A class of DC-free subcodes of convolutional codes

We describe a class of DC-free subcodes of convolutional codes that satisfy certain runlength constraints and that also possess error-correcting capability. The running disparity and the maximum runlength of these codes are bounded by quantities that are independent of the free distance. They can be decoded using a Viterbi decoder for the underlying convolutional code     

DC-free error-correcting convolutional codes [comment and reply]

In a recent Letter, Deng et. al. (see ibid., vol.29, no.22, pp.1910-1911, 1993) reported a new class of convolutional codes which have both DC-free and error-correcting properties. The presented codes have a null at DC. However, there are some flaws in these codes. When encoding the information sequence with controlling the polarity of disparity d(t) of the codeword, the decoded sequence is different from the information sequence despite the error free condition. We show this by an example. A reply by Deng and Li is included     

A simple strategy for constructing a class of DC-freeerror-correcting codes with minimum distance 4

A class of DC-free codes with minimum distance 4 which offer very simple encoding and decoding procedures is presented. Spectral analysis shows that in addition to being DC-free they offer strong spectral suppression at low frequencies. A comparison with similar codes in the literature shows that they provide a good compromise solution to the design of practically realizable, high-rate, DC-free error-correcting codes with strong low frequency suppression     

A further note on DC-free coset codes

The procedure introduced by R.H. Deng and M.A. Herro (see ibid., vol.IT-34, p.786-92, 1988) for identifying DC-free codes is considered further. Certain of the detailed statements relating to disparity and runlength are corrected and/or refined. While this is considered important for a proper interpretation of the codes and encoding procedure it is emphasized that it in no way detracts from the usefulness of the general algorithmic approach for producing these codes     

On detection of a class of synchronization errors (Corresp.)

A class of synchronization errors is defined and sufficient conditions are presented for synchronization error detection with a binary linear coset code. Some cyclic coset codes are proposed and their detecting capabilities are analyzed. Some previous results obtained for different kinds of synchronization errors are presented as particular cases.     

Generalized algorithm for design of DC-free codes based onmultilevel partition chain

A generalized algorithm for design of DC-free codes based on the multilevel partition chain is presented. The multilevel partition chain is formed from the code partition chain of Reed-Muller codes. Some parameters such as the maximum runlength and running digital sum (RDS) of DC-free codes are also obtained. The results show that the DC-free codes obtained by the presented design algorithm have good coding parameters     

Soft trellis-based decoder for linear block codes

A systematic design of a trellis-based maximum-likelihood soft-decision decoder for linear block codes is presented. The essence of the decoder is to apply an efficient search algorithm for the error pattern on a reduced trellis representation of a certain coset. Rather than other efficient decoding algorithms, the proposed decoder is systematically designed for long codes, as well as for short codes. Computational gain of up to 6 is achieved for long high-rate codes over the well-known trellis decoder of Wolf (1978). Efficient decoders are also obtained for short and moderate length codes     

Discrete multiple tone modulation with coset coding for thespectrally shaped channel

A discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample. This discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes     

DC-free error-control block codes

DC-free codes and error-control (EC) codes are widely used in digital transmission and storage systems. To improve system performance in terms of code rate, bit-error rate (BER), and low-frequency suppression, and to provide a flexible tradeoff between these parameters, this paper introduces a new class of codes with both dc-control and EC capability. The new codes integrate dc-free encoding and EC encoding, and are decoded by first applying standard EC decoding techniques prior to dc-free decoding, thereby avoiding the drawbacks that arise when dc-free decoding precedes EC decoding. The dc-free code property is introduced into standard EC codes through multimode coding techniques, at the cost of minor loss in BER performance on the additive white Gaussian noise channel, and some increase in implementation complexity, particularly at the encoder. This paper demonstrates that a wide variety of EC block codes can be integrated into this dc-free coding structure, including binary cyclic codes, binary primitive BCH codes, Reed-Solomon codes, Reed-Muller codes, and some capacity-approaching EC block codes, such as low-density parity-check codes and product codes with iterative decoding. Performance of the new dc-free EC block codes is presented.     

DC-free codes of rate (n-1)/n, n odd

We report on a new class of DC-free codes of rate (n-1)/n, odd. The spectral and runlength properties of the new codes have been evaluated by computer simulation     

Sphere-bound-achieving coset codes and multilevel coset codes

A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory     

Maximum likelihood soft decoding of binary block codes and decodersfor the Golay codes

Maximum-likelihood soft-decision decoding of linear block codes is addressed. A binary multiple-check generalization of the Wagner rule is presented, and two methods for its implementation, one of which resembles the suboptimal Forney-Chase algorithms, are described. Besides efficient soft decoding of small codes, the generalized rule enables utilization of subspaces of a wide variety, thereby yielding maximum-likelihood decoders with substantially reduced computational complexity for some larger binary codes. More sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the (24, 12) Golay code, yielding a computational gain factor of about 2 with respect to previous methods. A ternary single-check version of the Wagner rule is applied for efficient soft decoding of the (12, 6) ternary Golay code     

Vector coding for partial response channels

A linear technique for combining equalization and coset codes on partial response channels with additive white Gaussian noise is developed. The technique, vector coding, uses a set of transmit filters or `vectors' to partition the channel into an independent set of parallel intersymbol interference (ISI)-free channels for any given finite (or infinite) block length. The optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length, and the gains of the individual channels are the eigenvalues. An optimal bit allocation and energy distribution, are derived for the set of parallel channels, under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions. Examples are presented that demonstrate performance advantages with respect to zero-forcing decision feedback methods that use the same coset code on the same partial response channel. Only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system     

Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b ⩾1 length 2n+2r(d-1) for d⩽3 and length 2n+2r(d-1)(2d -1) for d>3, where r is the least integer ⩾log₂ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2²¹ codewords. A construction is presented for which from a given code C ₁ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C₂, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed     

高斯Wiretap模型下基于部分陪集的无线物理层强安全编码

针对无线物理层安全编码不能保证信息在有噪信道下进行强安全传输的问题,该文提出一种基于部分陪集的强安全编码方法。首先证明了当且仅当陪集母码的对偶码的最小汉明距离大于信息泄露位数时,利用部分陪集编码能够保证信息的强安全传输;然后证明了陪集编码的一系列性质,基于这些性质可以将陪集间最小汉明距离计算降低为1次查表运算,进而设计了一种基于树形深度优先的最大可用陪集集合搜索算法;最后分析得出一些典型线性分组码的抗窃听信道信息泄露和抗合法信道传输噪声的能力,以及相应的最大可用陪集集合。当陪集母码为BCH(15,11)的对偶码时,与传统陪集编码方案相比,该方法对合法信道的信道质量要求降低了5 dB,同时能够保证信息传输的强安全性。     

On covering radii and coset weight distributions of extremal binaryself-dual codes of length 56

We present a method to determine the complete coset weight distributions of doubly even binary self-dual extremal [56, 28, 12] codes. The most important steps are (1) to describe the shape of the basis for the linear space of rigid Jacobi polynomials associated with such codes in each index i, (2) to describe the basis polynomials for the coset weight enumerators of the assigned coset weight i by means of rigid Jacobi polynomials of index i. The multiplicity of the cosets of weight i have a connection with the frequency of the rigid reference binary vectors v of weight i for the Jacobi polynomials. This information is sufficient to determine the complete coset weight distributions. Determination of the covering radius of the codes is an immediate consequence of this method. One important practical advantage of this method is that it is enough to get information on 8190 codewords of weight 12 (minimal-weight words) in each such code for computing every necessary information     

DSC的超光谱图像无损压缩算法

有效的星载超光谱图像压缩技术对于解决超光谱图像实时传输极为重要。针对超光谱图像传统的联合编解码算法的不足,提出了一种基于分布式信源编码(Distributed Source Coding,DSC)的超光谱图像无损压缩算法。为利用超光谱图像的局部空间相关性,将超光谱图像进行分块处理;引入多元线性回归模型构建编码块的边信息,并为每个编码块选取最优的预测阶数,以有效利用超光谱图像的局部谱间相关性。根据(n,k)线性分组码的原理,通过多元陪集码实现超光谱图像的分布式无损压缩。实验结果表明:该算法能够取得较好的无损压缩性能,同时具有较低的编码复杂度,适合星载超光谱图像的压缩实现。     

Partitioned linear block codes for computer memory with 'stuck-at' defects

Linear block codes are studied for improving the reliability of message storage in computer memory with stuck-at defects and noise. The case when the side information about the state of the defects is available to the decoder or to the encoder is considered. In the former case, stuck-at cells act as erasures so that techniques for decoding linear block codes for erasures and errors can be directly applied. We concentrate on the complimentary problem of incorporating stuck-at information in the encoding of linear block codes. An algebraic model for stuck-at defects and additive errors is presented. The notion of a "partitioned" linear block code is introduced to mask defects known at the encoder and to correct random errors at the decoder. The defect and error correction capability of partitioned linear block codes is characterized in terms of minimum distances. A class of partitioned cyclic codes is introduced. A BCH-type bound for these cyclic codes is derived and employed to construct partitioned linear block codes with specified bounds on the minimum distances. Finally, a probabilistic model for the generation of stuck-at cells is presented. It is shown that partitioned linear block codes achieve the Shannon capacity for a computer memory with symmetric defects and errors.     

DC-free error-correcting codes based on convolutional codes

A new construction of direct current (DC)-free error-correcting codes based on convolutional codes is proposed. The new code is constructed by selecting a proper subcode from a convolutional code composed of two different component codes. The encoder employs a Viterbi algorithm as the codeword selector so that the selected code sequences satisfy the DC constraint. A lower bound on the free distance of such codes is proposed, and a procedure for obtaining this bound is presented. A sufficient condition for these codes to have a bounded running digital sum (RDS) is proposed. Under the assumption of a simplified codeword selection algorithm, we present an upper bound on the maximum absolute value of the RDS and derive the sum variance for a given code. A new construction of standard DC-free codes, i.e., DC-free codes without error-correcting capability, is also proposed. These codes have the property that the decoder can be implemented by simple symbol-by-symbol hard decisions. Finally, under the new construction, we propose several codes that are suitable for the systems that require small sum variance and good error-correction capability     

Jacobi polynomials for singly even self-dual codes and the coveringradius problems

In this correspondence, we develop a method to determine the complete coset weight distributions of the class of singly even self-dual binary codes. Our basic tool is the Jacobi polynomials for the code. It describes and controls the coset weight enumerators. As the results of our present method, we give the complete coset weight distributions of some extremal singly even self-dual codes of lengths 14, 22, 32, 36, and 40, respectively. We give the generator matrices of the used codes of lengths 36 and 40, respectively