Showing papers on "Sequential decoding published in 1974"

Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)

Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.

Convolutional codes II. Maximum-likelihood decoding

Abstract: Convolutional codes are characterized by a trellis structure. Maximum-likelihood decoding is characterized as the finding of the shortest path through the code trellis, an efficient solution for which is the Viterbi algorithm. A universal asymptotic bounding technique is developed and used to bound error probability, free distance, list-of-2 error probability, and other subsidiary quantities. The bounds are dominated by what happens at a certain critical length N erit . Termination of a convolutional code to length N erit or shorter results in an optimum block code. In general, block code exponents can be related to convolutional code exponents and vice versa by a graphical construction, called the concatenation construction. It is shown that termination is unnecessary with the Viterbi algorithm.

Free distance bounds for convolutional codes

Abstract: The best asymptotic bounds presently known on free distance for convolutional codes are presented from a unified point of view. Upper and lower bounds for both time-varying and fixed codes are obtained. A comparison is made between bounds for nonsystematic and systematic codes which shows that more free distance is available with nonsystematic codes. This result is important when selecting codes for use with sequential or maximum-likelihood (Viterbi) decoding since the probability of decoding error is closely related to the free distance of the code. An ancillary result, used in proving the lower bound on free distance for time-varying nonsystematic codes, furnishes a generalization of two earlier bounds on the definite decoding minimum distance of convolutional codes.

A decoding algorithm for binary block codes and J -ary output channels (Corresp.)

Abstract: A search algorithm is described to decode long binary block codes of any rate for the memoryless binary input J -ary output channel. It can be used directly to perform maximum-likelihood decoding or in a constrained version that gives considerably fewer searches at a small sacrifice in performance. Simulation results are given for a rate-l/2 code of length 128 and minimum Hamming distance 22 on the quantized Gaussian channel.

Uniform decoding of minimum-redundancy codes

Abstract: A high-speed decoding system and method for decoding minimumredundancy Huffman codes, which features translation using stored tables rather than a tracing through tree structures. When speed is of utmost importance only a single table access is required; when required storage is to be minimized, one or two accesses are required.

Convolutional codes III. Sequential decoding

Abstract: Sequential decoding is characterized as a sequential search for the shortest path through a trellis. An easily analyzed algorithm closely related to the stack and Fano algorithms is described. Martingale techniques are used to find the distribution of computation on totally symmetric channels. For general channels, our universal bounding technique yields the well-known Pareto distribution of computation, as well as a bound on error probability that is asymptotically optimum in the high-rate range. The performance-complexity relation is shown to be asymptotically Pareto for both sequential and maximum-likelihood (Viterbi) decoding, with the same exponent in either case. A semisequential list-of-L Viterbi algorithm is introduced to extend the analogies below Rcomp.

Practical applications of coding

Abstract: Coding applications have grown rapidly in the past several years with cost-effective performance demonstrated on several channels. Convolutional coding with soft-decision Viterbi decoding has emerged as a standard technique and is particularly well adapted to the commnnication satellite channel. Decoder implementations are discussed and examples are cited. Robustness of code performance is emphasized and instances of actual coding gain surpassing theoretical or basic coding gain are given. Some promising future directions are noted.

Real-Time Minimal-Bit-Error Probability Decoding of Convolutional Codes

Abstract: A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Δ branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A "real-time," i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.

A Tightened Upper Bound on the Error Probability of Binary Convolutional Codes with Viterbi Decoding

Abstract: Tighter upper bounds on the error event and the bit error probabilities, respectively, for maximum-likelihood decoding of binary convolutional codes on the binary symmetric channel are derived from upper bounds previously published by Viterbi [1]. The measured bit error rate P_b for a constraint length 3 decoder has been plotted versus the channel transition probability p and shows close agreement with the improved bound on the bit error probability.

Syndrome decoding of convolutional codes

Abstract: The classical Viterbi decoder recursively finds the trellis path (code word) closest to the received data. Given the received data, the syndrome decoder first forms a syndrome, instead. A recursive algorithm like Viterbi's is used to determine the noise sequence of minimum Hamming weight that can be a possible cause of this syndrome. Given the estimate of the noise sequence, one derives an estimate of the original data sequence. While the bit error probability of the syndrome decoder is no different from that of the classical Viterbi decoder, the syndrome decoder can be implemented using a read only memory (ROM), thus obtaining a considerable saving in hardware.

The optimum mean-square estimate for decoding binary block codes

Abstract: By the use of abstract Fourier analysis on groups, the optimum mean-square-error decoding rule is developed for a fixed block code. The optimum one-to-one coding role to be used with this optimum decoder is derived, and a procedure for simultaneous optimization over both encoding and decoding rules is given. It is shown that there is a linear encoding rule which is optimum. A system which implements the optimum decoding rule is outlined. The major difference between this work and others involving coding for mean-square error is that the decoding rule developed here is a mapping from binary n -tuples directly into the real numbers with the optimization being over all possible mappings into the real numbers. As such the system developed here replaces both the error-correction and digital-to-analog conversion components used in most numerical data transmission systems.

Upper bounds on sequential decoding performance parameters

Abstract: This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t -order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary Upper bounds on the Pareto exponent are also presented The G -values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths The G -optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel

A note on the observation of a Markov source through a noisy channel (Corresp.)

Abstract: A signal is sent by a two-state Markov source through a noisy channel. The objective is to develop a decoding scheme to obtain a reconstruction of the original signal. Necessary and sufficient conditions are presented, in both a sequential and a nonsequential context, for the optimality of several decoding schemes, including the singlet decoding rule and the data-independent decoding rule. A generalization of the simple noise process given by Drake [1] is presented, and analogous results are derived.

The bit error probability as a function path register length in the Viterbi decoder

Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Decoding beyond the BCH bound using multiple sets of syndrome sequences (Corresp.)

Abstract: Many cyclic codes are generated by polynomials possessing more than one set of consecutive roots. Thus more than one set of syndrome sequences are available for decoding. In this correspondence, a decoding method based on Berlekamp's iterative algorithm is presented which makes use of the multiple sets of syndrome sequences for decoding such cyclic codes beyond the BCH bound.

Further results on the Viterbi algorithm equalizer (Corresp.)

Abstract: A receiver structure recently proposed for the detection of pulse-amplitude modulation (PAM) signals is considered. The receiver is designed to reduce the complexity of the Viterbi decoder by equalizing the channel to an optimum desired short memory channel. Expressions for the optimum prefilter and short memory model are given. It is also shown that the minimum mean-square error achievable is a monotonic decreasing function of the model memory length. Numerical results for a specific channel are presented verifying this. A numerical investigation of the effect of shifting the reference tap is also included.

A Viterbi decoder

Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Sequential syntactical decoding

Abstract: It has been proposed that syntactical information be used as an aid in error detection, location, and correction. In the present paper the minimum distance syntactical decoding algorithm of Souza and Scholtz is improved with the use of sequential decoding techniques. Fano's algorithm is adapted to the syntactical case; simulation results show the drastic reduction in number of backtrackings afforded by the new algorithm. Comments are made on the results obtained, their implications, and topics for future research.

Error Correction for Voice Grade Data Communication Using a Communication Processor

Abstract: A general purpose communication processor is investigated as a vehicle for decoding two specific classes of cyclic codes having properties appropriate for voice grade data communication channels. First, a model of a processor is described, and then it is used in conjunction with two cost metrics to measure the complexity of programming the decoding functions. No special Galois field (GF) arithmetic instructions are used. For decoding both Bose-Chadhuri-Hocquenghem (BCH) and Fire codes, a method which allows the encoding program to be used in the initial steps of decoding is given and evaluated. The evaluation indicates that both encoding and decoding, for voice grade data communication facilities, can be done in contemporary communication processors with core storage in the 1000 word range and instruction cycles in the microsecond range. In addition, the results show how the cost metrics vary with parameters such as the block length, the number of errors or the burst length correctable, and the block error probability introduced by the channel. Other conclusions, such as the areas in which significant improvements are needed and in which hardware assist can improve performance are drawn from data giving the relative costs of the elements of the decoding process.

Convolutional code performance in fading channels

Abstract: The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail Short constraint length codes are considered in conjunction with binary phase-shift-keyed (BPSK) modulation and Viterbi maximum likelihood decoding while for longer constraint length codes we consider sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms For short constraint length codes we are primarily interested in the bit error probability performance parameterized by the fading channel parameters For longer constraint length codes interest will center on the effect of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms In either case the effects of simple block interleaving in combatting the memory of the channel is thoroughly explored The approach is analytic where possible otherwise resort is made to digital computer simulation

Convolutional codes. II - Maximum-likelihood decoding. III - Sequential decoding

Abstract: Maximum-likelihood decoding is characterized as the determination of the shortest path through a topological structure called a trellis. Aspects of code structure are discussed along with questions regarding maximum-likelihood decoding on memoryless channels. A general bounding technique is introduced. The technique is used to obtain asymptotic bounds on the probability of error for maximum-likelihood decoding and list-of-2 decoding. The basic features of sequential algorithms are discussed along with a stack algorithm, questions of computational distribution, and the martingale approach to computational bounds.

Buffer Management for Sequential Decoding

Abstract: Sequential decoding has been found to be an efficient means of communicating at low undetected error rates from deep space probes, but another failure mechanism known as erasure or computational overflow remains a significant problem. The erasure of a block occurs when the decoder has not finished decoding that block at the time that it must be output. The erasure rate can be unacceptably high even when the decoder is spending over half of its time idly awaiting incoming data. By drawing upon analogies in computer time sharing, this concise paper develops a buffer-management strategy which reduces the decoder idle time to a negligible level, and therefore improves the erasure probability of a sequential decoder. For a decoder with a speed advantage of ten and a buffer size of ten blocks, operating at an erasure rate of 10-2, use of this buffer-management strategy reduces the erasure rate to less than 10-4.

Multiple-path stack algorithms for decoding convolutional codes

Abstract: Structure of convolutional codes -- Decoding of convolutional codes -- Multiple path stack decoding algorithm -- Adaptive sequential decoding -- Conclusions and suggestions for further research.

Communications Research in Sweden

Abstract: Communications research in Sweden covers the following subjects: digital PAM, equalization of data channels, digital line links, modulation and transmission analysis, signal measurements and detection, time variable and nonlinear filters, group codes, source approximation, sequential decoding, and shift register sequences.

Comments on "Real-Time Minimal-Bit-Error Probability ' Decoding of Convolutional Codes

Abstract: The real-time minimal-bit-error probability (RTMBEP) decoding procedure recently presented by Lee is compared with the sequential compound decoding procedure originally described by Abend and Fritchman for the detection of symbols in the presence of intersymbol interference. We compare the number of computations and the amount of storage required for each algorithm as well as show how Lee's procedure can be made more efficient.

Performance of convolutional codes on fading channels typical of planetary entry missions

Abstract: The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail. The signal fading is due primarily to turbulent atmospheric scattering of the RF signal transmitted from an entry probe through a planetary atmosphere. Short constraint length convolutional codes are considered in conjunction with binary phase-shift keyed modulation and Viterbi maximum likelihood decoding, and for longer constraint length codes sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms are considered. Careful consideration is given to the modeling of the channel in terms of a few meaningful parameters which can be correlated closely with theoretical propagation studies. For short constraint length codes the bit error probability performance was investigated as a function of E sub b/N sub o parameterized by the fading channel parameters. For longer constraint length codes the effect was examined of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms. The effects of simple block interleaving in combatting the memory of the channel is explored, using the analytic approach or digital computer simulation.

An Error-Control System Based on Majority-Logic Decoding

Abstract: : The report describes the implementation of an error-control system based on majority logic decoding. Two new decoding concepts are used in the design and construction of the unit. The first, which applies only to the finite geometry codes, reduces the number of levels required to decode. The second, which applies (at least in principle) to any majority logic decodable code, reduces the number of gates required at each level. As evidenced by the decoder configuration, a significant reduction in complexity is obtained by a combination of these concepts. (Author)

A comparison of rate 1/n convolutional codes over a simulated noisy channel using the Viterbi decoding algorithm.

Abstract: The application of error detection and correction codes has advanced markedly with the advent of digital technology. However, the strides made towards employing the techniques, encoding and decoding, properly have been rather limited by the Naval forces in the United States. This paper develops a computer program, which if utilized properly, would aid in deciding what error correcting scheme is best suited for a specific channel. The results obtained from testing a rate 1/n convolutional code, over a simulated channel, using a Viterbi decoder shows that this is an effective analysis procedure. Though the test runs were lengthy, much of the time required was for noise simulation. This would not be a factor if actual channel noise recordings had been available.