scheme, a parallel decoding structure is developed to increase the decoding throughput with minor performance degradation compared with the serial structure. For both decoding architectures, a new helical interleaver is constructed to further improve the coding gain. In terms of decoding algorithm, the extremely simple Sign-Min decoding is alternatively derived with only three additions needed to compute each bit's extrinsic information. For performance evaluation, (16, 14, 2)² single parity check turbo product code with code rate 0.766 over AWGN channel using QPSK modulation is considered. The simulation results using Sign-Min decoding show that it can achieve bit-error-rate of 10^?5 at signal-to-noise ratio of 3.8 dB with 8 iterations. Compared to the same rate and codeword length turbo product code composed of extended Hamming codes, the considered scheme can achieve similar performance with much less complexity. Important implementation issues such as the finite precision analysis, efficient sorting circuit design and interleaver memory management are also presented.     

APPLICATION OF TURBO CODES IN HIGH-SPEED REAL-TIME CHANNEL

I. Introduction Turbo code has obtained comprehensive atten-tion and research due to its near-Shannon perform-ance since it was proposed in 1993[1], and has be-come a research hotspot in information and coding theory area. Application and realization methods of turbo codes in various communication systems have also attracted great interest of researchers. The good BER performance of turbo codes provides it a wide application prospect in deep space and mobile com- munication systems. The IT…     

删余型Turbo码分量编码器盲识别算法

摘 要:无法获得完整的递归系统卷积码(Recursive System Code,RSC)码字,传统的盲识别方法就不适用于删余型Turbo码的识别。于是该算法在识别序列的构造上进行了改进,针对Turbo码在删余位上的码字与对应的RSC码有所区别的情况,将该位上的码字视为“0”和“1”等概率出现的误码,从而对删余位进行归零处理并选取合适的截取序列进行匹配度计算,根据最后匹配度的总分布情况对删余型Turbo码分量编码器的参数进行识别。仿真结果表明针对码长为256,码率为1/2的删余型Turbo码,在最大误比特率不超过0.033的情况下正确识别率能保持在80%以上。      

Fast turbo codes with space‐time block codes in fast fading channels

In this paper, space‐time block coding has been used in conjunction with Turbo codes to provide good diversity and coding gains. A new method of dividing turbo encoder and decoder into several parallel encoding and decoding blocks is considered. These blocks work simultaneously and yield a faster coding scheme in comparison to classical Turbo codes. The system concatenates fast Turbo coding as an outer code with Alamouti's G2 space‐time block coding scheme as an inner code, achieving benefits associated with both techniques including acceptable diversity and coding gain as well as short coding delay. In this paper, fast fading Rayleigh and Rician channels are considered for discussion. For Rayleigh fading channels, a fixed frame size and channel memory length of 5000 and 10, respectively, the coding gain is 7.5 dB and bit error rate (BER) of 10^?4 is achieved at 7 dB. For the same frame size and channel memory length, Rician fading channel yields the same BER at about 4.5 dB. Copyright © 2013 John Wiley & Sons, Ltd.     

LT码和q-LDPC码级联方案在深空通信中的应用

该文针对深空通信对长纠删码的需求,提出了LT (Luby Transform)码和q-LDPC码的级联方案。在综合考虑性能和复杂度的情况下,选取8-LDPC码和8PSK的级联作为等效的删除信道,长度选择灵活、编译码简单的LT码实现纠删功能。文中设计了两种短8-LDPC码,并对整个级联系统的纠错性能进行了仿真。仿真结果表明8-LDPC码的性能优于信源信息速率和码率相同的二进制LDPC码,级联系统在等效包删除概率不超过0.1时,系统误比特率以概率1趋于0。     

Turbo-coded optical direct-detection CDMA system with PPMmodulation

The performance of an optical code division multiple access (CDMA) system with turbo coding is analyzed and simulated. Turbo codes are parallel concatenated convolutional codes (PCCCs) in which the information bits are first encoded by a recursive systematic convolutional code, and then, after passing through an interleaver, are encoded by a second systematic convolutional encoder. Turbo coding is superimposed on an intensity-modulated optical channel with pulse-position modulation (PPM) and direct detection of the received optical signal, and the performance is evaluated in terms of an upper bound on bit error probability. From the simulation results, it is seen that turbo coding offers considerable coding gain over other methods, with reasonable encoding/decoding complexity. Also, it is demonstrated that, for a fixed code rate, the performance of the optical CDMA system can be substantially improved by increasing the interleaver length and the number of iterations. Serially concatenated convolutional codes (SCCCs) are also considered, and are shown to perform comparably to PCCC in general and better than PCCCs for the case of large signal photocounts. The results in this paper can be applied, for example, to indoor optical wireless LANs     

Sequential Decoding of Convolutional Codes for Rayleigh Fading Channels

The performance of sequential decoding of long constraint length convolutional codes is evaluated for Rayleigh fading channels. Sequential decoding is not practical below a certain theoretical signal-to-noise ratio, and these theoretical limits are calculated for a number of modulation methods and code rates. As an example, with BPSK modulation, soft decisions and code rate 1/2, the theoretical signal-to-noise ratio per information bit is 5.7 dB. Above this limit the bit error rate can be made arbitrarily small by increasing the constraint length at no significant complexity cost. Furthermore, it is shown that with carefully chosen quantization steps, 8 level uniform quantization gives a negligible loss also for sequential decoding on a Rayleigh fading channel. Simulation results using 8 level quantization correspond well with the theoretical performance bounds. Also, the performance on a correlated channel with finite interleaving has been obtained. With an interleaver depth of 50×50 and a normalized doppler frequency equal to 0.01 we are only 0.5 dB away from the performance with perfect interleaving. Finally, bit error rate results show this scheme to compete well with Turbo codes.     

A Bandwidth Efficient Turbo Coding Scheme for VDSL Systems

The current forward error correction (FEC) scheme for very high bit-rate digital subscriber line (VDSL) systems in the ANSI standard employs a 16-state four-dimensional (4D) Wei code as the inner code and the Reed-Solomon (RS) code as the outer code. The major drawback of this scheme is that further improvement cannot be achieved without a substantial increase in the complexity and power penalty. Also, a VDSL system employing the 4D Wei-RS scheme operates far below the channel capacity. In 1993, powerful turbo codes were introduced whose performance closely approaches the Shannon limit. In this paper, we propose a bandwidth and power efficient turbo coding scheme for VDSL modems in order to obtain high data rates, extended loop reach and increased transmission robustness. We also propose a pipelined decoding scheme to reduce the latency at the receiver end. The objective of the proposed scheme is to provide a higher coding gain than that given by the 4D Wei-RS scheme, resulting in an improved performance of the VDSL modems in terms of bit rate, loop length and transmitting power. The scheme is investigated for various values of transmitting power, signaling frequencies and numbers of crosstalkers for a targeted bit error rate of 10⁻⁵ and is implemented in a system with a quadrature amplitude modulation in which a mixed set partitioning mapping is employed to reduce the decoding complexity. The effects of code complexity, interleaver length, the number of decoding iterations and the level of modulation on the performance of VDSL modems are explored. Simulation results are presented and compared to those of the 4D Wei-RS scheme. The results show that the choice of turbo codes not only provides a significant coding gain over the standard FEC scheme but also efficiently maximizes the loop length and bit rate at a very low transmitting power in the presence of dominant far-end crosstalk and intersymbol interference. In order to compare the hardware complexity, we synthesize the proposed and 4D Wei-RS schemes using SYNOPSYS with the target technology of Xilinx 4020e-3. The Xilinx field programmable gate array statistics of the proposed scheme is compared with that of the 4D Wei-RS scheme.     

一种基于增强奇偶校验码级联极化码的新型编译码方法

极化码作为一种纠错码,具有较好的编译码性能,已成为5G短码控制信道的标准编码方案。但在码长较短时,其性能不够优异。提出一种基于增强奇偶校验码级联极化码的新型编译码方法,在原有的奇偶校验位后设立增强校验位,对校验方程中信道可靠度较低的信息位进行双重校验,辅助奇偶校验码在译码过程中对路径进行修剪,以此提高路径选择的可靠性。仿真结果表明,在相同信道、相同码率码长下,本文提出的新型编译码方法比循环冗余校验(cyclic redundancy check,CRC)码级联极化码、奇偶校验(parity check,PC)码级联极化码误码性能更优异。在高斯信道下,当码长为128、码率为1/2、误码率为10-3时,本文提出的基于增强PC码级联的极化码比PC码级联的极化码获得了约0.3 dB增益,与CRC辅助的极化码相比获得了约0.4 dB增益。     

Multilevel turbo coding with short interleavers

The impact of the interleaver, embedded in the encoder for a parallel concatenated code, called the turbo code, is studied. The known turbo codes consist of long random interleavers, whose purpose is to reduce the value of the error coefficients. It is shown that an increased minimum Hamming distance can be obtained by using a structured interleaver. For low bit-error rates (BERs), we show that the performance of turbo codes with a structured interleaver is better than that obtained with a random interleaver. Another important advantage of the structured interleaver is the short length required, which yields a short decoding delay and reduced decoding complexity (in terms of memory). We also consider the use of turbo codes as component codes in multilevel codes. Powerful coding structures that consist of two component codes are suggested. Computer simulations are performed in order to evaluate the reduction in coding gain due to suboptimal iterative decoding. From the results of these simulations we deduce that the degradation in the performance (due to suboptimal decoding) is very small     

Simplification of Packet-Symbol Decoding With Errors, Deletions, Misordering of Packets, and No Sequence Numbers

In this paper, a new method is described which builds on Mitzenmacher's idea of adding a different pseudorandom number to each packet to help decode packet-symbol low-density codes, with deletions, errors, and out-of-order reception, without sequence numbers. The new method has lower decoding complexity than the original method. The most basic form of the new method applies to any parity-check code structure, but is limited to a rather small number of packets in the code. Decoding success is slightly inferior to an ideal erasure channel, which would require sequence numbering and error detection in each packet. Error detection is needed only for the whole code, amounting to usually less than one bit per packet symbol. Moreover, if error detection can resolve one of a small number of alternatives, the ordered case performs almost as well as the ideal erasure channel. Ways are shown to modify the basic algorithm for use with long codes, possibly approaching the erasure channel capacity limit.