Showing papers on "List 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.

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.

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.

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.

Multilevel data transmission system

Abstract: An improved multilevel code transmission system for transmission of a data signal in the form of an N-level code signal based on a partial response shaping employs a special differential coding prior to partial response shaping on the transmitter side and, on the receiver side subsequent to partial response decoding, a differential decoding corresponding to the differential coding. The system is characterized in that each pair of input, parallel binary codes is so arranged that only the most significant bit is different from each other and the remaining bits are represented by the same binary codes, and in that only the most significant bit is affected by the differential coding and decoding.

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.

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.

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 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.

A lower bound on the probability of decoding error for the finite-state channel (Corresp.)

Abstract: A new lower bound on the probability of decoding error for transmission at high rates over a finite-state channel is obtained. It is a dual to the random coding bound of Yudkin and is a generalization of the Arimoto converse to the coding theorem for discrete memoryless channels. It also implies the strong converse to the coding theorem for indecomposable channels.

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.

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)