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     

Low complexity concatenated coding schemes for digital satellite communications

A study of reduced complexity concatenated coding schemes, for commercial digital satellite systems with low-cost earth terminals, is reported. The study explored trade-offs between coding gain, overall rate and decoder complexity, and compared concatenated schemes with single codes. It concentrated on short block and constraint length inner codes, with soft decision decoding, concatenated with a range of Reed-Solomon outer codes. The dimension of the inner code was matched to the outer code symbol size, and appropriate interleaving between the inner and outer codes was used. Very useful coding gains were achieved with relatively high-rate, low-complexity schemes. For example, concatenating the soft decision decoded (9,8) single parity check inner code with the CCSDS recommended standard Reed-Solomon outer code gives a coding gain of 4.8dB at a bit error probability of 10^?5, with an overall rate of 0-78.     

A New Concatenated Coding SystemUsing Multilevel Inner Codes

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On bit-error probability of a concatenated coding scheme

This paper presents a method for evaluating the bit-error probability of a concatenated coding system for BPSK transmission over the AWGN channel. In the concatenated system, a linear binary block code is used as the inner code and is decoded with the soft-decision maximum likelihood decoding, and a maximum distance separable code (or its interleaved code) is used as the outer code and is decoded with a bounded distance decoding. The method is illustrated through a specific example in which the inner code is a binary (64.40.8) Reed-Muller subcode and the outer code is the NASA standard (255, 223, 33) Reed-Solomon code over GF(2⁸) interleaved to a depth of 5. This specific concatenated system is being considered for NASA's high-speed satellite communications. The bit-error performance is evaluated by a combination of simulation and analysis. The split weight enumerators for the maximum distance separable codes are derived and used for the analysis     

A concatenated coded modulation scheme for error control

A concatenated coded modulation scheme is presented for error control in data communications. The scheme is achieved by concatenating a Reed-Solomon outer code and a bandwidth efficient block inner code for M-ary phase-shift keying (PSK) modulation. Error performance of the scheme is analyzed for an additive white Gaussian noise (AWGN) channel. It is shown that extremely high reliability can be attained by using a simple M-ary PSK modulation inner-code and a relatively powerful Reed-Solomon outer code. Furthermore, if an inner code of high effective rate is used, the bandwidth expansion required by the scheme due to coding will be greatly reduced. The scheme is particularly effective for high-speed satellite communications for large file transfer where high reliability is required. A simple method is also presented for constructing block codes for M-ary PSK modulation. Soome short M-ary PSK codes with good minimum squared Euclidean distance are constructed. These codes have trellis structure and hence can be decoded with a soft-decision Viterbi decoding algorithm. Furthermore, some of these codes are phase invariant under multiples of 45° rotation     

On the probability of symbol error in Viterbi decoders

An upper bound is derived on the probability that at least one of a sequence of B consecutive bits at the output of a Viterbi (1979) decoder is in error. Such a bound is useful for the analysis of concatenated coding schemes employing an outer block code over GF(2^B) (typically a Reed-Solomon (RS) code), an inner convolutional code, and a symbol (GF(2^B)) interleaver separating the two codes. The bound demonstrates that in such coding schemes a symbol interleaver is preferable to a bit interleaver. It also suggests a new criterion for good inner convolutional codes     

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.     

A convolutional single-parity-check concatenated coding scheme forhigh-data-rate applications

The coding scheme uses a set of n convolutional codes multiplexed into an inner code and a (n,n-1) single-parity-check code serving as the outer code. Each of the inner convolutional codes is decoded independently, with maximum-likelihood decoding being achieved using n parallel implementations of the Viterbi algorithm. The Viterbi decoding is followed by additional outer soft-decision single-parity-check decoding. Considering n=12 and the set of short constraint length K=3, rate 1/2 convolutional codes, it is shown that the performance of the concatenated scheme is comparable to the performance of the constraint length K=7, rate 1/2 convolutional code with standard soft-decision Viterbi decoding. Simulation results are presented for the K=3, rate 1/2 as well as for the punctured K=3, rate 2/3 and rate 3/4 inner convolutional codes. The performance of the proposed concatenated scheme using a set of K=7, rate 1/2 inner convolutional codes is given     

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.     

Hybrid ARQ schemes employing coded modulation and sequencecombining

In this paper, we propose and analyze two hybrid automatic-repeat-request (ARQ) schemes employing bandwidth efficient coded modulation and coded sequence combining. In the first scheme, a trellis-coded modulation (TCM) is used to control channel noise; while in the second scheme a concatenated coded modulation is employed. The concatenated coded modulation is formed by cascading a Reed-Solomon (RS) outer code and a block coded modulation (BCM) inner code. In both schemes, the coded modulation decoder, by performing sequence combining and soft-decision maximum likelihood decoding, makes full use of the information available in all received sequences corresponding to a given information message. It is shown, by means of analysis as well as computer simulations, that both schemes are capable of providing high throughput efficiencies over a wide range of signal-to-noise ratios. The schemes are suitable for large file transfers over satellite communication links where high throughput and high reliability are required     

迭代译码的级联Reed-Solomon乘积码与卷积码

该文提出用Reed Solomon(RS)乘积码作为外码,卷积码作为内码的级联码方案并且内外码间用Congruential向量生成的交织图案对RS码符号进行重排列。对此级联码采用的迭代译码基于成员码的软译码算法。当迭代次数达到最大后,通过计算RS码的校正子,提出一种纠正残余错误的方法,进一步提高了系统的误比特性能。仿真结果表明,在AWGN信道中与迭代译码的级联RS/卷积码相比,当误比特率为1e-5时,新系统的编码增益大约有0.4 dB。     

Design and analysis of concatenated coded DS/CDMA systems inasynchronous channels

We propose and analyze concatenated coding schemes for direct-sequence code-division multiple-access (DS/CDMA) systems in asynchronous channels. In the concatenated coding, bandwidth-efficient 2 ^2L-2-state L/(L+1)-rate 2-MTCM with biorthogonal signal constellation is used for the inner code, and (2^L-1,[(2^L -1)/L/2]) RS code is used for the outer code. It is shown that we can get considerable performance gain over the uncoded system without sacrificing the data transmission rate. The proposed system can be used as a coding scheme for reliable and high-speed integrated information services of mobile communication systems     

List and soft symbol output Viterbi algorithms: extensions andcomparisons

The Viterbi algorithm (VA) is the maximum likelihood decoding algorithm for convolutionally encoded data. Improvements in the performance of a concatenated coding system that uses VA decoding (inner decoder) can be obtained when, in addition to the standard VA output, an indicator of the reliability of the VA decision is delivered to the outer stage of processing. Two different approaches of extending the VA are considered. In the first approach, the VA is extended with a soft output (SOVA) unit that calculates reliability values for each of the decoded output information symbols. In the second approach, coding gains are obtained by delivering a list of the L best estimates of the transmitted data sequence, namely the list Viterbi decoding algorithm (LVA). Our main interest is to evaluate the LVA and the SOVA in comparison with each other, determine suitable applications for both algorithms and to construct extended versions of the LVA and the SOVA with low complexity that perform the task of the other algorithm. We define a list output VA using the output symbol reliability information of the SOVA to generate a list of size L and that also has a lower complexity than the regular LVA for a long list size. We evaluate the list-SOVA in comparison to the LVA. Further, we introduce a low complexity soft symbol output viterbi algorithm that accepts the (short) list output of the LVA and calculates for each of the decoded information bits a reliability value. The complexity and the performance of the soft-LVA (LVA and soft decoding unit) is a function of the list size L. The performance of the soft-LVA and the SOVA are compared in a concatenated coding system. A new software implementation of the iterative serial version of the LVA is also included     

Channel coding for satellite mobile channels

The deployment of channel coding and interleaving to enhance the bit-error performance of a satellite mobile radio channel is addressed for speech and data transmissions. Different convolutional codes (CC) using Viterbi decoding with soft decision are examined with inter-block interleaving. Reed-Solomon (RS) codes with Berlekamp-Massey hard decision decoding or soft decision trellis decoding combined with block interleaving are also investigated. A concatenated arrangement employing RS and CC coding as the outer and inner coders, respectively, is used for transmissions via minimum shift keying (MSK) over Gaussian and Rayleigh fading channels. For an interblock interleaving period of 2880 bits, a concatenated arrangement of an RS(48,36). over the Galois field GF(256) and punctured PCC(3,1,7) yielding an overall coding rate of 1/2, provides a coding gain of 42dB for a BER of 10^?6, and an uncorrectable error detection probability of 1–10^?9.     

SOVA算法对Viterbi算法的修正

在Viterbi算法中引入软值进行修正之后的算法称作SOVA算法(Soft Output Viterbi Algorithm)。SOVA算法在Viterbi算法的基础上,路径量度引入了比特先验信息,对每位译码比特以后验概率似然比的形式提供软输出,因而可提供更高的译码性能。特别,SOVA算法可用于级联码的迭代译码,采用Tuobo原理使不同分量码之间交换软信息,从而可显著提高这类码的纠错能力。     

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     

Improved decoding for a concatenated coding system recommended byCCSDS

The concatenated coding system recommended by CCSDS (Consultative Committee for Space Data Systems) uses an outer (255,233) Reed-Solomon (RS) code based on 8-b symbols, followed by the block interleaver and an inner rate 1/2 convolutional code with memory 6. Viterbi decoding is assumed. Two new decoding procedures based on repeated decoding trials and exchange of information between the two decoders and the deinterleaver are proposed. In the first one, where the improvement is 0.3-0.4 dB, only the RS decoder performs repeated trials. In the second one, where the improvement is 0.5-0.6 dB, both decoders perform repeated decoding trials and decoding information is exchanged between them     

Forced sequence sequential decoding: a concatenated coding systemwith iterated sequential inner decoding

We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low as E_b/N₀=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported by simulation results that are also extended to other parameters     

BER performance of turbo-coded PPM CDMA systems on optical fiber

We obtain upper bounds on the bit error rate (BER) for turbo-coded optical code-division multiple-access (CDMA) systems using pulse position modulation (PPM). We use transfer function bounding techniques to obtain these bounds, so our results correspond to the average bound over all interleavers of a given length. We consider parallel concatenated coding (PCC) schemes that use recursive convolutional codes as constituent codes. We consider systems using an avalanche photodiode (APD), and treat APD noise, thermal noise, and multi-user interference using a Gaussian approximation. We compare the performance of turbo-coded systems with that of BCH-coded systems with soft-decision decoding, and that of concatenated coding systems with outer Reed-Solomon (RS) code and inner convolutional code. We show that turbo-coded systems have better performance than BCH-coded systems. We also show that concatenated systems have better performance than turbo-coded systems when the block length is small and the received laser power is somewhat large     

High rate concatenated coding systems using multidimensionalbandwidth-efficient trellis inner codes

A concatenated coding system using two-dimensional trellis-coded MPSK inner codes and Reed-Solomon outer codes for application in high-speed satellite communication systems was proposed previously by the authors (ibid., vol.37, no.5, p.420-7, May 1989). The authors extend their results to systems using symbol-oriented, multidimensional, trellis-coded MPSK inner codes. The concatenated coding systems are divided into two classes according to their achievable effective information rates. The first class uses multidimensional trellis-coded 8-PSK inner codes and achieves effective information rates around 1 b/dimension (spectral efficiency 2 b/s/Hz). The second class employs multidimensional trellis-coded 16-PSK inner codes and provides effective information rates around 1.5 b/dimension (spectral efficiency 3 b/s/Hz). Both classes provide significant coding gains over an uncoded reference system with the same effective information rate as the coded system. The results show that the symbol-oriented nature of multidimensional inner codes can provide an improvement of up to 1 dB in the overall performance of a concatenated coding system when these codes replace bit-oriented two-dimensional codes