Showing papers on "List decoding published in 1991"

Binary image processing for decoding self-clocking glyph shape codes

Abstract: Binary image processing techniques are provided for decoding bitmap image space representations of self-clocking glyph shape codes and for tracking the number and locations of the ambiguities (sometimes referred to herein as "errors") that are encountered during the decoding of such codes. A substantial portion of the image processing that is performed in the illustrated embodiment of this invention is carried out through the use of morphological filtering operations because of the parallelism that is offered by such operations.

Error-correcting codes for list decoding

Abstract: In the list-of-L decoding of a block code the receiver of a noisy sequence lists L possible transmitted messages, and is in error only if the correct message is not on the list. Consideration is given to (n,e,L) codes, which correct all sets of e or fewer errors in a block of n bits under list-of-L decoding. New geometric relations between the number of errors corrected under list-of-1 decoding and the (larger) number corrected under list-of-L decoding of the same code lead to new lower bounds on the maximum rate of (n,e,L) codes. They show that a jammer who can change a fixed fraction p >

Bit-level soft-decision decoding of Reed-Solomon codes

Abstract: A Reed-Solomon decoder that makes use of bit-level soft-decision information is presented. A Reed-Solomon generator matrix that possesses a certain inherent structure in GF(2) is derived. This structure allows the code to be represented as a union of cosets, each coset being an interleaver of several binary BCH codes. Such partition into cosets provides a clue for efficient bit-level soft-decision decoding. Two decoding algorithms are derived. In the development of the first algorithm a memoryless channel is assumed, making the value of this algorithm more conceptual than practical. The second algorithm, which is obtained as a modification of the first, does account for channel memory and thus accommodates a bursty channel. Both decoding algorithms are, in many cases, orders of magnitude more efficient than conventional techniques. >

Decoding binary 2-D cyclic codes by the 2-D Berlekamp-Massey algorithm

Abstract: A method of decoding two-dimensional (2-D) cyclic codes by applying the 2-D Berlekamp-Massey algorithm is proposed. To explain this decoding method, the author introduces a subclass of 2-D cyclic codes, which are called 2-D BCH codes due to their similarity with BCH codes. It is shown that there are some short 2-D cyclic codes with a better cost parameter value. The merit of the approach is verified by showing several simple examples of 2-D cyclic codes. >

Discrete Hartley transform in error control coding

Abstract: A new class of real-valued linear code obtained by using the discrete Hartley transform (DHT) is defined. The authors have derived the limitation on the choice of parity frequencies so as to define DHT codes with the cyclic-shift property. Then, by introducing the well-established encoding/decoding algorithm for cyclic codes in error control coding, they have constructed the encoder/decoder for the DHT cyclic codes. >

Multilevel error-control codes for data storage channels

Abstract: The authors present a coding architecture suitable for magnetic storage systems. In data storage devices, several types of errors may occur. This includes random errors as well as burst errors of different lengths. A class of error control codes is presented, based on a multilevel coding architecture, that can correct several types of errors. The parameters of the multilevel codes can be adjusted to match the probability of each error type. The decoding algorithms of these codes allow for fast-error recovery since they are based on decoding algorithms for simple codes. A class of multilevel codes is constructed, based on Reed-Solomon codes, whose redundancy is minimal. >

Runlength-limited codes for mixed-error channels

Abstract: The mixed-error channel (MC) combines the binary symmetric channel and the peak shift channel. The construction of (d, k) constrained t-MC-error-correcting block codes is described. It is demonstrated that these codes can achieve a code rate close to the (d, k) capacity. The encoding and decoding procedures are described. The performance of the construction depends on a particular partitioning of (d, k) constrained block codes. This partitioning is discussed and various tables of codes are included. Examples on encoding/decoding and on code performance are given. >

Image signal decoding system for decoding modified Huffman codes at high speeds

Abstract: An image signal decoding system for decoding a variable length image data compressed by a modified Huffman code. The decoding object data is cut by a fixed length of 13 bits and the cut data is decoded by using a decode-encode circuit for decoding the input of the modified Huffman code with its end portion equalized and for encoding and generating the code length, the code kind and the run-length number on the basis of the decoded contents, and by using a rotator for shifting the bit data. For decoding a code which immediately follows, the data is shifted with the rotator by the bit number of the code length of the decoding output result, the end portion of the next decoding output result, the end portion of the next decoding object data is equalized with the input end portion of the encode-decode circuit, and it is placed after the immediately following decoding object data and is then input into the decode-encode circuit and decoded.

On maximum likelihood soft-decision decoding of binary linear codes

Abstract: Two new implementations of a maximum-likelihood soft-decision decoding algorithm for binary linear codes are derived. Instead of checking only error patterns yielding a codeword when added to the rounded-off version of the received vector, these implementations principally consider all possible column patterns. Compared to known implementations, this allows a more efficient use of branching and bounding techniques. >

A table-driven (feedback) decoder

Abstract: The authors present a table-driven technique for decoding of convolutionally encoded data. The approach can be used in either the feedback or the direct mode. A data-independent syndrome vector is generated on the transmitted bits. If it is different from zero it is used to address pre-computed tables of corrections for the encoded bits. The decoding is performed as a separate step. When the feedback mode is used the error propagation is minimized by appropriate choice of the codes, the table construction and the decoding algorithms. The approach allows hardware simplicity comparable to majority-logic decoding, but has error correcting capabilities that can be made as close to the optimal as desired through the adjustment of the syndrome vector length and the correction table size. This makes the method very attractive for high speed satellite and network applications. The performance of the method can be further enhanced through soft detection. >

On two probabilistic decoding algorithms for binary linear codes

Abstract: A generalization of the Sullivan inequality (1967) on the ratio of the probability of a linear code to that of any of its cosets is proved. Starting from this inequality, a sufficient condition for successful decoding of linear codes by a probabilistic method is derived. A probabilistic decoding algorithm for low-density parity-check codes is also analyzed. This method of analysis enables one to estimate experimentally the probability of successful decoding for any given linear code and for any chosen family of parity-check sets. Using the example of a linear (512,100) code, the author illustrates the dependence of the successful probability on the channel noise level. >

BER analysis of convolution coded QDPSK, in digital mobile radio

Abstract: The bit error rate (BER) performance of convolutional coded quaternary differential phase-shift keying (QDPSK) with Viterbi decoding is theoretically investigated in Rayleigh fading environments. The probability density functions of the path and branch metric values of Viterbi decoding are derived. The BERs after decoding due to additive white Gaussian noise and cochannel interference are theoretically analyzed. Rate 1/2 codes and their symbol punctured high-rate codes are considered, and the symbol positions for deletion to minimize the BER after decoding are presented for the codes with a constraint length K=3-7. It is shown that Viterbi decoding considerably reduces the desired signal-to-interference power ratio as well as the signal energy per information bit-to-noise power spectrum density ratio necessary to achieve a certain BER. The spectrum efficiency of the cellular mobile radio system, achievable by the use of the symbol punctured codes, is also evaluated. >

On Blahut's decoding algorithms for two-dimensional BCH codes

Abstract: It is shown that decoding of cyclic codes in the DFT domain is equivalent to an appropriate deconvolution problem. A two-dimensional (2-D) generalization of Blahut's (1979) one-dimensional (1-D) linear complexity theorem is obtained and utilized to determine the error-correcting capability of 2-D BCH codes, as afforded by code's defining array of zeros, with regard to correction of burst-errors. The 2-D linear complexity theorem is further utilized to present a new approach for decoding of cyclic codes, in general, and 2-D BCH codes in particular. An alternative exposition of Blahut's decoding algorithms, in the DFT domain, for random and burst error correction in 2-D BCH codes is given from a deconvolution viewpoint. Some modifications for efficient implementation of Blahut's decoding algorithms for random and burst error correction are suggested and improved decoding algorithms are presented. It is shown that the improved decoding algorithm requires at most half the number of passes through the Berlekamp-Massey algorithm compared to the Blahut's decoding algorithm. It is shown that Blahut's decoding algorithms have optimal error-correcting capability and improved decoding algorithms have less computational complexity. A comparative study of various time- and spectral-domain implementations of 2-D BCH decoding algorithms is also given.

Breaking the bottleneck of sequential decoding for high-speed digital communication

Abstract: An efficient ASIC architecture for the sequential stack decoding (SSD) algorithm used for channel coding is presented It is different from the maximal likelihood (ML) Viterbi decoder (VD), mainly in the search for the correct memory path Due to the dedicated memory organization, the storage space and required hardware can be reduced while the decoding efficiency remains almost the same The proposed architecture results from step by step design of the I/O interface, high-level memory management, dedicated data paths, and controller The ordering of these steps is important in optimizing the final solution In addition, the construction of this hardware organization can be made by using the available hardware building blocks >

Reed-Solomon encoder/decoder application using a neural network

Abstract: Reed-Solomon codes are widely used in deep-space communication, compact disc audio systems, and frequency-hopped systems. However, the VLSI implementation of these codes is still very complex, and encoding/decoding by using these chips is very time consuming. Neural network implementation of these codes has resulted in reduced complexity, enhanced error correction capability, fast processing, and improved signal-to-noise ratio. The proposed scheme requires less bandwidth, utilizes soft decision decoding, and exploits the redundancy in the English language.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Parallel decoding of binary BCH codes

Abstract: A parallel decoding procedure for the BCH codes is introduced, which is particularly useful for decoding BCH codes with small error-correcting capability. The high regularity inherent in the scheme enable it to be easily implemented with VLSI circuits.

Soft decision decoding for bandwidth efficient RS coded MPSK schemes over a Rayleigh fading channel

Abstract: The authors consider the performance of the bandwidth-efficient RS (Reed-Solomon) coded MPSK schemes using soft-decision decoding over a Rayleigh fading channel. For the short codes it is practical to perform soft-decision decoding by introducing a trellis structure and using the Viterbi algorithm. The authors carried out upper bound analysis and computer simulation for Viterbi decoding of two short RS-coded 8PSK (phase shift keying) schemes, namely, RS

Multi-stage decoding for multi-level block modulation codes

Abstract: In this paper, we investigate various types of multi-stage decoding for multi-level block modulation codes, in which the decoding of a component code at each stage can be either soft-decision or hard-decision, maximum likelihood or bounded-distance Error performance of codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived Based on our study and computation results, we find that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity In particular, we find that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum decoding of the overall code is very small: only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6) Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity

Soft decision decoding of block codes and concatenated block-convolutional codes using the stack algorithm

Abstract: An approach to soft decision-decoding of block codes and concatenated block-convolutional codes is presented. These codes are shown to have a convenient tree structure that allows depth-first and metric-first sequential decoding techniques to be used to decode them. The unique features of the metric used for decoding are discussed, and a complete decoder of acceptable complexity is presented. For the additive white Gaussian noise (AWGN) channel, gains in excess of 1 dB at reasonable bit error rates (BER) with respect to conventional hard decision algebraic decoding are demonstrated for the (23,12) Golay code and for two Reed-Solomon codes. >

"System, devices and algorithms for the error correction in digital transmission"

Abstract: A system for error correction in digital transmissions using the so-called Reed Solomon coding/decoding techniques. At the reception side, the received data stream is processed using a new decoding algorithm. Also, with the described decoding algorithm, error correction is implemented using more simplified equipment than that found in other types of conventional error correction systems. The components making up the error correction system of the invention basically consist of: (1) a central timing unit, (2) a preset unit and (3) at least one Reed Solomon coding/decoding circuit operating in accordance with the proposed algorithm.

Soft Decoding for Block Codes Obtained from Convolutional Codes

Abstract: Bounds for the minimum distance and the error probability of decoding for tail biting convolutional codes are presented. We propose a decoding algorithm for these codes and obtain a bound for the asymptotical complexity of almost maximum likelihood decoding.

Partial Ordering of Error Patterns for Maximum Likelihood Soft Decoding

Abstract: The error patterns, encountered in maximum likelihood soft decision syndrome decoding of a binary linear block code, can be partially ordered in a way that only the minimal elements have to be scored. The ordering requires a usually short sorting proceedure applied to the confidence values of the hard-detected bits. In this paper some properties of the minimal elements are derived. We also present bounds on the number of minimal elements with particularly large Hamming weight.

Method of decoding MR codes of continuous vertical mode data for the same change points

Abstract: In decoding method of MR codes, decoding procedure is omitted at a part of V(0) continuing in one line, and the run length code of the reference line is copied and the process is repeated in the number less than the continuing number by one, thereby the decoding process can be carried out at high speed.

Multistage decoding using erasing technique for multilevel coding

Abstract: Families of BCM (block-coded modulation) that allow the use of suboptimal multistage decoding procedures having performance/complexity advantages over MLD (maximum likelihood decoding) are proposed. The process of decoding is performed in two steps: a first estimate of the codeword is obtained by a hard decision device, and the associated decoding is carried out to correct the eventual errors. The criterion of erasing, i.e. how to define the erasing procedure in the first step of decoding in order to maximize the coding gain, is discussed for both PSK and QAM modulations. The erasing technique is performed by defining some 'erasing-areas'. The analytic results show that significant coding gain can be achieved with respect to a nonerased equivalent scheme. >

Bidirectional sequential decoding for convolutional codes

Abstract: Sequential decoding is a very powerful decoding technique for convolutional codes. The main drawback of sequential decoding is the variability of the computational effort. Efficient bidirectional sequential decoding (BSD) algorithms are presented. With the bidirectional decoding algorithms, the tree code is searched simultaneously from the root and end nodes of the tree. It is shown that the distribution of the number of computations per decoded block of the bidirectional algorithms is still Pareto. However, the advantage of these bidirectional sequential decoding algorithms appears as an increase in the Pareto exponent, and hence in the computational variability. With the bidirectional algorithms, the Pareto exponent is twice that of the unidirectional sequential decoding (USD) algorithm. >

Process for decoding bar codes

Abstract: A process for reliably decoding bar codes on separators for use in combination with the documents of a print job to input programming instructions to an electronic reprographics/printing machine in which variable decoding threshold values are calculated and updated for each bar code in accommodation of the image condition of the bar code.