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。     

一种新的两用户协作分集方案及其性能研究

该文提出了一种基于信道编码和分布式空时分组码级联下的两用户协作分集方案,并且在准静态的瑞利衰落信道下对此方案的系统容量,中断概率以及误比特率进行了理论推导和系统仿真,分别给出了解析表达式和数值结果。通过将信道编码和空时码引入到协作分集中,系统容量得到显著改善,同时中断概率也明显降低。在协作用户间信道存在噪声的情况下,对卷积码与分布式空时分组码级联下的发射方案进行了性能分析和仿真。仿真结果表明:即使协作用户间的信道存在噪声,该文所提方案在各方面都优于传统协作分集,系统容量明显增大,中断概率及误比特率大大降低。     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.     

Unequal error protection for MPEG-2 video transmission over wireless channels

This paper proposes an unequal error protection (UEP) method for MPEG-2 video transmission. Since the source and channel coders are normally concatenated, if the channel is noisy, more bits are allocated to channel coding and fewer to source coding. The situation is reversed when the channel conditions are more benign. Most of the joint source channel coding (JSCC) methods assume that the video source is subband coded, the bit error sensitivity of the source code can be modeled, and the bit allocations for different subband channels will be calculated. The UEP applied to different subbands is the rate compatible punctured convolution channel coder. However, the MPEG-2 coding is not a subband coding, the bit error sensitivity function for the coded video can no longer be applied. Here, we develop a different method to find the rate-distortion functions for JSCC of the MPEG-2 video. In the experiments, we show that the end-to-end distortion of our UEP method is smaller than the equal error protection method for the same total bit-rate.     

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.     

Progressive transmission of images over memoryless noisy channels

An embedded source code allows the decoder to reconstruct the source progressively from the prefixes of a single bit stream. It is desirable to design joint source-channel coding schemes which retain the capability of progressive reconstruction in the presence of channel noise or packet loss. Here, we address the problem of joint source-channel coding of images for progressive transmission over memoryless bit error or packet erasure channels. We develop a framework for encoding based on embedded source codes and embedded error correcting and error detecting channel codes. For a target transmission rate, we provide solutions and an algorithm for the design of optimal unequal error/erasure protection. Three performance measures are considered: the average distortion, the average peak signal-to-noise ratio, and the average useful source coding rate. Under the assumption of rate compatibility of the underlying channel codes, we provide necessary conditions for progressive transmission of joint source-channel codes. We also show that the unequal error/erasure protection policies that maximize the average useful source coding rate allow progressive transmission with optimal unequal protection at a number of intermediate rates     

A vector set partitioning noisy channel image coder with unequalerror protection

A vector enhancement of Said and Pearlman's set partitioning in hierarchical trees (SPIHT) methodology, named VSPIHT, has been proposed for embedded wavelet image compression. A major advantage of vector-based embedded coding with fixed length VQs over scalar embedded coding is its superior robustness to noise. We show that vector set partitioning can effectively alter the balance of bits in the bit steam so that significantly fewer critical bits carrying significant information are transmitted, thereby improving inherent noise resilience. For low noise channels, the critical bits are protected, while the degradation in reconstruction quality caused by errors in noncritical quantization information, can be reduced by appropriate VQ indexing, or designing channel optimized VQs for the successive refinement systems. For very noisy channels, unequal error protection to the critical and noncritical bits with either block codes or convolution codes are used. Additionally, the error protection for the critical bits is changed from pass to pass. A buffering mechanism is used to produce an unequally protected bit stream without sacrificing the embedding property. Extensive simulation results are presented for noisy channels, including bursty channels     

Multistage recursive interleaver for turbo codes in DS-CDMA mobileradio

A multistage recursive block interleaver (MIL) is proposed for the turbo code internal interleaver. Unlike conventional block interleavers, the MIL repeats permutations of rows and columns in a recursive manner until reaching the final interleaving length. The bit error rate (BER) and frame error rate (FER) performance with turbo coding and MIL under frequency-selective Rayleigh fading are evaluated by computer simulation for direct-sequence code-division multiple-access mobile radio. The performance of rate-1/3 turbo codes with MIL is compared with pseudorandom and S-random interleavers assuming a spreading chip rate of 4.096 Mcps and an information bit rate of 32 kbps. When the interleaving length is 3068 bits, turbo coding with MIL outperforms the pseudorandom interleaver by 0.4 dB at an average BER of 10^-6 on a fading channel using the ITU-R defined Vehicular-B power-delay profile with the maximum Doppler frequency of f_D = 80 Hz. The results also show that turbo coding with MIL provides superior performance to convolutional and Reed-Solomon concatenated coding; the gain over concatenated coding is as much as 0.6 dB     

Modulation-assisted unequal error protection over the fadingchannel

Unequal error protection (UEP) is essential when different portions of the source data do not contribute evenly to the overall duality of the decoded information. Conventional techniques achieve UEP by independent coding of the bit streams or by adopting conventional unequal error-protection codes. In this paper, we propose a practical alternative to the QPSK-based transmission systems with explicit UEP, such as GSM or IS-54 wireless transmission standards. In this scheme, the task of providing unequal protection is divided between the channel encoder and a nonuniform signal set, which discriminates in favor of the more important bits. The new approach allows for a simpler convolutional encoder and, hence, a less complex decoding procedure. Specifically, a reduction by more than half in the number of encoder states can easily be achieved using our scheme. Countering the degradation of the less important bits, we propose to adopt a high-rate punctured convolutional code to minimize the incurred transmission rate penalty. We also discuss a pilot sequence transmission scheme which realizes a coherent reception. Decentralizing the bit protection culminates in an extra degree of freedom which, in turn, introduces more flexibility into the system design     

级联纠错编码DS/BPSK系统性能分析与仿真

为了研究级联编码对DS/BPSK系统性能的影响,设计了一种基于RS与卷积码级联编码的DS/BPSK系统,分析了该级联编码直扩系统的性能,仿真了在纠错编码参数发生改变时的系统性能。仿真结果表明,级联编码的DS/BPSK系统性能比单码编码的DS/BPSK系统性能要好。在RS码参数保持不变时,降低卷积码的码率,采用软判决方式译码以及多比特软判决,能有效提升系统性能;同时,交织在一定程度上能改善系统的性能。     

The Design of a High-Performance Error-Correcting Coding Scheme for the Canadian Broadcast Telidon System Based on Reed-Solomon Codes

Error correction can greatly improve the performance and extend the range of broadcast teletext systems. In this paper, the requirements for an error-correcting scheme for broadcast teletext in North America (NABTS) are set down. An error-correction scheme which meets all these requirements is then described. The simplest case employs the one parity bit in each 8 bit byte and no suffix of parity check bits at the end of each data block. The next level also uses a single byte of parity check bits at the end of each data block. Adding a second byte of parity checks at the end of each data block results in a Reed-Solomon code, called theCcode, for each data block. Adding one data block of parity checks afterh - 1data blocks results in a set ofhdata packets being encoded into a bundle, in which verticalCcodes provide powerful interleaving. In a final alternative, two data blocks hold the check bytes for the vertical codewords, and the most powerful coding scheme, the double bundle code, results. The detailed mathematical definitions of the various codes are referred to or described, formulas for performance calculations are referred to, and performance curves are presented for the AWGN channel as well as for measured field data. These performance curves are discussed and compared to the performance of a difference set cyclic code, originally designed for the Japanese teletext system, which corrects any 8 bits in error in a packet.     

Sliding window criterion codes and concatenation scheme formitigating timing-jitter-induced errors in WDM fiber transmissions

We propose a concatenated coding scheme, which effectively reduces bit errors induced by soliton-soliton collisions (SSC) in wavelength division multiplexing (WDM) soliton transmission systems. A block line coding scheme, the sliding window criterion (SWC) code, is developed based on the nature of SSC-induced timing jitter in soliton communications. We show, by simplified collision model simulations, that the SWC code alone can decrease the SSC-induced timing jitter and, by concatenation to a Reed-Solomon (RS) code, improve both the bit rate and the channel spacing capacity in WDM systems. We compare the performance of our scheme both analytically and by simulations with those of various RS codes and concatenated RS-convolutional code used in optical fiber transmission systems, and show that high redundancy (overhead) does not always give better code performance. Finally, by using full simulations, we show that the SWC code is an effective and promising technique for dispersion-managed fiber WDM systems     

Training overhead for decoding random linear network codes in wireless networks

We consider multicast communications from a single source to multiple destinations through a wireless network with unreliable links. Random linear network coding achieves the min-cut flow capacity; however, additional overhead is needed for end-to-end error protection and to communicate the network coding matrix to each destination. We present a joint coding and training scheme in which training bits are appended to each source packet, and the channel code is applied across both the training and data. This scheme allows each destination to decode jointly the network coding matrix along with the data without knowledge of the network topology. It also balances the reliability of communicating the network coding matrices with the reliability of data detection. The throughput for this scheme, accounting for overhead, is characterized as a function of the packet size, channel properties (error and erasure statistics), number of independent messages, and field size. We also compare the performance with that obtained by individual channel coding of training and data. Numerical results are presented for a grid network that illustrate the reduction in throughput due to overhead.     

Recent Results on the Use of Concatenated Reed-Solomon/Viterbi Channel Coding and Data Compression for Space Communications

The development of sophisticated adaptive source coding algorithms together with inherent error sensitivity problems fostered the need for efficient space communication at very low bit error probilbilities(leq 10^{-6}). This led to the specification and implementation of a concatenated coding system using an interleaved Reed-Solomon code as the outer code and a Viterbi-decoded convolutionai code as the inner code. This paper presents the experimental results of this channel coding system under an emulatedS-band uplink andX-band downlink two-way space communication channel, where both uplink and downlink have strong carrier power. Test results verify that at a bit error probability of 10^-6or less, this concatenated coding system does provide a coding gain of 2.5 dB or more over the viterbi-decoded convolutional-only coding system. These tests also show that a desirable interleaving depth for the Reed-Solomon outer code is 8 or more. The imptict of this "virtually" error-free space communication link on the transmission of images is discussed and examples of Simulation results are given.     

无线光通信中的空时编码研究进展(四)

级联编码是一种提高系统纠错能力以逼近香农限的高效编码方式。当信道编码与空时编码结合使用时性能会大大提升,因此级联空时码研究成为空时编码研究的重要方向之一。笔者介绍了RS 码、LDPC 码与空时码的级联方案,以及在不同大气湍流条件下的误码率特性,并对其进行了仿真分析。结果表明:级联空时码可以极大地改善大气激光通信系统的性能,抑制大气湍流效应,有利于获得编码增益,进一步改善系统的误码性能。     

Performance of H.263 video transmission over wireless channelsusing hybrid ARQ

This paper proposes a hybrid ARQ error control scheme based on the concatenation of a Reed-Solomon (RS) code and a rate compatible punctured convolutional (RCPC) code for low-bit-rate video transmission over wireless channels. The concatenated hybrid ARQ scheme we propose combines the advantages of both type-I and type-II hybrid ARQ schemes. Certain error correction capability is provided in each (re)transmitted packet, and the information can be recovered from each transmission or retransmission alone if the errors are within the error correction capability (similar to type-I hybrid ARQ). The retransmitted packet contains redundancy bits which, when combined with the previous transmission, result in a more powerful RS/convolutional concatenated code to recover information if error correction fails for the individual transmissions (similar to type-II hybrid ARQ). Bit-error rate (BER) or signal-to-noise ratio (SNR) of a radio channel changes over time due to mobile movement and fading. The channel quality at any instant depends on the previous channel conditions. For the accurate analysis of the performance of the hybrid ARQ scheme, we use a multistate Markov chain (MSMC) to model the radio channel at the data packet level. We propose a method to partition the range of the received SNR into a set of states for constructing the model so that the difference between the error rate of the real radio channel and that of the MSMC model is minimized. Based on the model, we analyze the performance of the concatenated hybrid ARQ scheme. The results give valuable insight into the effects of the error protection capability in each packet, the mobile speed, and the number of retransmissions. Finally, the transmission of H.263 coded video over a wireless channel with error protection provided by the concatenated hybrid ARQ scheme is studied by means of simulations     

Unveiling turbo codes: some results on parallel concatenated codingschemes

A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes, have been previously shown to yield remarkable coding gains close to theoretical limits. They have been named, and are known as, “turbo codes”. We propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length. The analytical bounding technique is then used to shed some light on some crucial questions, which have been floating around in the communications community since the proposal of turbo codes     

Fast algorithm for rate-based optimal error protection of embedded codes

Embedded image codes are very sensitive to channel noise because a single bit error can lead to an irreversible loss of synchronization between the encoder and the decoder. P.G. Sherwood and K. Zeger (see IEEE Signal Processing Lett., vol.4, p.191-8, 1997) introduced a powerful system that protects an embedded wavelet image code with a concatenation of a cyclic redundancy check coder for error detection and a rate-compatible punctured convolutional coder for error correction. For such systems, V. Chande and N. Farvardin (see IEEE J. Select. Areas Commun., vol.18, p.850-60, 2000) proposed an unequal error protection strategy that maximizes the expected number of correctly received source bits subject to a target transmission rate. Noting that an optimal strategy protects successive source blocks with the same channel code, we give an algorithm that accelerates the computation of the optimal strategy of Chande and Farvardin by finding an explicit formula for the number of occurrences of the same channel code. Experimental results with two competitive channel coders and a binary symmetric channel showed that the speed-up factor over the approach of Chande and Farvardin ranged from 2.82 to 44.76 for transmission rates between 0.25 and 2 bits per pixel.     

Near-optimal, single-synchronization-error-correcting code

A synchronization error is said to occur when either a bit which does not belong is detected in a channel between bits which were transmitted, or a bit which was transmitted is never detected at the output. A block code which corrects a single synchronization error per block is presented, and it is shown that this code has, at most, three bits more redundancy than that of an optimal code for this class of errors. The code has the beneficial property that it is possible to separate the information positions from the check positions, and an appropriate method of encoding is shown.     

A novel bit mapping scheme for high-order polar coded modulation systems

In order to improve the spectrum efficiency of the high-order polar coded modulation systems, the polar code is used as the component code of the bit-interleave coded modulation (BICM) system, a novel bit mapping scheme is proposed considering of the channel polarization and successive cancellation (SC) decoding principle of polar codes as well as the unequal protection of equivalent channels by modulator. In this scheme, the frozen bits on the unreliable split channel are allocated to the equivalent channel with the low protection of the modulator, while the equivalent channels with the high protection are used to transmit the information bits. Thus, the error-correcting performance of polar codes is improved. Compared with some bit mapping schemes, the proposed bit mapping scheme only needs to divide and choose the parameters of the split channels reliability measurement, the complexity does not increase obviously, and simulation results show that the proposed scheme has the better performance under the quadrature amplitude modulation (QAM) modulation based on the Gray mapping.