scispace - formally typeset
Search or ask a question

Showing papers on "List decoding published in 1987"


Journal ArticleDOI
TL;DR: A generalized VA (GVA) is proposed that makes comparisons on the basis of a label of length L(L\leq K) that decoding theorems for a discrete memoryless channel are proved for GVA decoding and shown to be natural generalizations of those for VA decoding.
Abstract: The Viterbi algorithm (VA), an optimum decoding rule for a Q -ary trellis code of constraint length K , operates by taking the best survivor from each of Q^{K-1} lists of candidates at each decoding step. A generalized VA (GVA) is proposed that makes comparisons on the basis of a label of length L(L\leq K) . It selects, incorporating the notion of list decoding, the S best survivors from each of Q^{L-1} lists of candidates at each decoding step. Coding theorems for a discrete memoryless channel are proved for GVA decoding and shown to be natural generalizations of those for VA decoding. An example of intersymbol interference removal is given to illustrate the practical benefits that the GVA can provide.

155 citations


Journal ArticleDOI
TL;DR: A number of coding techniques for future satellite communication are discussed, including Reed-Solomon error decoding for message blocks, probabilistic decoding techniques for punctured convolutional codes, and planar Euclidean geometry difference set codes for random multiple access applications.
Abstract: This paper discusses a number of coding techniques for future satellite communication; they include Reed-Solomon error decoding for message blocks, probabilistic decoding techniques for punctured convolutional codes, and planar Euclidean geometry difference set codes for random multiple access applications. The provision of code concatenation, helical interleaving, and simulation results of new punctured convolutional codes are included. A number of coded satellite systems that demonstrate the usefulness of coding in satellite communications are described.

89 citations


Journal ArticleDOI
H. Tanaka1
TL;DR: The tree structure is presented by a two-dimensional array which can be applied for the decoding of Huffman codes as a state transition table of the finite-state decoding automaton.
Abstract: The data structure of Huffman codes and its application to efficient encoding and decoding of Huffman codes are studied in detail. The tree structure is presented by a two-dimensional array which can be applied for the decoding of Huffman codes as a state transition table of the finite-state decoding automaton. Inversion produces a one-dimensional state transition table of the semiautonomous finite-state sequential machine which can be used as a Huffman encoder with a push-down stack. The encoding and decoding procedures are simple and efficient. It is not only possible to implement by simple hardware but is also applicable to software implementation.

37 citations


Journal ArticleDOI
TL;DR: This correspondence presents a special decoding technique for double-byte-error-correcting (DBEC), triple- byte- error-detecting (TBED) RS codes which is capable of high-speed operation.
Abstract: A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K bit DRAM's are organized in 32K × 8 bit-bytes. Byte-oriented codes such as Reed-Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. In this correspondence we present a special decoding technique for double-byte-error-correcting (DBEC), triple-byte-error-detecting (TBED) RS codes which is capable of high-speed operation. This technique is designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

21 citations


Journal ArticleDOI
TL;DR: For quadratic residue arrays (uniformly redundant arrays-URAs), this work has developed fast deconvolution algorithms based on conventional decoding methods but taking advantage of the mathematical properties of the decoding matrices.
Abstract: Coded mask aperture imaging techniques are now used in various fields, in particular in x-ray and gamma-ray astronomy. With such systems it is possible to construct apertures which have autocorrelation functions with perfectly flat sidelobes. For quadratic residue arrays (uniformly redundant arrays—URAs), we have developed fast deconvolution algorithms based on conventional decoding methods but taking advantage of the mathematical properties of the decoding matrices. Balanced decoding, delta decoding, and finely sampled decoding are discussed.

17 citations


Proceedings ArticleDOI
01 Oct 1987
TL;DR: An analysis of the Ideal-Selective-Repeat ARQ scheme shows that the use of code combining yields a significant throughput even at very high channel error rates, thus making it a very robust hybrid FEC/ARQ system.
Abstract: In this paper we consider sequential decoding with ARQ and code combining under the time-out condition That is whenever the decoding time of a given packet exceeds some predetermined duration, decoding is stopped and retransmission of the packet is requested However the unsuccessfull packets are not discarded, but are combined with their retransmitted copies We show that the use of code combining allows sequential decoding to operate efficiently even when the coding rate R exceeds the computational cut-off rate R como Furthermore, an analysis of the Ideal-Selective-Repeat ARQ scheme shows that the use of code combining yields a significant throughput even at very high channel error rates, thus making it a very robust hybrid FEC/ARQ system

14 citations


Journal ArticleDOI
TL;DR: This research shows how to optimize the choice of a generator matrix and decoding map simultaneously to minimize the error rates for all message symbols.
Abstract: Given any fixed linear block code, the error rates for the message symbols depend both on the encoding function and on the decoding map. This research shows how to optimize the choice of a generator matrix and decoding map simultaneously to minimize the error rates for all message symbols. The model used assumes that the distribution of messages is flat and that the distribution of error vectors defining the channel is independent of the message transmitted. In addition, it is shown that, with proper choice of coset leaders, standard array decoding is optimal in this circumstance. The results generalize previously known results on unequal error protection and are sufficiently general to apply when a code is used for error detection only.

13 citations


Journal ArticleDOI
TL;DR: A recursive soft decision maximum likelihood Hadamard transform decoding rule for binary code is derived, which achieves the computational efficiency of the Viterbi algorithm and simplifies the VLSI implementation of decoders.
Abstract: A recursive soft decision maximum likelihood Hadamard transform decoding rule for binary code is derived. This algorithm, with computational complexity that varies inversely with the code rate for a fixed code length, is efficiently applicable for decoding convolutional codes and high rate block codes. An even more significant reduction in decoder complexity is obtained when the algorithm is applied for decoding product codes and concatenated codes. This algorithm achieves the computational efficiency of the Viterbi algorithm. In addition, its structural regularity simplifies the VLSI implementation of decoders.

10 citations


Journal ArticleDOI
01 Oct 1987
TL;DR: An illustrative design of a (128, 112, 2) binary BCH decoder using the 16-bit 8086 microprocessor is presented and complexity, memory space and decoding time are discussed.
Abstract: A fast decoding algorithm for binary double error-correcting BCH codes is presented. A binary-decision approach to the Chien search is introduced to reduce the search time by a factor of two, and hence to increase the decoding speed. This algorithm is suitable for microprocessorbased implementation. An illustrative design of a (128, 112, 2) binary BCH decoder using the 16-bit 8086 microprocessor is presented. Complexity, memory space and decoding time are discussed.

10 citations


Book
07 Apr 1987
TL;DR: The concept of generalised hybrid automatic repeat request (GH-ARQ) for adaptive error control in digital communication systems is discussed, which utilises the redundant information available upon successive retransmissions in an efficient manner so as to provide high throughput during poor channel conditions.
Abstract: In this work, the correspondence between linear (n,k,d) codes and algorithms for computing a system of k bilinear forms over GF(p('m)) is explored. A number of properties are established for the linear codes that follow from a computational procedure of this type. A particular system of bilinear forms is considered and a class of linear codes is derived with varying k and d parameters. The codelength n is equal to the multiplicative complexity of the computation of an aperiodic convolution and an efficient computation thereof leads to the shortest codes possible using this approach. Many of the codes obtained are optimal or near optimal in terms of their rate and distance. A new decoding procedure for this class of codes is presented which exploits the block structure of the generator matrix. This decoding procedure can be realised using parallel architecture. These codes are characterised by their modular structure which, in turn, can be used to design codes with variable minimum distance but having a similar encoding/decoding procedure. Several observations which are very important from a practical standpoint are made on the nature of the codes obtained as a result of the computational method used for the system of bilinear forms. Such a computation can be generalised to include other bilinear forms and the related classes of codes. The concept of generalised hybrid automatic repeat request (GH-ARQ) for adaptive error control in digital communication systems is discussed. This scheme utilises the redundant information available upon successive retransmissions in an efficient manner so as to provide high throughput during poor channel conditions. The class of linear codes derived in this work, is proposed as an excellent candidate for such an application. One unique 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.

3 citations



Journal ArticleDOI
TL;DR: An analysis of the BER performance of sequential decoding with stack algorithm is presented and the coding gain achievable by the sequential decoder is presented for given constraint length of the code and the memory capacity in the decoder, which will be useful for the hardware design.
Abstract: An analysis of the BER performance of sequential decoding with stack algorithm is presented for rate 1/2 code. A tight upper bound of BER performance for maximum likelihood decoding is calculated by specific code distance profiles for evaluating the proto error probability of the simulation results. Block error probability is also considered through the random coding theory so that the simulation results satisfy its upper bound. Finally, the coding gain achievable by the sequential decoder is presented for given constraint length of the code and the memory capacity in the decoder, which will be useful for the hardware design.

DOI
01 Dec 1987
TL;DR: A computer simulation comparison of the tolerances to additive white Gaussian noise of two maximum-likelihood trellis decoding systems for use on discrete memoryless channels shows that the Viterbi and Yamada decoding systems give identical error performance for the same code.
Abstract: A computer simulation comparison of the tolerances to additive white Gaussian noise of two maximum-likelihood trellis decoding systems for use on discrete memoryless channels is presented. The first decoding system applies the Viterbi algorithm to the encoder trellis of a convolutional code; this is the well known standard Viterbi decoding system. The second decoding system, proposed by Yamada, uses the same algorithm but applies it to the syndrome-former trellis of the code. High-rate (n, n-1) systematic and nonsystematic convolutional codes, with rates 1/2, 3/4, 5/6 and 7/8 are used throughout the tests. Simulation results are presented for hard- and soft-decision decoding with BPSK modulation and coherent detection. Results show that the Viterbi and Yamada decoding systems give identical error performance for the same code. The implementation complexity of the systems is also examined; a useful reduction in the number of binary comparisons required by the Yamada system can be achieved.

15 Aug 1987
TL;DR: A construction is proposed to introduce memory on block codes, and simulation results are shown for a trellis code derived from the Nordstrom-Robinson code.
Abstract: The performance of certain binary block codes with soft-decision decoding is evaluated by simulation. A construction is proposed to introduce memory on block codes, and simulation results are shown for a trellis code derived from the Nordstrom-Robinson code.

Journal ArticleDOI
TL;DR: A simplified error and erasure decoding algorithm for double-error-correcting Reed-Solomon codes is presented that can be easily implemented in software and requires a small number of Galois field operations.
Abstract: A simplified error and erasure decoding algorithm for double-error-correcting Reed-Solomon codes is presented. The algorithm presupposes the existence of at least one erasure in the received vector. It can be easily implemented in software and requires a small number of Galois field operations.


Proceedings ArticleDOI
01 Oct 1987
TL;DR: It is shown that in a fading environment a list decoding system can accommodate five times more users than the best hard decision system, and that an adaptive metric doubles the capacity of the static list metric.
Abstract: Multiple Access (MA) performance of list metric decoding is evaluated for frequency hopped (FH), noncoherent M-ary frequency shift keying (NCMFSK). In a list decoding receiver, the demodulator constructs an energy-ordered list of the channel symbols, and the decoder then awards each symbol a score based on its ranking in this list. We considered two cases: in one, the decoder assigns the same set of scores on each use of the channel; in the other, the decoder is adaptive and assigns metrics which award one of M sets of scores depending on how many energy detector outputs were believed to have contained user signals. We show that in a fading environment a list decoding system can accommodate five times more users than the best hard decision system, and that an adaptive metric doubles the capacity of the static list metric.

Journal ArticleDOI
TL;DR: The hardware design of a bit-slice microprocessor-based realtime cyclic error-correcting communications decoder is presented and is versatile: different decoding algorithms can be executed by changing the microprogram.