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.     

A cooperative turbo coding scheme for wireless fading channels

A coded cooperative transmission scheme based on turbo encoding/decoding, in which only newly generated parity bits of the partner are sent if the user successfully decodes its partner's information in order to improve bandwidth efficiency is proposed. The proposed encoding structure introduces correlation between users' data over multiple frames, which offers effectively longer codes and facilitates high-performance iterative multi-user decoding at the destination. Additionally, the iterative decoding over multiple frames can provide time diversity besides spatial diversity inherent in user cooperation even for flat block fading channels. Simulation results show that the proposed scheme significantly outperforms direct transmission for the same transmitted power and bandwidth efficiency.     

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.     

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.     

General differential modulation scheme for quasi-orthogonal space?time block codes with partial or full transmit diversity

A general and simple differential modulation scheme that can be applied to both partial-diversity quasi-orthogonal space-time block codes and full-diversity quasi-orthogonal space-time block codes is reported. A new class of quasi-orthogonal coding structures is presented for various number of transmit antennas. Differential encoding and decoding can be simplified to differential Alamouti codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. For the codes with partial transmit diversity, the new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition, it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low signal-to-nose ratio for current communication systems. For codes with full transmit diversity achieved by constellation rotation, the proposed scheme has performance equal to the best full-rate quasi-orthogonal schemes previously described in the literature with the benefit of a simpler detector. Moreover, a simple linear detector is also presented for the case when two orthogonal ASK constellations are used. Extension to more than four transmit antennas is also considered.     

Comprehensive partial decoding approach for two-level relay networks

Partial decoding scheme is a scheme in which each relay decodes only part of the transmitted message. Obviously, the achievable rates proposed by the partial decoding scheme subsume the achievable rates proposed by the full decoding scheme. The other motivation of using partial decoding scheme is that there are some special classes of relay networks such as semi-deterministic and orthogonal relay networks such that their capacities are obtained via this scheme. The authors propose a comprehensive partial decoding scheme based on regular encoding/sliding window decoding analysis to propose a new achievable rate for two-level relay networks. In contrast with the previously proposed methods, here the authors consider all possible partial decoding states that can occur between the different parts of the messages of the source and the relays in a two-level relay network. In this way, the common and private parts of the message transmitted by the source are defined to be decoded by the appropriate relays. Moreover, in the proof, the authors take advantage of regular encoding/sliding window decoding scheme that has superiorities to regular encoding/backward decoding and irregular encoding/random partitioning, in having less delay and yielding higher rates, respectively.     

Multitrack Digital Data Storage: A Reduced Complexity Architecture

We describe a low-complexity noniterative detector for magnetic and optical multitrack high-density data storage. The detector is based on the M-algorithm architecture. It performs limited breadth-first detection on the equivalent one-dimensional (1-D) channel obtained by column-by-column helical unwinding of the two-dimensional (2-D) channel. The detection performance is optimized by the use of a specific 2-D minimum-phase factorization of the channel impulse response by the equalizer. An optimized path selection scheme maintains the complexity close to practical 1-D Viterbi. This scheme is based on an approximate path metric parallel sort network, taking advantage of the metrics' residual ordering from previous M-algorithm iterations. Such an architecture approaches maximum-likelihood performance on a high areal density uncoded channel for a practical number of retained paths M and bit error rate (BER) below 10^-4. The performance of the system is evaluated when the channel is encoded with multi-parity check (MPC) block inner code and an outer interleaved Reed-Solomon code. The inner code enhances the minimum error distance of the equalized channel and reduces the correct path losses of the M-algorithm path buffer. The decoding is performed noniteratively. Here, we compare the performance of the system to the soft iterative joint decoding of the read channels for data pages encoded with low-density parity check (LDPC) codes with comparable rates and block length. We provide an approximation of the 2-D channel capacity to further assess the performance of the system     

Soft-decision array decoding for volume holographic memory systems

We study the use of soft-decision array decoding in a volume holographic memory (VHM) system that is corrupted by interpixel interference (IPI) and detector noise. Soft-decision methods can unify equalization and error decoding. A highly parallel array decoder is presented in the context of two-dimensional low-pass channel mitigation and error correction. The new decoding algorithm is motivated by iterative turbo-decoding methods and is capable of incorporating a priori knowledge of the corrupting IPI channel during decoding. The resulting joint detection decoding algorithm is shown to offer VHM capacity and density performance superior to that of hard-decision n = 255 Reed-Solomon codes in concatenation with a Wiener filter.     

基于比特可靠性的LDPC码编译码算法

提出了一种基于比特可靠性的低密度奇偶校验(LDPC)码编码算法和一种加权置信传播(BP)译码算法.该编码算法首先利用蒙特卡罗仿真得到LDPC码各个比特节点的出错概率,然后用已知信息替换易出错比特节点进行编码;该译码算法根据比特节点可靠性的差异,在译码时为每个比特节点赋予相应的权值,以调整它们对译码的影响程度.仿真表明,新的编译码算法使得系统性能大大提高,同时加快了译码迭代收敛速度.     

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.     

Viterbi decoding and the power spectral densities of some rate one half binary DC free modulation codes

The Hamming distance properties are investigated, and some experimental results obtained with the following R = 1/2 binary dc free modulation codes are presented: the (b, l, C) = (1, 5, 3) Miller²code and codes with (b, l, C), respectively, (1, 4, 3), (0, 3, 3), and (0, 1, 2). A R = 3/6, (b, l, C) = (0, 3, 2) combined error-correcting/ modulation code is also investigated. State systems, power spectral densities, and the bit error rates after computer simulated decoding of these codes on both the binary symmetric channel and a burst erasure channel are presented.     

水声通信系统中分布式空时分组码的研究

协作传输可以获得无线信道内在的空间分集,有效改善通信系统的性能,增加通信系统的覆盖范围。对水声通信系统中两中继节点协作的译码转发方案进行了研究,提出了基于译码转发协议(DF)的分布式空时分组扩频编码(DSTBSC)方案,该方案可以克服多径衰落对分布式空时分组码(DSTBC)信号正交性的影响。给出了DSTBSC方案的系统模型,着重分析了在采用两中继译码转发时,中继节点的误码对水声通信系统性能的影响。在接收端不考虑信号冲突的情况进行仿真,结果表明,与直接传输方案相比,采用两中继节点、译码转发的DSTBSC方案,在两中继节点处均无误码和一个中继有误码时在相同的比特误码率(BER)条件下均可获得约4dB的分集增益,增加了传输距离。     

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.     

Improved low-complexity low-density parity-check decoding

A practical low-complexity decoding of low-density parity-check codes is studied. A fast decoding scheme for weighted bit-flipping (WBF) based algorithms is first proposed. Then, an optimised 2 bit decoding scheme and its VLSI architecture are presented. It is shown that the new approach has significantly better decoding performance while having comparable hardware complexity compared with WBF-based algorithms.     

Analysis of error-correction constraints in an optical disk

The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.     

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed–Solomon code against a decoding algorithm of a Reed–Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed–Solomon codes and show that performance is somewhat better than our estimates.     

Improved Identification Schemes Based on Error-Correcting Codes

As it is often the case in public-key cryptography, the first practical identification schemes were based on hard problems from number theory (factoring, discrete logarithms). The security of the proposed scheme depends on an NP-complete problem from the theory of error correcting codes:the syndrome decoding problem which relies on the hardness of decoding a binary word of given weight and given syndrome. Starting from Stern’s scheme [18], we define a dual version which, unlike the other schemes based on the SD problem, uses a generator matrix of a random linear binary code. This allows, among other things, an improvement of the transmission rate with regards to the other schemes. Finally, by using techniques of computation in a finite field, we show how it is possible to considerably reduce: — the complexity of the computations done by the prover (which is usually a portable device with a limited computing power), — the size of the data stored by the latter. Received March 10, 1995; revised version December 1, 1995     

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.     

Decoding of the (24, 12, 8) extended golay code up to four errors

A new decoder is proposed to decode the (24, 12, 8) binary extended Golay code up to four errors. It consists of the conventional hard decoder for correcting up to three errors, the detection algorithm for four errors and the soft decoding for four errors. For a weight-4 error in a received 24-bit word, Method 1 or 2 is developed to determine all six possible error patterns. The emblematic probability value of each error pattern is then defined as the product of four individual bit-error probabilities corresponding to the locations of the four errors. The most likely one among these six error patterns is obtained by choosing the maximum of the emblematic probability values of all possible error patterns. Finally, simulation results of this decoder in additive white Gaussian noise show that at least 93% and 99% of weight-4 error patterns that occur are corrected if the two E/sub b//N/sub 0/ ratios are greater than 2 and 5 dB, respectively. Consequently, the proposed method can achieve a better percentage of successful decoding for four errors at variable signal-to-noise ratios than Lu et al.?s algorithm in software. However, the speed of the method is slower than Lu et al.?s algorithm.     

Performance of Reed?Solomon codes using the Guruswami?Sudan algorithm with improved interpolation efficiency

List decoding is a novel method for decoding Reed-Solomon (RS) codes that generates a list of candidate transmitted messages instead of one unique message as with conventional algebraic decoding, making it possible to correct more errors. The Guruswami-Sudan (GS) algorithm is the most efficient list decoding algorithm for RS codes. Until recently only a few papers in the literature suggested practical methods to implement the key steps (interpolation and factorisation) of the GS algorithm that make the list decoding of RS codes feasible. However, the algorithm's high decoding complexity is unsolved and a novel complexity-reduced modification to improve its efficiency is presented. A detailed explanation of the GS algorithm with the complexity-reduced modification is given with simulation results of RS codes for different list decoding parameters over the AWGN and Rayleigh fading channels. A complexity analysis is presented comparing the GS algorithm with our modified GS algorithm, showing the modification can reduce complexity significantly in low error weight situations. Simulation results using the modified GS algorithm show larger coding gains for RS codes with lower code rates, with more significant gains being achieved over the Rayleigh fading channels.