Showing papers on "BCH code published in 2002"

Turbo Coding, Turbo Equalisation and Space-Time Coding for Transmission over Fading Channels

Abstract: Acknowledgments.Historical Perspective, Motivation and Outline. I Convolutional and Block Coding. Convolutional Channel Coding. Block Coding. Soft Decoding and Performance of BCH Codes. II Turbo Convolutional and Turbo Block Coding. Turbo Convolutional Coding. The Super Trellis Structure of Convolutional Turbo Codes. Turbo BCH Coding. Redundant Residue Number System Codes. III Coded Modulation: TCM, TTCM, BICM, BICM ID. Coded Modulation Theory and Performance. IV Space Time Block and Space Time Trellis Coding. Space time Block Codes. Space Time Trellis Codes. Turbo coded Adaptive QAM versus Space time Trellis Coding. V Turbo Equalisation. Turbo coded Partial response Modulation. Turbo Equalisation for Partial response Systems. Turbo Equalisation Performance Bound. Comparative Study of Turbo Equalisers. Reduced complexity Turbo Equaliser. Turbo Equalisation for Space time Trellis coded Systems. Summary and Conclusions. Bibliography. Subject Index. Author Index. About the Authors.Other Related Wiley and IEEE Press Books.

Error Control Coding: From Theory to Practice

Abstract: From the Publisher: Error Control Coding: From Theory to Practice provides a concise introduction to basic coding techniques and their application. The fundamental concepts of coding theory are explained using simple examples with minimum use of complex mathematical tools. The selection of appropriate codes and the design of decoders are discussed. Bridging the gap between digital communications and information theory, this accessible approach will appeal to students and practising engineers alike. The clear presentation and practical emphasis make this book an excellent tool for both communications and electronic engineering students. Practitioners new to the field will find this text an essential guide to coding. Features include: End of chapter problems to test and develop the readers understanding of the most popular codes and decoding methodsFinite field arithematic and algebraic decoding methods for BCH and Reed-Solomon codesDetailed coverage of Viterbi decoding and related implementation issuesTurbo codes and related code types, including Gallager codes and turbo product codesPractical examples of MAP and SOVA decoding for turbo codes

Finding roots of polynomials over finite fields

Abstract: We propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speedup of the decoding process of Bose-Chaudhuri-Hocquenghem, Reed-Solomon, and some other error-correcting codes.

A robust DWT-based video watermarking algorithm

Abstract: In this paper, we propose a DWT-based video watermarking algorithm It embeds multiple information bits into uncompressed video sequences Its features include: i) embedding data in the LL subband; ii) reducing error probabilities of detection by exploiting the BCH code; iii) combating bursts of errors by using a novel 3-D interleaving technique; iv) developing an effective temporal synchronization technique (compared with the sliding correlation proposed by Hartung and Girod, our synchronization technique is more advance); and v) a valid secure key is needed in watermarking extraction Experimental results demonstrate that the hidden data with the proposed algorithm is visually transparent, robust against MPEG-2 compression, scaling 20, and the detection error rate with 3-D interleaving is much lower than that without 3-D interleaving when frame loss rate is below 50% The imperceptible high bit rate watermark thus embedded is robust and blind extracted The experiments have demonstrated the effectiveness of the proposed algorithm

The Theory of Cyclic Codes and a Generalization to Additive Codes

Abstract: We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed.

A parallel decoder for low latency decoding of turbo product codes

Abstract: There has been intensive focus on turbo product codes (TPCs) which have low decoding complexity and achieve near-optimum performances at low signal-to-noise ratios. Different than the original TPC decoder, which performs row and column decoding in a serial fashion, we propose a parallel decoder structure. Simulation results show that with this approach, decoding latency of TPCs can be halved while maintaining virtually the same performance level.

One-way communication and error-correcting codes

Abstract: We establish a further connection between one-way communication where a sender conveys information to a receiver who has related information, and error-correction coding where a sender attempts to communicate reliably over a noisy channel. Using this connection we obtain three results on the two problems. We derive an often-tight lower bound on the number of bits required for one-way communication based on the largest code for the corresponding error-correction problem. We construct an error-correcting code whose minimum distance properties are similar to those of Bose-Chaudhuri-Hocquenghem (BCH) codes based on a one-way communication protocol for set reconciliation. Finally, we prove that one-way communication is suboptimal for a large class of Hamming-distance problems.

Apparatus and method for acquiring frame synchronization in a mobile communication system

Abstract: A method for acquiring frame synchronization of a broadcast channel (BCH) in an asynchronous mobile telecommunication system. The method according to the invention includes steps of acquiring a system timing through a synchronous channel (SCH), demodulating a primary common control physical channel (PCCPCH) based on the system timing, checking a cyclic redundancy check (CRC) by decoding a predetermined time interval of the demodulated PCCPCH, and acquiring frame synchronization of the BCH by reference to the CRC checked result.

Divisibility properties for covering radius of certain cyclic codes

Abstract: We are presenting a new method to obtain the covering radius of codes and in particular to prove quasi-perfection in codes. Our techniques combine divisibility results of Ax-Katz and Moreno-Moreno as well as coding theoretic methods. We answer a problem posed by Cohen-Honkala-Litsyn-Lobstein in the book covering radius for Bose-Chaudhuri-Hocquenghem (BCH) codes. We also obtain the covering radius for many new classes of codes.

Comparative study of turbo equalization schemes using convolutional, convolutional turbo, and block-turbo codes

Abstract: Turbo equalizers have been shown to be successful in mitigating the effects of inter-symbol interference introduced by partial response modems and by dispersive channels for code rates of R/spl les/ 1/2. We comparatively studied the performance of a range of binary phase-shift keying turbo equalizers employing block-turbo codes, namely Bose-Chaudhuri-Hocquenghen (1960, 1959) turbo codes, convolutional codes, and convolutional turbo codes having high code rates, such as R=3/4 and R=5/6, over a dispersive five-path Gaussian channel and an equally weighted symbol-spaced five-path Rayleigh fading channel. These turbo equalization schemes were combined with an iterative channel estimation scheme in order to characterize a realistic scenario. The simulation results demonstrated that the turbo-equalized system using convolutional turbo codes was the most robust system for all code rates investigated.

Error correction improvement for concatenated codes

Abstract: An enhanced forward error correction system is disclosed Transmitted data is encoded into codewords in multiple dimensions The decoding of received data by a decoder is performed in multiple passes in each dimension, with corrected data provided as an output from each pass into another decoder for the next decode pass The encoder in one embodiment comprises a parallel inner RS(247,239) encoder or encoders and parallel outer BCH(255,247) encoder or encoders Additional steps are added for error multiplication reduction The system provides an approach to detect generally uncorrectable patterns for concatenated codes and provides a correction mechanism for improving error correction performance

Third generation FEC employing turbo product code for long-haul DWDM transmission systems

Abstract: In this paper, we describe the design concept of the third generation forward error correction (FEC) employing turbo product code (TPC) based on BCH product code using soft input soft output iterative decoding. The proposed TPC is composed of two constituent BCH codes, BCH(128,113,6) and BCH(256,239,6), so that the TPC has minimum distance 36 and code rate 0.82 (21.3% of redundancy). Simulation results demonstrate a coding gain of 10.1 dB, which can be applied to the next generation submarine cable systems.

Apparatus for processing OTN frames utilizing an efficient forward error correction

Abstract: An apparatus and method utilizing an efficient forward error correction (FEC), targeted for processing optical transport network (CTN) signals having transmission rates in excess of 10 Gbps. The FEC uses an advanced implementation of the Bose Chaudhuri Hocquenghem (BCH) code. The use of the BCH code for the FEC improves the performance over prior art solutions for both error correction and detection.

Iterative Viterbi decoding, trellis shaping, and multilevel structure for high-rate parity-concatenated TCM

Abstract: We define and apply a new algorithm called the iterative Viterbi decoding algorithm (IVA) to decode a high-rate parity-concatenated TCM system in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. With trellis shaping, the IVA can achieve a performance 1.25 dB away from the Shannon limit at a BER of 3/spl times/10/sup -5/ with low complexity. By augmenting the system with a binary BCH code, the error floor can be reduced to 10/sup -9/ with very little additional cost.

Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks

Abstract: This paper addresses the problem of error-correction for extremely noisy channels (BER from 0.1 to 0.5), such as those obtained for image or video watermarking. Minimum distance arguments are used to identify a region for which no other code is as efficient as repetition codes, whatever the rate, at least when bounded decoding is considered. However, in order to obtain a reasonable and sufficiently low BER, repetition codes are not very efficient. We present a coding scheme concatenating a repetition code with another one, and design rules in order to select these codes for a given watermarking application are developed. The repetition code lowers the huge channel BER, as no other code can do this part of the job. Then, the second more powerful code working at a lower BER achieves a larger BER reduction. In this paper, this role is devoted to BCH codes, as members of a classical family. Thanks to their moderate decoding complexity, they turn out to be an interesting cost versus performance trade-off, while more efficient coding schemes based on soft decoding are far more complex. However, we also provide an idea of the solutions to consider for watermarking applications with fewer complexity limitations, for which more powerful decoding techniques can be implemented. (C) 2002 Published by Elsevier Science B.V.

Block turbo codes for multicarrier local loop transmission

Abstract: We investigate the performance of different block turbo codes in the context of Enhanced VDSL. We first describe the VDSL system used in our simulation link. We then propose an iterative decoding algorithm based on Pyndiah's (1998) SISO decoder for product turbo block codes that can be implemented with reasonable complexity. We also illustrate several results for various QAM modulation schemes. The coding gains obtained for the different codes and modulations then allow us to predict the attainable bit rates as a function of the line length. We show that such a turbo block decoding outperforms the classical Reed Solomon hard decoding used in the ADSL system.

High-performance iterative Viterbi algorithm for conventional serial concatenated codes

Abstract: The Viterbi algorithm (1967) and conventional serial concatenated codes (CSCC) have been widely applied in digital communication systems over the last 30 years. We show that the Shannon capacity of additive white Gaussian noise (AWGN) channels can be approached by CSCCs and the iterative VA (IVA). We firstly study the algebraic properties of CSCCs. We then present the IVA to decode these codes. We also analyze the performance of the IVA and conclude that a better performance can be achieved if we replace the powerful block codes by some simple parity codes. One of the key results in this paper shows that by using a proper design for the decoding method, codes with small loops can be very efficiently decoded using a min-sum type algorithm. The numerical results show that the IVA can closely approach the Shannon sphere-packing lower bound and the Shannon limit. For block sizes ranging from 56 information bits to 11970 information bits, the IVA can perform to within about 1 dB of the Shannon sphere-packing lower bound at a block error rate of 10/sup -4/. We show that the IVA has a very low complexity and can be applied to many current standard systems, for example, the Qualcomm code-division multiple-access (CDMA) system and the NASA concatenated system, with very little modification or, for some cases, without any modification.

Correcting errors in disk drive read back signals by iterating with the Reed-Solomon decoder

Abstract: A signal detector comprises a first detector that generates raw decisions as a function of a read back signal. A selector generates a modified decision by at least one of applying a correction technique to soft information that is based on the raw decisions and marking an erasure in the soft information. A decoder decodes the modified decision to generate a final decision and determines whether a correct codeword is generated by evaluating the final decision. The decoder performs at least one of Reed-Solomon decoding, Bose Chaudhuri Hocquerghen (BCH) decoding, Hamming decoding, and Trellis decoding.

High speed VLSI architecture design for block turbo decoder

Abstract: In this paper, a sub-optimal algorithm for decoding BCH (t /spl ges/ 2) turbo codes is presented. A high speed VLSI decoder architecture is proposed for codes constructed over extended GF(2/sup 5/). While the algorithm applies to higher order BCH product codes, it is shown that this particular block turbo codes, when decoded using the proposed algorithm, gives the best performance (achieving 10/sup -6/ bit error rate at a signal to noise ratio of 2.4 dB) among all two dimensional turbo product codes. Following an analysis of the impact of finite word-length effect on the performance of the SISO decoder, full parallel decoding architecture at the top level and a number of lower level high speed implementation strategies such as applying lookahead technique to reduce the critical path of the merge sort circuit and fast finite field operations are presented. Area and timing estimates obtained by logic synthesis (0.18 /spl mu/m, 1.5V CMOS technology) from VHDL descriptions are given to show how the design strategies translate into the area consumption and decoding throughput (> 32 Mbits/s.) of the VLSI implementation.

Custom coding, adaptive rate control, and distributed detection for Bluetooth

Abstract: Three strategies for improving the performance of point-to-point Bluetooth links are presented. All of the strategies are implemented on the host computer, and therefore no modification of the Bluetooth standard is necessary. The first strategy is custom error control coding, which is achieved by transporting BCH codewords within AUX1 packets. The second concept is adaptive rate control, which involves dynamically selecting the packet type that offers the best throughput for the current channel SNR. Finally, a distributed detection technique is proposed, whereby each packet is broadcast to a group of two or more receivers that are linked over a reliable backbone, and the packet is accepted if it is received correctly at any receiver in the group.

Effect of channel coding on the performance of spatial watermarking for copyright protection

Abstract: We present a spatial-domain-watermarking scheme for data hiding and copyright protection of still images using the attack characterization approach and demonstrate the effect that the application of channel coding has on the watermark detection performance. The scheme uses techniques such as direct sequence spread spectrum modulation, perceptual analysis and diversity to maximize the robustness of the watermark while keeping it imperceptible. Furthermore, Bose-Chaudhuri-Hocquenghem (BCH) block codes and turbo codes are used to provide error protection against attacks in the watermark channel. Simulation results are provided to demonstrate the improved performance when the proposed approach is implemented with and without channel coding. The superiority of turbo codes against BCH block codes is demonstrated and some constraints involving the application of these codes to watermarking are also discussed.

Soft-input soft-output list-based decoding algorithm

Abstract: List-based SISO decoding algorithms calculate extrinsic information using a list of codewords They try to produce a list containing the closest codewords to the soft input by encoding or decoding test sequences Ideally for each position in the code, there is at least one codeword in the list with a '1' in that position and at least one with a '0' The extrinsic information must be estimated in positions where there is not We focus on encoding-based algorithms since they retain performance as the minimum Hamming distance of the code, d/sub H,min/, increases, whereas, decoding-based algorithms generally become increasingly inefficient We consider product codes with extended BCH component codes They are transmitted using BPSK over a memoryless additive white Gaussian noise channel The proposed algorithm can easily be extended to different channel models, modulation schemes and concatenated codes

Transmission device provided with error correction function

Abstract: PROBLEM TO BE SOLVED: To realize, in a transmission device provided with an error correction function, the error correction function offering a greater error correction capability than Reed-Solomon codes RS (255, 239), while retaining the same data signaling rate. SOLUTION: A BCH (2040, 1919, 11) code check bit calculation insertion portion 1-11 of a transmitter unit 1-10 adds a check bit, by using a parity check area of a frame format of RS (255, 239) codes in accordance with ITU-T recommendations G. 709/G. 975 and outputs a signal at the same data signaling rate as that for the RS (255, 239) codes. The coded signal is rearranged by a scrambler 1-12 and converted to a corresponding optical signal, by an optical signal transmitter circuit 1-13, before being transmitted to an optical transmission path. A receiver unit 1-20 then performs the following functions. An optical signal receiver circuit 1-21 converts the optical signal to a corresponding electrical signal. A descrambler 1-22 arranges the order of the signal data back to an original state. An error position detecting and correcting portion 1-23 performs an error detecting and correcting processing to output a main signal (information). COPYRIGHT: (C)2003,JPO

Spatial frequency band division in human visual system based-watermarking

Abstract: In this paper, a robust watermarking algorithm in DWT domain against geometric distortion is proposed. We introduce a distance measure between the distorted and undistorted images/video in order to determine the distortion. We can then inverse the geometric distortion to regain synchronization. An efficient algorithm searching for the synchronization parameters has been developed. Using multi-resolution coarse-fine searching to prune the searching space, the computation of algorithm is reduced drastically. The BCH code and 2-D interleaving are exploited to lower detection error probability. Our watermarking algorithm can successfully resist geometrical distortion, including rotation, scaling, translation, shearing, cropping, jitter attack and linear transformations.

Perfromance Analysis of Forward Error Correction Codes for Various Degradatin Factors in Optical Transmission System

Abstract: Error-correction performance of standard RS and BCH codes used in optical transmission system has been experimentally studied It was found that the RS code has better error correcting capability than the BCH code when bit error characteristics become less random

A comparative study of search techniques applied to the minimum distance problem of bch codes

Abstract: BCH codes have been shown to be excellent errorcorrecting codes among codes of short lengths. The errorcorrecting capability of a code is directly related to its minimum distance. It is computationally very difficult to determine the true minimum distance of BCH codes. We analyze and compare the behaviour of different heuristic search techniques when applied to the problem of finding the true minimum weight of BCH codes. A basic genetic algorithm significantly outperformed hill-climbing, tabu search and hybrid techniques.

Syndrome decoding and performance analysis of DFT codes with bursty erasures

Abstract: In this paper, we analyze the performance of DFT codes with bursty erasures in the framework of syndrome decoding. Bursty erasures give rise to a syndrome decoding matrix which has very large elements depending on the code parameters and the burst length. The largeness of the elements of the syndrome decoding matrix is studied by establishing various relationships between the syndrome decoding matrix, and the parity and the generator polynomial coefficients. With a suitable model for the quantization error, the reconstruction error performance of DFT codes in the context of the syndrome decoding is analyzed and then applied to the case of bursty erasures. Simulation results with a Gauss-Markov source verify the theoretical results obtained with the assumed quantization error model.