Reliability and Throughput Analysis of a Concatenated Coding Scheme

In this paper, the performance of a concatenated coding scheme for error control in ARQ systems is analyzed for both randomerror and burst-error channels. In particular, the probability of undetected error and the system throughput are calculated. In this scheme, the inner code is used for both error correction and error detection, and the outer code is used for error detection only. Interleaving/deinterleaving of the outer code is assumed. A retransmission is requested if either the inner code or the outer code detects the Presence of errors. Various coding examples are considered. The results show that concatenated coding can provide extremely high system reliability (i.e., low probability of undetected error) and high system throughput.     

DSD (double soft decision) concatenated FEC scheme in mobilesatellite communication systems

In order to realize a higher-code-gain forward error correction scheme in mobile satellite communication systems, a novel concatenated coding scheme employing soft decision decoding for not only inner codes but also outer codes (double soft decision, or DSD, concatenated forward error correction scheme) is proposed. Soft-decision outer decoding can improve the bit error probability of inner decoded data. In this scheme, likelihood information from an inner Viterbi decoder is used in the decoding of outer codes. A technique using the path memory circuit status 1.0 ratio for likelihood information is proposed, and is shown to be the most reliable even though it requires the simplest hardware among the alternative methods. A computer simulation clarifies that the DSD scheme improves Pe performance to one-third of that of the conventional hard-decision outer decoding. Moreover, to reduce the interleaving delay time in fading channels or inner decoded data of concatenated codes, a parallel forward error correction scheme is proposed     

An integrated error correction and detection system for digitalaudio broadcasting

Hybrid in-band on-channel digital audio broadcasting systems deliver digital audio signals in such a way that is backward compatible with existing analog FM transmission. We present a channel error correction and detection system that is well-suited for use with audio source coders, such as the so-called perceptual audio coder (PAC), that have error concealment/mitigation capabilities. Such error mitigation is quite beneficial for high quality audio signals. The proposed system involves an outer cyclic redundancy check (CRC) code that is concatenated with an inner convolutional code. The outer CRC code is used for error detection, providing flags to trigger the error mitigation routines of the audio decoder. The inner convolutional code consists of so-called complementary punctured-pair convolutional codes, which are specifically tailored to combat the unique adjacent channel interference characteristics of the FM band. We introduce a novel decoding method based on the so-called list Viterbi algorithm (LVA). This LVA-based decoding method, which may be viewed as a type of joint or integrated error correction and detection, exploits the concatenated structure of the channel code to provide enhanced decoding performance relative to decoding methods based on the conventional Viterbi algorithm (VA). We also present results of informal listening tests and other simulations on the Gaussian channel. These results include the preferred length of the outer CRC code for 96-kb/s audio coding and demonstrate that LVA-based decoding can significantly reduce the error flag rate relative to conventional VA-based decoding, resulting in dramatically improved decoded audio quality. Finally, we propose a number of methods for screening undetected errors in the audio domain     

A New Error Control Scheme for Hybrid ARQ Systems

This paper introduces the concept of a generalized hybrid ARQ (GH-ARQ) scheme for adaptive error control in digital communication systems. This technique utilizes the redundant information available upon successive retransmissions in an efficient manner so as to provide high throughput during poor channel conditions. A new class of linear codes is proposed for the GH-ARQ system application. The main feature of this class of codes is that the encoder/decoder configuration does not change as the length of the code is varied. As a result, the receiver uses the same decoder for decoding the received information after every retransmission while the error correcting capability of the code increases, thereby leading to an improved performance and minimum complexity for the overall system implementation.     

Channel Modeling and Signal Processing for Probe Storage Channels

Probe-storage devices employ large arrays of probes to write/read data in parallel in some storage medium, and combine ultra-high density, low access times, and low power consumption. A particular probe-storage technique utilizes thermomechanical means to store and retrieve information in thin polymer films. In this paper, a system-level channel model for the thermomechanical probe-storage channel is presented. Each of the components of the proposed model is derived by extensive characterization of experimentally obtained readback signals from probe recording tests. Moreover, detection techniques that are actually utilized in a probe-storage prototype implementation are described, followed by coding techniques for added reliability in the presence of particles or other impurities of the storage medium. In addition to low-complexity coding constructs, a concatenated coding scheme with an outer LDPC and inner modulation code is considered, in order to establish a benchmark for overall system performance. A novel methodology for joint decoding of outer LDPC and inner (d,k) modulation codes is developed. Furthermore, an optimal soft decoder for the modulation code is proposed, based on a modification of the decoder metrics to accurately account for the probe storage channel output statistics. Experimental results are used throughout the paper to validate the channel model and identify its relevant parameters, as well as to verify the system performance obtained by simulations.     

Coupled Decoding of Block-Convolutional Concatenated Codes

Straightforward implementation of a maximum likelihood decoder implies a complexity that grows algebraically with the inverse of error probability. Forney has suggested an approach, concatenation, for which error probability decreases exponentially with increasing complexity. This paper presents the results of an evaluation of a particular concatenation system, structurally similar to the hybrid system of Falconer, employing a Reed-Solomon outer code and an inner convolutional code. The inner decoder is a Viterbi decoder of constraint length less than the corresponding encoding constraint length (nonmaximum likelihood). The outer decoder assumes one of three possible forms, all employing the likelihood information developed by the inner decoder to assist in outer decoding. Error corrections and erasure fill-ins achieved by the outer decoder are fed back to the inner decoder. Performance is evaluated through computer simulation. The three outer decoders are found to provide approximately the same performance, all yielding low error probabilities at rates somewhat above Rcompof sequential decoding and at signal energy to noise density ratios per information bit around 1.7 dB.     

基于SSCANL译码器的联合迭代检测译码算法

为了提升基于极化码的稀疏码多址接入（sparse code multiple access,SCMA）系统接收机性能,提出了基于简化软消除列表（simplify soft cancellation list,SSCANL）译码器的循环冗余校验（cyclic redundancy check,CRC）辅助联合迭代检测译码接收机方案。该方案中极化码译码器使用SSCANL译码算法,采用译码节点删除技术对软消除列表（soft cancellation list,SCANL）算法所需要的L次软消除译码（soft cancellation, SCAN）进行简化,通过近似删除冻结位节点,简化节点间软信息更新计算过程,从而降低译码算法的计算复杂度。仿真结果表明,SSCANL算法可获得与SCANL算法一致的性能,其计算复杂度与SCANL算法相比有所降低,码率越低,算法复杂度降低效果越好;且基于SSCANL译码器的CRC 辅助联合迭代检测译码接收机方案相较基于SCAN译码器的联合迭代检测译码（joint iterative detection and decoding based on SCAN decoder, JIDD-SCAN）方案、基于SCAN译码器的CRC辅助联合迭代检测译码（CRC aided joint iterative detection and decoding based on SCAN decoder,C-JIDD-SCAN）方案,在误码率为10^-4时,性能分别提升了约0.65 dB、0.59 dB。     

Improving concatenated coding communications by employing signal editing techniques

Signal editing (SE) is a technique used to locate and erase unreliable data before error correction decoding. Consider a concatenated coding (CC) communication system in which the inner code employs convolutional encoding with Viterbi decoding (CEVD) and the outer code could employ either a convolutional or a Reed-Solomon code. In this study, we show that useful information can be derived from the inner Viterbi decoding process to perform two special operations: (i) to locate and erase unreliable decoded data and (ii) to estimate the input channel noise level. As a result, the number of errors input to the outer decoder is reduced and the overall CC system performance is improved.     

High rate concatenated coding systems using bandwidth efficienttrellis inner codes

High-rate concatenated coding systems with bandwidth-efficient trellis inner codes and Reed-Solomon (RS) outer codes are investigated for application in high-speed satellite communication systems. Two concatenated coding schemes are proposed. In one the inner code is decoded with soft-decision Viterbi decoding, and the outer RS code performs error-correction-only decoding (decoding without side information). In the other the inner code is decoded with a modified Viterbi algorithm, which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, whereas branch metrics are used to provide reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. The two schemes have been proposed for high-speed data communication on NASA satellite channels. The rates considered are at least double those used in current NASA systems, and the results indicate that high system reliability can still be achieved     

An error control system with multiple-stage forward errorcorrections

A robust error control coding system is presented. This system is a cascaded FEC (forward error control) scheme supported by parity retransmissions for further error correction in the erroneous data words. The error performance and throughput efficiency of the system are analyzed. Two specific examples of the error control system are studied. The first example does not use an inner code, and the outer code, which is not interleaved, is a shortened code of the NASA standard RS code over GF(2⁸). The second example, as proposed for NASA uses the same shortened RS code as the base outer code C₂, except that it is interleaved to a depth of 2. It is shown that both examples provide high reliability and throughput efficiency even for high channel bit-error rates in the range of 10^-2     

On a Reduced‐Complexity Inner Decoder for the Davey‐MacKay Construction

The Davey‐MacKay construction is a promising concatenated coding scheme involving an outer 2^k‐ary code and an inner code of rate k/n, for insertion‐deletion‐substitution channels. Recently, a lookup table (LUT)‐based inner decoder for this coding scheme was proposed to reduce the computational complexity of the inner decoder, albeit at the expense of a slight degradation in word error rate (WER) performance. In this letter, we show that negligible deterioration in WER performance can be achieved with an LUT as small as 7·2^k+n–1, but no smaller, when the probability of receiving less than n–1 or greater than n+1 bits corresponding to one outer code symbol is at least an order of magnitude smaller than the WER when no LUT is used.     

Correction of extrinsic information for iterative decoding in a serially concatenated multiuser DS-CDMA system

The system under study is a coded asynchronous DS-CDMA system with orthogonal modulation in time-varying Rayleigh fading multipath channels. Information bits are convolutionally encoded, block interleaved, and mapped to M-ary orthogonal Walsh codes, where the last step is essentially a process of block coding. This paper aims at tackling the problem of joint iterative decoding of this serially concatenated inner block code and outer convolutional code and estimating frequency-selective fading channels in multiuser environments. The (logarithm) maximum a posteriori probability, (Log)-MAP criterion is used to derive the iterative decoding schemes. In our system, the soft output from inner block decoder is used as a priori information for the outer decoder. The soft output from outer convolutional decoder is used for two purposes. First, it may be fed back to the inner decoder as extrinsic information for the systematic bits of the Walsh codeword. Secondly, it is utilized for channel estimation and multiuser detection (MUD). We also show that the inner decoding can be accomplished without extrinsic information, and in some cases, e.g., when the system is heavily loaded, yields better performance than the decoding with unprocessed extrinsic information. This implies the need for correcting the extrinsic information obtained from outer decoder. Different schemes are examined and compared numerically, and it is shown that iterative decoding with properly corrected extrinsic information or with non-extrinsic/extrinsic adaptation enables the system to operate reliably in the presence of severe multiuser interference, especially when the inner decoding is assisted by decision directed channel estimation and interference cancellation techniques.     

Selective serial concatenation of turbo codes

A serial concatenation scheme consisting of a Bose-Chaudhuri-Hocquenghem (BCH) outer code and a turbo inner code is proposed. We first establish that only a small number of bit positions at the turbo decoder output are likely to be in error at high signal-to-noise ratios. A double-error correcting BCH outer code is used to protect these particular error prone bits. Simulation results for an additive white Gaussian noise (AWGN) channel show that the bit-error rate (BER) floor of the turbo code can be lowered by using this serial concatenation scheme. The proposed technique offers higher throughput efficiency and lower complexity than other serial concatenation schemes     

Turbo encoding and decoding of Reed-Solomon codes through binary decomposition and self-concatenation

This paper presents a two-stage turbo-coding scheme for Reed-Solomon (RS) codes through binary decomposition and self-concatenation. In this scheme, the binary image of an RS code over GF(2/sup m/) is first decomposed into a set of binary component codes with relatively small trellis complexities. Then the RS code is formatted as a self-concatenated code with itself as the outer code and the binary component codes as the inner codes in a turbo-coding arrangement. In decoding, the inner codes are decoded with turbo decoding and the outer code is decoded with either an algebraic decoding algorithm or a reliability-based decoding algorithm. The outer and inner decoders interact during each decoding iteration. For RS codes of lengths up to 255, the proposed two-stage coding scheme is practically implementable and provides a significant coding gain over conventional algebraic and reliability-based decoding algorithms.     

Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes

A list decoder generates a list of more than one codeword candidates, and decoding is erroneous if the transmitted codeword is not included in the list. This decoding strategy can be implemented in a system that employs an inner error correcting code and an outer error detecting code that is used to choose the correct codeword from the list. Probability of codeword error analysis for a linear block code with list decoding is typically based on the "worst case" lower bound on the effective weights of codewords for list decoding evaluated from the weight enumerating function of the code. In this paper, the concepts of generalized pairwise error event and effective weight enumerating function are proposed for evaluation of the probability of codeword error of linear block codes with list decoding. Geometrical analysis shows that the effective Euclidean distances are not necessarily as low as those predicted by the lower bound. An approach to evaluate the effective weight enumerating function of a particular code with list decoding is proposed. The effective Euclidean distances for decisions in each pairwise error event are evaluated taking into consideration the actual Hamming distance relationships between codewords, which relaxes the pessimistic assumptions upon which the traditional lower bound analysis is based. Using the effective weight enumerating function, a more accurate approximation is achieved for the probability of codeword error of the code with list decoding. The proposed approach is applied to codes of practical interest, including terminated convolutional codes and turbo codes with the parallel concatenation structure     

Concatenated Coding Systems Employing a Unit-Memory Convolutional Code and a Byte-Oriented Decoding Algorithm

Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively modest coding complexity, it is proposed to concatenate a byte-oriented unit-memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real-time minimal-byte-error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.     

Erasure decoding in burst-error channels

Burst-error channels have been used to model a large class of modern communication media, and the problem of communicating reliably through such media has received much study [1]-[9]. Existing techniques include two-way communication schemes that involve error detection and retransmission, and schemes that utilize error correcting codes in code interleaving. The error-detection and retransmission scheme is simple, but its applicability has been restricted to limited environments. On the other hand, the concept of code interleaving has proved to be versatile and effective. Code interleaving distributes the error detection and correction burden among the component codes and thus lowers the overall redundancy requirement. However, the memory characteristics of the burst-error channel have not been used. This omission has prompted the investigation presented in this paper to utilize the inherent information embedded in the code interleaving scheme when used with burst-error channels. The concept of erasure decoding is introduced, leading to some useful coding and decoding strategies. Theoretical formulations are devised to predict code performance, and their validity is verified with computer simulations.     

纠正随机错误与长突发删除的多进制乘积码研究

考虑多进制LDPC码的符号特性，以及对其残留错误和删除的分析，本文采用多进制LDPC码作为内码，相同Galois域下的高码率RS码作为外码来构造多进制乘积码；并提出了一种低复杂度的迭代译码方案，减少信息传输的各类错误。在译码时，只对前一次迭代中译码失败的码字执行译码，并对译码正确码字所对应的比特初始概率信息进行修正，增强下一次迭代多进制LDPC译码符号先验信息的准确性，减少内码译码后的判决错误，从而充分利用外码的纠错能力。仿真结果显示，多进制乘积码相较于二进制LDPC乘积码有较大的编码增益，并通过迭代进一步改善了性能，高效纠正了信道中的随机错误和突发删除。对于包含2%突发删除的高斯信道，在误比特率为10-6时，迭代一次有0.4 dB左右的增益。      

A sequential soft-decision decoder for Reed-Solomon codes appliedto encoded PSK in Rayleigh-fading channels

A soft-decision stack algorithm with a variable-bias-term branch metric and accurate channel state information estimate is applied to a Reed-Solomon-encoded phase-shift keying (PSK) system in the presence of memoryless Rayleigh fading. To compensate for the variable decoding delay inherent in sequential decoding algorithms, a time-out mechanism is used by the inner decoder: if a time-out occurs before complete decoding of a given block, the decoder declares an erasure. An erasures-and-errors correction decoding algorithm is implemented at the outer decoder to recover any incorrect or incompletely decoded inner code words. Simulation results show that significant improvement over uncoded modulation can be achieved with this approach with moderate cost in decoding complexity     

纠正同步错误的反转级联水印码的迭代译码

为提高插入删节信道下反转级联水印码（Reverse Concatenated Watermark Code）的译码性能,本文设计了一种反转级联水印码的硬判决迭代译码方案。该方案在反转级联水印码内译码器中引入外译码器输出的硬判决估计序列,交织后的硬判决序列和水印序列的异或作为内译码器的更新后的参考序列,从而减小了码字序列对水印码的影响,改善了水印译码器的参考信息。前后向估计方法利用该参考序列和更新后的有效替代错误概率计算输出概率,进一步用于计算前向度量值和后向度量值,提高了内译码器输出的每个比特的似然信息的可靠度,改善了整体性能。仿真结果表明,当反转级联水印码方案采用硬判决迭代译码算法时,整体性能得到有效提高。