Showing papers on "List decoding published in 1981"

Error-Correction Coding for Digital Communications

Abstract: 1. Fundamental Concepts of Coding.- 2. Group Codes.- 3. Simple Nonalgebraic Decoding Techniques for Group Codes.- 4. Soft Decision Decoding of Block Codes.- 5. Algebraic Techniques for Multiple Error Correction.- 6. Convolutional Code Structure and Viterbi Decoding.- 7. Other Convolutional Decoding Techniques.- 8. System Applications.- Appendix A. Code Generators for BCH Codes.- Appendix B. Code Generators for Convolutional Codes.- B.1. Viterbi Decoding.- B.2. Table Look-up Decoding.- B.3. Threshold Decoding.- B.4. Sequential Decoding.- References.

Linear unequal error protection codes

Abstract: The properties of linear codes over GF (q) that provide unequal error protection (UEP) of information digits are discussed. A design is proposed for optimal binary systematic linear UEP codes. Broad classes of iterative and concatenated UEP codes are constructed. Majority decoding algorithms for linear iterative UEP codes are described.

A dynamic programming algorithm for simultaneous phase estimation and data decoding on random-phase channels

Abstract: The problem of simultaneously estimating phase and decoding data symbols from baseband data is posed. The phase sequence is assumed to be a random sequence on the circle, and the symbols are assumed to be equally likely symbols transmitted over a perfectly equalized channel. A dynamic programming algorithm (Viterbi algorithm) is derived for decoding a maximum {\em a posteriori} (MAP) phase-symbol sequence on a finite dimensional phase-symbol trellis. A new and interesting principle of Optimality for simultaneously estimating phase and decoding phase-amplitude coded symbols leads to an efficient two-step decoding procedure for decoding phase-symbol sequences. Simulation results for binary, 8 -ary phase shift keyed (PSK), and 16-quadrature amplitude shift keyed (QASK) symbol sets transmitted over random walk and sinusoidal jitter channels are presented and compared with results one may obtain with a decision-directed algorithm or with the binary Viterbi algorithm introduced by Ungerboeck. When phase fluctuations are severe and when occasional large phase fluctuations exist, MAP phase-symbol sequence decoding on circles is superior to Ungerboeck's technique, which in turn is superior to decision-directed techniques.

An Efficient Algorithm for Soft-Decision Decoding of the (24, 12) Extended Golay Code

Abstract: An efficient algorithm for soft-decision decoding of the (24, 12) extended Golay code is described. Results obtained for white Gaussian noise are presented which show that performance is only a few tenths of a decibel away from that of an ideal correlator.

Multistage decoding of frequency-hopped fsk system

Abstract: A recent paper described an unproved decoding scheme for a frequency-hopped multilevel FSK system. We examined this multiple access communication system for possible application in satellite communication and mobile radio telephony. The new decoder, using the known algebraic structure of the users' addresses, reduces mutual interference and achieves a 50 to 60 percent increase in efficiency over conventional decoding. The present paper shows how additional decoding can further increase the efficiency, bringing it very close (within half a percent) to optimum. The scheme makes use of information derived while decoding the messages of other users and thus is especially attractive for the base station, where such information is readily available and does not require a significant increase in complexify. Compared to conventional decoding, the new scheme more than doubles the number of simultaneous users.

N-user trellis coding for a class of multiple-access channels (Corresp.)

Abstract: Trellis coding is investigated for a class of N -user multiple-access channels It is shown that N -user trellis coding, in conjunction with Viterbi or sequential decoding, permits the multiple-access function to be combined with forward error correction The distance and rate properties are analyzed for linear (convolutional) N -user trellis codes, and the use of nonlinear N -user trellis coding is discussed A procedure is given for constructing N -user convolutional-code N -tuples with large free distance Finally the error performance is analyzed, and coding gains of several decibels over uncoded time sharing are verified by simulation results

High-speed decoding of BCH codes (Corresp.)

Abstract: A general algorithm is derived for the calculation of the error location polynomial in decoding a Bose-Chaudhuri-Hocquenguem (BCH) code. A shorter decoding time is required by the algorithm for low-weight errors because only a subset of the syndrome equations are to be satisfied. The application of the general algorithm to Berlekamp's algorithm is also presented.

Soft Decision Decoding of Block Codes

Abstract: The use of soft decisions with block codes provides the engineer with another degree of freedom when designing a communication system. The additional information provided by the soft decisions in most instances can provide about 2 dB of additional coding gain and can, therefore, significantly increase the usefulness of a particular code. Soft decision decoding is particularly effective when used with moderate length block codes and provides substantial performance benefits over a broad range of signal-to-noise ratios. It is also effective in concatenation schemes (see Chapter 8) which utilize two or more levels of encoding and decoding. In this case the use of soft decisions is restricted to the innermost coder/decoder, and it is necessary for the soft decision decoding method to provide near optimum performance at word error rates in the range of 10−2 to 10−3. This is in contrast to the usual system requirement that the decoding scheme be effective at error rates less than 10−5.

Soft-decision minimum-distance sequential decoding algorithm for convolutional codes

Abstract: The maximum-likelihood decoding of convolutional codes has generally been considered impractical for other than relatively short constraint length codes, because of the exponential growth in complexity with increasing constraint length. The soft-decision minimum-distance decoding algorithm proposed in the paper approaches the performance of a maximum-likelihood decoder, and uses a sequential decoding approach to avoid an exponential growth in complexity. The algorithm also utilises the distance and structural properties of convolutional codes to considerably reduce the amount of searching needed to find the minimum soft-decision distance paths when a back-up search is required. This is done in two main ways. First, a small set of paths called permissible paths are utilised to search the whole of the subtree for the better path, instead of using all the paths within a given subtree. Secondly, the decoder identifies which subset of permissible paths should be utilised in a given search and which may be ignored. In this way many unnecessary path searches are completely eliminated. Because the decoding effort required by the algorithm is low, and the decoding processes are simple, the algorithm opens the possibility of building high-speed long constraint length convolutional decoders whose performance approaches that of the optimum maximum-likelihood decoder. The paper describes the algorithm and its theoretical basis, and gives examples of its operation. Also, results obtained from practical implementations of the algorithm using a high-speed microcomputer are presented.

Decoding of triple and quadruple error‐correcting BCH codes by direct solving of error‐locator polynomials

Abstract: The error-correcting codes have been used extensively to increase the reliability of digital systems in data communication. However, with increasing error-correcting capability, the complexity of decoders also increases. At present, only one-bit and two-bit error-correcting codes are used. This paper proposes a decoding algorithm for triple and quadruple error-correcting BCH codes. In decoding the BCH codes, the error-locator polynomials must be solved by Chien's algorithm. In his method, however, with increasing code length, the decoder becomes complicated and the efficiency deteriorates. In the method proposed in this paper, the fourth-or lower-order equations are reduced to the quadratic equation and, therefore, the efficiency is good. This method is also independent of the code length. Its function and efficiency are confirmed by simulation using microcomputer. The present decoding algorithm enables one to realize an efficient decoder with hardware construction using the ROM.

Error control using sequential decoding with repeat request (Ph.D. Thesis abstr.)

Abstract: Contributions to the problem of efficient spectrum utilization in mobil radio communication systems are presented. A new frequency channel assignment algorithm is proposed and studied by computer simulations for applications to mobile telephone systems and combined mobil telephone and dispatch systems. Spectrum efficient modulation techniques, namely duobinary coded minimum shift keying (MSK) and TFM, are studied for the application of data transmission via mobile radio. The performance of coherent and noncoherent detections is studied under the mobile radio environments. The probability of error is calculated for both discriminator detection and differential detection. The steady-state phase error probability of a digital phase-locked loop with a phase step input is calculated under the assumption of fast fading mobile radio environments.

A decoding failure test for the transform decoder of Reed-Solomon code

Abstract: Using a finite field transform, a transform decoding algorithm is able to correct erasures as well as errors of any (n,k,d) Reed-Solomon code over the finite field GF(q). A pitfall of transform decoding and how to avoid it are discussed. A simple test is given so that the decoder fails to decode instead of introducing additional errors, whenever the received word contains too many errors and erasures.

Heuristic decoding of convolutional codes.

Abstract: The decoding of convolutional codes is presented as a path-searching in corresponding \"code graph\". Applying some heuristic search techniques new decoding algorithms were obtained, which have improved the decoding process significantly.