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.     

Distributed source coding using symbol-based and non-binary turbo codes - applications to wireless sensor networks

A simple but powerful scheme for distributed source coding (DSC) based on the concept of binning and syndromes and non traditional turbo codes is proposed. The previous works on the compression with side information using turbo codes and the binning technique are focused on binary turbo codes. The source is considered to be binary or is converted to a binary stream. This conversion, however, reduces the redundancy that could be exploited by the compression algorithm. To achieve higher compression efficiency, the authors propose using a scheme based on a turbo decoder that decides over symbols rather than bits. In the same direction and for further performance improvement, at the cost of increased encoder complexity, they also present a DSC scheme based on non-binary turbo codes. The results demonstrate improved performance. Based on the suggested algorithms, a scheme for gathering real data in wireless sensor networks and assess the corresponding energy savings is proposed.     

SISO algorithms based on Max-Log-MAP and Log-MAP turbo decoding

Novel soft-input soft-output (SISO) decoding algorithms suitable for turbo codes are proposed with good compromise between complexity and bit error rate (BER) performance. The algorithms are based on the application of the max/max* (i.e. Jacobian logarithm) operations at different levels when computing the decoder soft-output value. It is observed that some decoding schemes from the authors' previously published work fall into the family of methods described here. The effect is to provide a range of possibilities allowing system designers to make their own choices for turbo code BER performance against complexity     

Modified sum-product algorithms for decoding low-density parity-check codes

The authors deal with the sum-product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10^-6. Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly     

EXIT chart analysis of nonlinear turbo coding over GF(4)

The behaviour of nonlinear turbo codes that use nonlinear finite state sequential machines (FSSMs), designed over the finite field GF(4), as constituent encoders is studied. These FSSMs show a nonzero output for the all-zero input case. The state-transitions structure and the randomness of the output for the all-zero input response of these FSSMs are studied for different initial state conditions. A relationship is found between these two characteristics and the BER performance or, equivalently, the form of the extrinsic information transfer chart of the corresponding turbo code. It is found that FSSMs with responses of the form of long closed cycles, and good randomness properties of the corresponding output are the best options as constituent encoders of nonlinear turbo codes designed over GF(4). A coefficient called the random behaviour coefficient is defined, to provide a quantitative measure of the behaviour of these FSSMs as constituent encoders of a turbo code.     

极化码在OFDM水声通信中的应用研究

极化码(Polar code)因其高可靠性、实用的线性编、译码复杂度和理论上唯一可达香农极限等特点,成为信道编码领域新的研究热点.其编、译码方法的研究扩展至多种信道类型和应用领域,但在水声信道中的理论证明和应用研究相对较少且滞后.针对具有显著多途、多普勒扩散和有限带宽等复杂特性的水声信道,文章提出了与之相匹配的极化码信...     

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.     

Construction and performance analysis of 2-D codes for M-ary OFFH?CDMA systems

A new family of two-dimensional (2-D) codes constructed by combining frequency-hop and time-spreading codes is presented. The proposed codes are designed to overcome the limitation imposed on the maximum permissible number of simultaneous users in optical code-division multiple-access (OCDMA) systems. To increase the data transmission rate, the 2-D codes employ a M-ary signalling scheme. The proposed family of codes has the favourable characteristics of a zero autocorrelation constraint and a cross-correlation constraint of one. The performance of the 2-D code is analysed in terms of the bit error rate (BER) and is compared with that of a conventional OCDMA system using optical orthogonal code (OOC). The numerical and simulation results reveal that the proposed system outperforms conventional OCDMA systems both in terms of the BER and the data transmission rate. In addition, the system capacity is sufficient to ensure reliable communication (BERles10^-9) in local area networks     

Fast decoding of non-binary first order Reed-Muller codes

A minimum distance decoding algorithm for non-binary first order Reed-Muller codes is described. Suggested decoding is based on a generalization of the fast Hadamard transform to the non-binary case. We also propose a fast decoding algorithm for non-binary first order Reed-Muller codes with complexity proportional to the length of the code. This algorithm provides decoding within the limits guaranteed by the minimum distance of the code.Partly supported by the Guastallo Fellowship. This work was presented in part at the 9th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, New Orleans, USA, October 1991     

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     

Full-rate full-diversity space-time block codes for any odd number of transmit antennas

The authors propose a new class of space-time block codes (STBCs) achieving full-rate and full spatial diversity for general quadrature amplitude modulation (QAM) when using any odd number of transmit antennas under quasi-static Rayleigh fading channels. These codes are the extended works of the conventional Alamouti-ST constellation-rotating (CR) codes which are designed by serially concatenating CR precoders with the Alamouti scheme for an even number of transmit antennas. From the computer simulation results, it is observed that the best code in this class outperforms the existing ST-CR code and also exhibits error performance within only about 1-dB of the maximal ratio combining receiver. The codes possessing quasi-orthogonal (QO) characteristic are also included in this class, allowing simple maximum likelihood (ML) decoding with almost the same error performance as the best code in this class and the conventional QO-STBCs with full diveristy. These codes have identical or much lowered ML decoding complexity compared with the conventional QO-STBCs.     

迫零对Turbo码的性能影响

从距离谱的角度对迫零在Turbo码中的作用进行了理论分析。通过仿真，研究了迫零对Turbo码性能的影响。仿真结果表明，Turbo码编码器迫零处理有助于改善Turbo码的性能。     

Bounds and constructions of asymmetric or unidirectional error-correcting codes

Binary block codes for correctingt symmetric, asymmetric and unidirectional errors are calledt-SyEC codes,t-AsEC codes andt-UEC codes respectively. Two tables with bounds on the cardinality of binary block codes for correcting asymmetric and unidirectional errors respectively are presented. They include many improvements over the existing literature. The lower bounds follow from explicit constructions, while the upper bounds are obtained by applying combinatorial arguments to the weight structure of such codes.The authors are with Department of Mathematics and Computing Science of Eindhoven University of Technology, The Netherlands. Part of this work was presented at the IEEE International Symposium on Information Theory, Budapest, 1991     

Rate allocation for serial concatenated convolutional codes

The paper proposes an analytical method to solve the rate allocation problem in serial concatenated convolutional codes (SCCCs). The goal is to find the best rate allocation between the inner and the outer constituent convolutional codes of an SCCC for constant overall code rate, interleaver size and complexity. Simulation results are shown in the paper to demonstrate the optimum and superior design criteria. In addition, the `density evolution' model is shown to verify the proposed rate allocation method, while indicating that a high rate inner code should not be used for SCCCs. Finally, it is also shown that the upper bounds on BER of ML decoded SCCCs do not provide good design criteria for allocating the rate in iteratively decoded SCCCs     

Improved regular and semi-random rate-compatible low-density parity-check codes with short block lengths

Powerful rate-compatible codes are essential for achieving high throughput in hybrid automatic repeat request (ARQ) systems for networks utilising packet data transmission. The paper focuses on the construction of efficient rate-compatible low-density parity-check (RC-LDPC) codes over a wide range of rates. Two LDPC code families are considered; namely, regular LDPC codes which are known for good performance and low error floor, and semi-random LDPC codes which offer performance similar to regular LDPC codes with the additional property of linear-time encoding. An algorithm for the design of punctured regular RC-LDPC codes that have low error floor is presented. Furthermore, systematic algorithms for the construction of semi-random RC-LDPC codes are proposed based on puncturing and extending. The performance of a type-ll hybrid ARQ system employing the proposed RC-LDPC codes is investigated. Compared with existing hybrid ARQ systems based on regular LDPC codes, the proposed ARQ system based on semi-random LDPC codes offers the advantages of linear-time encoding and higher throughput.     

Low-density parity-check codes for volume holographic memory systems

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.     

Design and evaluation of a high data rate optical wireless system for the diffuse indoor channel using barker spreading codes and RAKE reception [optical wireless communications]

The performance of a high data rate optical wireless system (OWS) over the diffuse indoor infrared channel based on direct sequence spread spectrum (DSSS) techniques is highly sensitive to the properties of the aperiodic autocorrelation function and the spreading factor of the spreading sequence used. Ideally, the aperiodic autocorrelation function should have zero sidelobes in order to eliminate intersymbol interference caused by multipath propagation. In practice, such an ideal sequence does not exist in the binary field when data modulation is applied. For high data rates, a small spreading factor is desired in order to avoid an excessive system bandwidth. The family of Barker sequences is investigated in a DSSS-OWS. The Barker sequences are binary spreading sequences which exhibit small aperiodic autocorrelation values and short spreading factors. The system bit error rate (BER) performance is characterized on the diffuse indoor infrared channel when using RAKE reception. Results of BER against Eh/NQ are presented with data rate and spreading factor as parameters. The results demonstrate that of the seven Barker sequences existing, the length three Barker sequence {0 0 1} provides the best system design trade-off in respect of good BER performance and low implementation complexity.     

Performance of multiantenna multicarrier direct-sequence code division multiple access using orthogonal variable spreading factor codes-assisted space?time spreading in time-selective fading channels

A downlink (base-to-mobile) multicarrier direct-sequence code-division multiple-access (MC DS-CDMA) system employing multiple antennas at both the base station and each of the mobile terminals is investigated, when communicating over fast time-varying fading channels resulting in time-selective fading. In the considered multiantenna MC DS-CDMA, space-time spreading (STS) based on the family of orthogonal variable spreading factor (OVSF) codes is proposed in order to achieve the time diversity because of the time-selective fading, in addition to the transmit/receive diversity. In this contribution, the closed-form expressions for the single-user bit-error rate (BER) are derived, in order to gain insight into the achievable BER performance of the multiantenna MC DS-CDMA. The BER performance of the multiantenna MC DS-CDMA system is investigated, when communicating over correlated time-selective Rayleigh fading channels. The study and performance results show that the multiantenna MC DS-CDMA using OVSF codes-assisted STS constitutes a high-efficiency downlink space-time transmission scheme. It is capable of achieving the full diversity provided by the time- selective fading and multiple transmit/receive antennas. Furthermore, the proposed multiantenna MC DS-CDMA is capable of achieving a self-balance between the time diversity achieved and the multiuser interference suppression capability, when using low-complexity correlation detection.     

BER performance analysis of compound chaotic sequence (CCS)-based NR-DCSK system under multipath fading channel

This paper presents the performance analysis of compound chaotic sequence (CCS)-based noise reduction differential chaos shift keying (NR-DCSK) system under multipath Rayleigh fading channel conditions. The special characteristics of chaotic sequences are their deterministic randomness behaviour that adds security and multipath immunity to the data when used as a carrier in communication systems. In this paper, the chaotic sequences are generated by combining the outputs of chaotic maps, such as logistic map, Chebyshev map, Bernoulli shift map, tent map, etc., leading to new complex sequences known as CCSs. This sequence possesses more randomness, overcomes severe interference levels encountered during transmission and provides higher multipath immunity compared with those of pseudo-noise (PN) codes. Since NR-DCSK is a spread spectrum technique, its performance in wireless multipath fading channels has important considerations. The CCS is used as a carrier in NR-DCSK systems, which leads to improved bit error rate (BER) performance. Comparisons of simulation results to theoretical BER expressions of additive white Gaussian noise (AWGN) and Rayleigh fading channels have been carried out to test the efficiency of the proposed CCS-based NR-DCSK system.     

Adaptive code-division multiple-access system for communications over indoor wireless optical channels based on random optical codes

The authors have designed an adaptive optical codes-based system for communications over the indoor wireless optical channel when large numbers of users access to the channel simultaneously. This system uses a code-division multiple access (CDMA) scheme based on the named random optical codes (ROC). The authors present the characteristics of this kind of optical codes and several results about its performance over noisy indoor wireless optical channels. Finally, the authors describe a CDMA system which adapts its performance to the number of users which are accessing simultaneously to the channel. The proposed system is able to maintain a target bit error rate adapting its data throughput independently of the number of simultaneous users in the optical environment, whenever certain conditions are accomplished.