A robust rate-adaptive hybrid ARQ scheme for frequency-hoppedspread-spectrum multiple-access communication systems

This paper considers the application of rate-adaptive coding (RAC) to a spread spectrum multiple access (SSMA) communication system. Specifically, RAC using a variable rate Reed-Solomon (RS) code with a single decoder is applied to frequency-hopped SSMA. We show that this combination can accommodate a larger number of users compared to that with conventional fixed-rate coding. This increase is a result of a reduction in the channel interference from other users. The penalty for this improvement in most cases is a slight increase in the delay (composed of propagation and decoding delay). The throughput and the undetected error probability for a M-ary symmetric channel are analyzed, and performance results are presented     

A transform decoder for Reed-Solomon codes in multiple-user communication systems

Encoding and decoding algorithms for Reed-Solomon codes based on Fourier-like transforms on finite field and finite rings are discussed. Classes of codes are proposed for two different types of multiple-user communication systems: a multichannel communication system and a multiaccess communication system. For the first system, a fast decoding algorithm is developed that uses transforms on a finite ring which is isomorphic to a direct sum of Galois fields. For the second system, an efficient (in terms of information rate) coding scheme is proposed which utilizes a direct sum of Galois fields.     

Burst-error-correcting algorithm for Reed-Solomon codes

A new decoding algorithm for burst-error-correction is proposed. The proposed algorithm can effectively correct burst errors of length approaching n-k symbols for (n, k) Reed-Solomon (RS) codes. Compared with existing algorithms, the algorithm enables much faster decoding with far less computational complexity     

VLSI implementation of Reed-Solomon encoder algorithm for communication systems

Reed Solomon codes are used to identify and correct data errors in transmission and storage systems. In this paper we designed a compact RS(255, 223) encoder structure based on analysis of the Reed-Solomon (RS) coding theory used in deep space communications. The encoder is implemented with 32 optimized finite multipliers, of which the redundant operations are reduced to minimize the number of modulo 2 additions or XOR gates based on analyzing the structure of multipliers in RS encoder that are simple and can ensure high speed operations. The simulation results show that the designed structure has advantages such as high efficiency and low complexity ensuring good coding performance.     

Very low rate convolution codes for maximum theoretical performanceof spread-spectrum multiple-access channels

A spread-spectrum multiple-access (SSMA) communication system is treated for which both spreading and error control is provided by binary PSK modulation with orthogonal convolution codes. Performance of spread-spectrum multiple access by a large number of users employing this type of coded modulation is determined in the presence of background Gaussian noise. With this approach and coordinated processing at a common receiver, it is shown that the aggregate data rate of all simultaneous users can approach the Shannon capacity of the Gaussian noise channel     

Trellis decoding of Reed-Solomon codes in low bit rate speechcommunications

The residual redundancy that persists in the transmitted parameters of a low bit rate speech coder are exploited to reduce the computational complexity of a Reed-Solomon (RS) trellis decoder. The use of RS codes for mobile telephony provides the opportunity for avoiding channel interleaving and so reduces one-way delay     

A burst-error-correcting algorithm for Reed-Solomon codes

It is known that for a burst-error environment, the error-correcting capability of Reed-Solomon codes can be extended beyond the Singleton bound with a high degree of confidence. This is significant in that an (n, k) code with an arbitrarily small probability of a miscorrection can correct more than (n- k)/2 errors. A decoding algorithm for correcting a burst of length greater than (n-k)/2 is presented     

Modified minimum-weight decoding for Reed-Solomon codes

The authors describe an improvement to the minimum-weight decoding (MWD) algorithm for Reed-Solomon (RS) codes. The modification improves the probability of the MWD algorithm `trapping' the error pattern by squaring each of the terms in the received codeword resulting in a transformation which changes the order of the symbols while maintaining the cyclic properties of the codeword. The results of computer simulations are presented which show that the modified decoder provides an improvement in error performance of ~1 dB over the conventional technique with no increase in decoder complexity. The results show that the modified technique achieves an error performance close to that of maximum-likelihood algorithms with ~1/6 the complexity     

A programmable decoder for Reed-Solomon codes

A programmable decoder for Reed-Solomon codes is described. The decoder is constructed using the Am2900 family of bit-slice elements and it is designed to perform error-correction erasure-filling decoding. The decoding rates obtained, lie in the range of 87 to 22 kilobits per second depending on the code and the error-erasure pattern encountered     

LOW RATE SPACE-TIME TRELLIS CODES INPOWER LIMITED WIRELESSCOMMUNICATION SYSTEMS

Space-time trellis codes can achieve the best tradeoff among bandwidth efficiency, diversity gain, constellation size and trellis complexity. In this paper, some optimum low rate space-time trellis codes are proposed. Performance analysis and simulation show that the low rate space-time trellis codes outperform space-time block codes concatenated with convolutional code at the same bandwidth efficiency, and are more suitable for the power limited wireless communication system.     

A new class of carrier-hopping codes for code-division multiple-access optical and wireless systems

Carrier-hopping codes, a collection of two-dimensional (2-D) patterns with good correlation properties, find applications in frequency-hopping code-division multiple-access (CDMA) wireless and wavelength-hopping CDMA fiber-optic systems. This kind of codes were usually designed under the assumptions that one pulse per row is used in the 2-D patterns and the number of available carriers is the same as code weight. While the assumptions restrict code cardinality, there are scenarios in which the number of available carriers is more than the actual number of carriers needed in the patterns. To provide flexible code design without these assumptions, this letter reports a new family of carrier-hopping codes with expanded cardinality, while maintaining ideal correlation properties. The cardinality of the new codes is shown to be asymptotically optimal.     

Modified time-domain algorithm for decoding Reed-Solomon codes

A technique for reducing the number of inversions in the time-domain decoding algorithm based on an algebraic decoder (Blahut's decoder) is introduced. It is proved that the modified algorithm is equivalent to the original one. The modified algorithm can be used in the universal Reed-Solomon decoder to decrease complexity     

Reed-Solomon codes for land mobile satellite channels

The performance of Reed-Solomon codes is determined for land mobile satellite communications where a shadowed Rician channel model is used. An effective coding/interleaving scheme is proposed which uses the multipath fading and shadowing statistics of the channel.<>     

Reed-Solomon codes for correcting phased error bursts

A code structure is introduced that represents a Reed-Solomon (RS) code in two-dimensional format. Based on this structure, a novel approach to multiple error burst correction using RS codes is proposed. For a model of phased error bursts, where each burst can affect one of the columns in a two-dimensional transmitted word, it is shown that the bursts can be corrected using a known multisequence shift-register synthesis algorithm. It is further shown that the resulting codes posses nearly optimal burst correction capability, under certain probability of decoding failure. Finally, low-complexity systematic encoding and syndrome computation algorithms for these codes are discussed. The proposed scheme may also find use in decoding of different coding schemes based on RS codes, such as product or concatenated codes.     

On decoding of Reed-Solomon codes

It is shown how nonsystematic Reed-Solomon (RS) codes encoded by means of the Chinese remainder theorem can be decoded using the Berlekamp algorithm. The Chien search and calculation of error values are not needed but are replaced by a polynomial division and added calculation in determining the syndrome. It is shown that for certain cases of low-rate RS codes, the total decoding computation may be less than the usual method used with cyclic codes. Encoding and decoding for shorter length codes is presented.     

High-speed decoder of Reed-Solomon codes

A high speed decoding algorithm using a modified step-by-step method for t-error-correcting Reed-Solomon codes is introduced. Based on this algorithm, a sequential decoder and a vector decoder are then proposed. These two decoders can be constructed by four basic modules: the syndrome calculation module, the comparison module, the decision module, and the shift-control module. These decoders can be applied for both binary and nonbinary data transmissions working at high data rate. Because of the simplicity in structure and circuit realization, a decoder employing this algorithm can be easily implemented in a monolithic chip by the VLSI technology     

Orthogonality of binary codes derived from Reed-Solomon codes

The author provides a simple method for determining the orthogonality of binary codes derived from Reed-Solomon codes and other cyclic codes of length 2^m-1 over GF(2^m) for m bits. Depending on the spectra of the codes, it is sufficient to test a small number of single-frequency pairs for orthogonality, and a pair of bases may be tested in each case simply by summing the appropriate powers of elements of the dual bases. This simple test can be used to find self-orthogonal codes. For even values of m, the author presents a technique that can be used to choose a basis that produces a self-orthogonal, doubly-even code in certain cases, particularly when m is highly composite. If m is a power of 2, this technique can be used to find self-dual bases for GF(2 ^m). Although the primary emphasis is on testing for self orthogonality, the fundamental theorems presented apply also to the orthogonality of two different codes     

一种适用于光通信系统中的QC-LDPC码的构造

为了满足快速发展的光通信系统不断扩大的需求 ,基于有限域的两个不同本原元提出了一种准循环低密度奇偶校 验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码的构造方法,构造的基矩阵 中不含4环,译码时纠错性能良好。将两 个本原元组合,通过调整基矩阵结构,使构造的码字最小距离增大,从而提升码字的纠错性 能。仿真结果表明:在相同 的仿真环境下,当误比特率(Bit Error Rate,BER)为10－6时 ,构造的码率为93.7%的QC-LDPC(3780540)码的净编码增益(Net Coding Gain,NCG)比同样是利用有限域本原元(Primitive Elements,PE)构造的PE-QC-L DPC(3780540)码,提高了0.38dB;同 时,与适用于光通信中利用有限域中两个不同子群(Sub-Groups,SG)构造的SG-QC-LDPC( 3780540)码和已广泛应用于光通 信的ITU-T G.975.1标准中的LDPC(32 640,30592)码相比,净编码增益 分别有0.2dB和0.72dB的提升。     

Generalized low-density parity-check codes for optical communication systems

This paper is concerned with investigating the performance of regular and irregular, randomlike and structured generalized low-density parity-check (GLDPC) codes for long-haul transmission. The proposed GLDPC codes outperform currently known turbo and low-density parity-check (LDPC) coding schemes with comparable parameters utilized in optical communication systems. For a GLDPC coding scheme with 23.6% redundancy, the largest so far reported coding gain of at least 11dB (at 40 Gb/s) is demonstrated.     

Double-weight signature pattern codes for multicore-fibercode-division multiple-access networks

To transmit digitized image pixels in optical code-division multiple-access (CDMA) networks with multicore fiber, classes of two-dimensional (2-D) patterns, so-called optical orthogonal signature pattern codes (OOSPCs), have previously been proposed. The new technology enables parallel transmission and simultaneous access of multiple 2-D images in multiple-access environments. In this letter, we construct two new families of “double-weight” OOSPCs without the assumption of identical weight for all signature patterns in a code set. Since the performance of a signature pattern varies with its weight, these new double-weight OOSPCs are especially useful for optical CDMA networks with multiple performance requirements