An efficient technique for detecting catastrophic convolutional codes

Catastrophic convolutional codes (CC) cause an infinite number of decoded data bit errors when decoding a finite number of code symbols. A CC displays a catastrophic error propagation if the generating polynomials have a common factor. An efficient algorithm for polynomial factorization in GF(2^m) is used for detecting catastrophic CC for any rate n/m and constraint length k. A general formula is derived to calculate the number of catastrophic codes in any (m, n, k) CC.     

Performance evaluation of high rate space?time trellis-coded modulation using Gauss?Chebyshev quadrature technique

The performance analysis of high rate space-time trellis-coded modulation (HR-STTCM) using the Gauss-Chebyshev quadrature technique is presented. HR-STTCM is an example of space-time codes that combine the idea used in trellis coded modulation (TCM) design that is signal set expansion and set partitioning into its construction. HR-STTCM construction is based on the concatenation of an outer TCM encoder and inner space-time block code. This paper evaluates the exact pairwise error probability of HR- STTCM based on the Gauss-Chebyshev quadrature formula. Comparison of numerical and simulation results shows that the proposed method is accurate. The method used is shown to be computationally simpler than those in the literature.     

DC-free trellis-based error-control codes

Trellis-based error-control (EC) codes, such as convolutional or turbo codes, are integrated with guided scrambling (GS) multimode coding to generate DC-free GS-convolutional/ turbo codes. On the basis of the generators of the convolutional/turbo code, we employ puncturing or flipping to ensure that the EC-coded sequences are DC-free. At the receiver, convolutional/turbo decoding is performed before GS decoding to circumvent the performance degradation that can occur when GS decoding is performed prior to EC decoding. Performance of the new DC-free GS-convolutional/turbo codes is evaluated in terms of both spectral suppression and bit error rate (BER). It is shown that the new codes can provide superior BER performance and approximately the same suppression of low frequencies as the conventional concatenation of convolutional/turbo codes and DC-free GS codes.     

Iterative optimization for joint design of source and channel codes using genetic algorithms

Abstract

This paper presents a novel algorithm for the joint design of source and channel codes. In the algorithm, channel‐optimized vector quantization (COVQ) and rate‐punctured convolutional coding (RCPC) are used for design of the source code and the channel code, respectively. We employ the genetic algorithm (GA) to prevent the design of COVQ from falling into a poor local optimum. We also adopt the GA to reduce the computational time needed for realizing the unequal error protection scheme best matched to the COVQ. Both the GA‐based source coding and channel coding scheme are then iteratively combined to achieve a near global optimal solution for the joint design. Numerical results show that the algorithm can be an effective alternative for applications where high rate‐distortion performance and low computational complexity are desired.     

Coding techniques for link adaptation in multicarrier systems

A novel technique for improving coding and diversity gains in orthogonal frequency division multiplexing (OFDM) systems is proposed. Multidimensional symbol design based on complex field codes with interleaving across frequency has been known for some time now. However, such symbols cannot be concatenated to convolutional codes owing to the prohibitive complexity of decoding. A novel way of designing multidimensional symbols that allow to concatenate them to convolutional codes while maintaining a low decoding complexity is shown. The proposed multidimensional symbols are based on tailbiting convolutional codes and the design of codes is discussed with desirable properties. Also the design of bit interleaved coded modulation-type and trellis-coded modulation-type codes over these multidimensional symbols is shown. Simulations show that the proposed coding scheme provides significant performance and/or complexity improvements over existing alternatives and also provides more degrees of freedom for channel-based link adaptation.     

Maximum Distance Separable Convolutional Codes

A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/n and a fixed code degree δ. In order to achieve this result we will introduce a natural upper bound for the free distance generalizing the Singleton bound. The main result of the paper shows that this upper bound can be achieved in all cases if one allows sufficiently many field elements. Received: December 10, 1998; revised version: May 14, 1999     

On minimum distance bounds for abelian codes

This paper is an exposition of two methods of formulating a lower bound for the minimum distance of a code which is an ideal in an abelian group ring. The first, a generalization of the cyclic BCH (Bose-Chaudhuri-Hoquenghem) bound, was proposed by Camion [2]. The second method, presented by Jensen [4], allows the application of the BCH bound or any of its improvements by viewing an abelian code as a direct sum of concatenations of cyclic codes. This second method avoids the mathematical analysis required for a direct generalization of a cyclic bound to the abelian case. It can produce a lower bound that improves the generalized BCH bound. We present simple algorithms for 1) deriving the generalized BCH bound for an abelian code 2) determining direct sum decompositions of an abelian code to concatenated codes and 3) deriving a bound on an abelian code, viewed as a direct sum of concatenated codes, by applying the cyclic BCH bound to the inner and outer code of each concatenation. Finally, we point out the applicability of these methods to codes that are not ideals in abelian group rings.     

Bandwidth efficient concatenated coding schemes

Concatenated coded modulation is a powerful method for constructing coding schemes with large coding gain and low decoding complexity. For the concatenated scheme, the outer code has redundancy and the overall transmission rate is reduced. The problem of bandwidth expansion can be overcome by two procedures. First, the code rate of inner codes is increased with a special coding design. Second, a two-level concatenated scheme is constructed to compensate the rate loss. This way, the low-complexity concatenated coded modulation schemes can be designed without bandwidth expansion as compared with the uncoded scheme.     

Modified multi-wavelength optical orthogonal code for spectral efficiency improvement in two-dimensional optical CDMA system

Classical multi-wavelength optical orthogonal code (MWOOC) constructions impose several conditions on the code parameters. These limit the optical code division multiple access (OCDMA) system potentialities in terms of performance and practical implementation. A modified MWOOC construction is used to overcome these limitations. Indeed, this method permits the design of 2D codes with a low temporal code length value and a low number of wavelengths. Considering a multi-user receiver named parallel interference cancellation, the number of users and the data rate per user the system can provide for a low bit error rate value are evaluated. For a given performance, it is shown that the spectral efficiency using the modified MWOOC is significantly improved. Thus, the simplicity of the modified code design and the spectral efficiency increase constitute an advantage for practical implementation of OCDMA network.     

Packet-LDPC codes for tape drives

In this paper, we introduce packet low-density parity-check (packet-LDPC) codes for high-density tape storage systems. We report on the performance of two error control code (ECC) architectures based on the packet-LDPC codes. The architectures are designed to be (approximately) compatible with the widely used ECMA-319 ECC standard based on two interleaved concatenated 8-bit Reed-Solomon (RS) codes. One architecture employs an inner RS code; the other employs an inner turbo product code with single parity-check constituent codes (TPC-SPC). Both employ a packet-LDPC code as the outer code. As for the ECMA-319 system, both schemes are required to correct noise bursts due to media defects and synchronization loss, as well as the loss of one of eight tracks (due to a head clog, for example). We show that the first packet-LDPC code architecture substantially outperforms the ECMA-319 scheme and is only a few tenths of a decibel inferior to a long, highly complex 12-bit RS scheme. The second architecture outperforms both the ECMA-319 and the long RS code scheme.     

Bandwidth-efficient code design for coordinate interleaved coded cooperation

A two-user coordinate interleaved coded cooperation scheme is proposed for quasi-static Rayleigh fading channels, where cooperative and modulation diversity techniques are properly combined to take their full advantage. Two selective cooperation schemes are considered related to whether users know the cooperation case or not. Pairwise error probability (PEP) analysis is performed for all cooperation cases and code design criteria are derived from the PEP upper bounds. Bandwidth-efficient 4-, 8- and 16-state rate 2/4 cooperative quadrature phase shift keying (QPSK) trellis codes are obtained based on these criteria by means of exhaustive computer search. The error performances of the new codes evaluated by computer simulations show their superiority compared to the corresponding best space-time codes used in cooperation with coordinate interleaving. The simulation results are supported by an upper bound on the bit error probability developed using union bounding technique.     

Super-orthogonal space-time-frequency trellis coded OFDM

Super-orthogonal space-time trellis codes (SOSTTCs) given in the literature are full rate and provide full spatial diversity with high coding gain in narrowband quasistatic fading channels. The high number of parallel transitions in their trellis structure restricts their performance in wideband channels where the code performance suffers from multipath. Code design criteria are derived and a computer search based method is proposed to design full-rate optimised SOSTTCs exploiting full spatial and multipath diversity for multiple-input multiple-output orthogonal frequency division multiplexing systems. The proposed codes have codewords defined in space, time, and frequency. We evaluate the codeword error rates of the new 16, 32 and 64-state super-orthogonal space-time-frequency trellis codes for quadrature phase shift keying by computer simulation and show that they provide significant error performance improvement compared to their counterparts with equivalent delay length     

Blind turbo-detection in the presence of phase noise

Blind coherent detection of convolutional turbo codes is a hard problem in the presence of strong phase noise. Since the operating signal-to-noise ratio is usually very low, phase synchronisation algorithms suffer from phase ambiguities and cycle slips. A possible remedy is to perform joint phase estimation and decoding on a combined state-space model for the time-varying phase and the component convolutional codes. We demonstrate that joint phase estimation and decoding is in fact mandatory only for one component code, while ordinary BCJR decoding can be used for the second component code. Monte Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.     

平坦快衰落条件下天线数较多时空时格码的设计

空时格码技术是近年来无线通信领域的一个研究热点，空时格码的设计准则问题一直是该技术的一个难点。在平坦快衰落条件下且天线数目较多时，基于最小平方欧式距离最大化的空时格码设计准则虽然优于经典的距离－积准则，但仍不完善。从平方距离分布与平方距离和方－方和比分布的角度对此进行了改进，得到改进的准则以及性能为目前最优的新码。还对快慢2种衰落条件下码性能差异的原因给出了新的解释，并将改进的码设计准则应用于智贪码的设计。     

The synthesis of magnetic recording trellis codes with good hamming distance properties

In this paper we present, by means of an example, a systematic procedure to synthesize combined modulation/error correcting trellis codes, suitable for Viterbi decoding. This synthesis is based on firstly selecting a suitable linear convolutional code, secondly by analysing the state system of this code to determine the important Hamming distance building properties, and finally by mapping a code with the desired restrictions on its sequences onto this state system. As an example we develop a R = 3/6 dc free (b,l,c) = (0,3,2) code withd_{min} = 4. This code improves on the best codes in [1]. Codes havingb geq 1, and which will thus be more suitable for magnetic recording, can also be synthesized following the proposed procedure.     

Multilayered linear dispersion codes for flat fading multiple-input multiple-output channels

The authors investigate the design of linear dispersion (LD) codes, aiming at flexible encoding schemes that allow various rate-performance tradeoffs under a common coding structure. First, the capacity of LD codes is studied. It is shown that the maximum attainable multiplexing gain of a linear dispersion code is the number of symbols per channel use of the code (i.e. coding rate in symbols). In addition, conditions on the construction of linear dispersion matrices for various multiplexing gains are established. A general multilayered linear dispersion coding scheme that allows various multiplexing gains is then proposed. In the proposed scheme, coding rate can be adapted by employing different numbers of dispersion matrices. Furthermore, phase shifting among input symbols is applied to optimise the error performance without loss of multiplexing gain. The construction of dispersion matrices and the optimisation of the phase shifts together constitute a structured approach for the design of linear dispersion codes. Simulation results demonstrate that the new codes outperform conventional LD codes at various data rates.     

A comprehensive reliability allocation method for design of CNC lathes

In the design and development of computerized numerical control lathes, an effective reliability allocation method is needed to allocate system level reliability requirements into subsystem and component levels. During the allocation process, many factors have to be considered. Some of these factors can be measured quantitatively while others have to be assessed qualitatively. In this paper, we consider seven criteria for conducting reliability allocation. A comprehensive failure rate allocation method is proposed for conducting the task of reliability allocation. Example data from field studies are used to illustrate the proposed method.     

Power optimised channel coding in wireless sensor networks using low-density parity-check codes

Energy consumption of low-density parity-check (LDPC) codes in different implementations is evaluated. Decoder's complexity is reduced by finite precision representation of messages, that is, quantised LDPC decoder, and replacement of function blocks with look-up tables. It is shown that the decoder's energy consumption increases exponentially with the number of quantisation bits. For the sake of low-power consumption, 3-bit magnitude and 1-sign bit representation for messages are used in the decoder. It is concluded that high-rate Gallager codes are as energy efficient as the Reed-Solomon codes, which till now have been the first choice for wireless sensor networks (WSNs). Finally, it is shown that using LDPC codes in WSNs can be justified even more by applying the idea of trading the transmitter power with the decoder energy consumption. By exploiting the trade-off inherent in iterative decoding, the network lifetime is increased up to four times with the 3-6 regular LDPC code. Hence, it is inferred that the LDPC codes are more efficient than the block and the convolutional codes.     

Weight distribution of turbo codes with convolutional interleavers

A simple algorithm for the weight calculation of turbo codes with convolutional interleavers is presented. For codes with short interleaver lengths, the weight distributions are computed using conventionally proposed methods and then utilised together with the interleaver properties to determine the weight specifications for the code with a longer desired length. Based on the calculated weights, a new upper bound for the code is computed. It agrees with simulation results of the code performance in the error-floor region     

Rational optimization of reliability and safety policies

Optimization of structures for design has a long history, including optimization using numerical methods and optimality criteria. Much of this work has considered a subset of the complete design optimization problem—that of the technical issues alone. The more general problem must consider also non-technical issues and, importantly, the interplay between them and the parameters which influence them. Optimization involves optimal setting of design or acceptance criteria and, separately, optimal design within the criteria. In the modern context of probability based design codes this requires probabilistic acceptance criteria. The determination of such criteria involves more than the nominal code failure probability approach used for design code formulation. A more general view must be taken and a clear distinction must be made between those matters covered by technical reliability and non-technical reliability. The present paper considers this issue and outlines a framework for rational optimization of structural and other systems given the socio-economic and political systems within which optimization must be performed.