Concatenated multilevel block coded modulation

Encoding and decoding schemes for concatenated multilevel block codes are presented. By one of these structures, a real coding gain of 5.6-7.4 dB for the bit error range of 10^-6 to 10^-9 is achieved for transmission through the additive white Gaussian noise channel. Also, a rather large asymptotic coding gain is obtained. The new coding schemes have very low decoding complexity and increased coding gain in comparison with the conventional block and trellis coded modulation structures. A few design rules for concatenated (single and) multilevel block codes with large coding gain are also provided     

Computing error probabilities of multilevel modulation codes

We describe a computational algorithm for the evaluation of error probabilities of multilevel modulation codes. This is based on the derivation of a trellis cataloging the words of the component codes and of a suitable set of branch labels depending on the channel on which the transmission takes place (additive white Gaussian noise channel, fading channel with or without channel state information). The error probability is upper bounded by the transfer function of this trellis, which is derived in closed form.     

On constructing embedded multilevel trellis codes

A design technique to reduce the search time for trellis codes with multilevel phase modulation is presented. Codes are constructed by connecting trellis diagrams for codes with fewer states in parallel. For example, an N-state code can be constructed by connecting two N/2-state codes. The way in which the embedded codes are connected increases the upper limit on minimum free distance otherwise imposed by parallel transitions between states. In some cases, this technique can reduce the number of codes in a code search by a factor of approximately 2^ν, the number of coder states. A computer search incorporating this technique for eight-level amplitude modulation (8-AM) codes having 2¹¹ and 2¹² states produced codes with greater minimum free distance than reported previously (i.e. greater than 6 dB coding gain). New eight-level phase-shift-keying (8-PSK) codes, which have a different structure from previously reported codes, are also presented     

空时分组码的自适应调制

本文讨论了空时分组码的自适应调制技术.在接收端分集合并后的等效信道模型下,通过对自适应STBC信道容量的讨论证明了随着天线数的增加,自适应调制的重要性降低.之后针对二发一收的低价分集系统,讨论了其STBC基础上的自适应调制技术,同时给出了离散功率离散速率自适应调制区间端点的封闭解.     

Combined coding and modulation using block codes

The author presents a combined coding and modulation scheme which at the same data rate and bandwidth as binary signalling gives considerable coding gains. The redundancy is packed entirely into the modulation scheme. As a further advantage, the synchronisation is very simple.<>     

On multilevel codes and iterative multistage decoding

This paper develops an approach to iterative multistage decoding of multilevel codes. This involves passing reliability information to previous and subsequent decoders instead of only hard decisions to subsequent decoders. The paper also develops an adaptive version of the suboptimal soft output decoding algorithm of Picart and Pyndiah (1996). This adaptive algorithm provides a gain of approximately 0.24 dB at a bit error rate (BER) of 10^-5 after four iterations and approximately 0.43 dB after ten iterations over the algorithm of Picart et al. If the adaptive algorithm is used in conjunction with iterative multistage decoding then a gain of approximately 0.62 dB is obtained at a BER of 10^-5 after four iterations and approximately 0.9 dB after ten iterations over the algorithm of Picart et al     

On the iterative decoding of multilevel codes

Iterative decoding of multilevel coded modulation is discussed. Despite its asymptotic optimality with proper design, the error correcting capability of multilevel codes may not be fully exploited for finite block length with conventional multistage decoding. This fact stems from the suboptimality of multistage decoding giving rise to increased error multiplicity at lower index stages and the associated error propagation to higher stages. Such problems can be overcome in many situations by introducing iterative decoding which often significantly compensates the suboptimality of a staged decoder. The class of multilevel codes achieving practically important bit-error performance near the Shannon limit becomes far wider with iterative decoding     

数字调幅广播中多级编码的译码方案

数字调幅广播采用了基于码率匹配的删除卷积码的多级编码调制技术,结合 OFDM信道估计,研究了其译码方案。提出基于软判决的并行译码、多级译码和迭代多级译码 3种译码方案,仿真了其在长、中、短波段各信道的性能。试验结果表明,迭代多级译码方案性 能最优,但从实现的复杂度和性能改善程度来看,在AWGN信道采用迭代多级译码方案,中短 波信道采用多级译码方案更合适。     

On binary sliding block codes

Sliding block codes are an intriguing alternative to the block codes used in the development of classical information theory. The fundamental analytical problem associated with the use of a sliding block code (SBC) for source encoding with respect to a fidelity criterion is that of determining the entropy of the coder output. Several methods of calculating and of bounding the output entropy of an SBC are presented. The local and global behaviors of a well-designed SBC also are discussed. The so-called "101-coder," which eliminates all the isolated zeros from a binary input, plays a central role. It not only provides a specific example for application of the techniques developed for calculating and bounding the output entropy, but also serves as a medium for obtaining indirect insight into the problem of characterizing a good SBC. An easily implementable SBC subclass is introduced in which the outputs can be calculated by simple logic circuitry. The study of this subclass is shown to be closely linked with the theory of algebraic group codes.     

On diagonal algebraic space-time block codes

Theoretical and practical aspects of diagonal algebraic space-time block codes over n transmit and m receive antennae are examined. These codes are obtained by sending a rotated version of the information symbols over the principal diagonal of the n /spl times/ n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two predecoding filters and two decoding algorithms are derived. Analysis of the information loss incurred by using the codes considered is used to clarify their structures, and the expected performances. Different algebraic real and complex rotations presented in the literature are analyzed and compared as regards the achieved coding gains, the complexities, performances, and peak-to-mean envelope power ratios.     

Construction of block modulation codes over rings for fading channels

A new methodology is described for construction of block coded modulation (BCM) over modulo-8 rings for fading channels. Code construction criteria are defined to obtain the maximum use of channel characteristics and to achieve the phase invariance property. Some code examples are presented.<>     

Joint design of block source codes and modulation signal sets

The problem of designing block source codes and modulation signal sets that are both energy and bandwidth constrained is considered. For the class of linear estimator-based decoders, necessary conditions for optimality for the encoder, decoder and modulation signal set are derived. An algorithm that iteratively solves these necessary conditions to converge to a locally optimum solution has been developed. By studying the performance of the previous class of digital communication systems in the limit of infinite encoding rates, it is demonstrated that the MSE of a bandwidth and energy constrained digital system is bounded from below by that of a block pulse amplitude modulation system. This bound is readily computable in terms of the eigenvalues of the source and channel covariance matrices. The results indicate that for a correlated source, a sufficiently noisy channel and specific source block sizes and bandwidths, the digital system performance coincides with the optimum performance theoretically attainable. Further, significant performance improvements over the standard VQ-based system are demonstrated when the channel is noisy     

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     

On coded modulation using LDPC convolutional codes

A new construction combining LDPC convolutional codes and multilevel coding/modulation is suggested and analyzed. In the case of QPSK, we demonstrate that it has a better performance than an LDPC convolutional code combined with conventional Gray mapping.     

On the error performance of multilevel block-coded modulation

Multidimensional multilevel block-coded modulation employing quadrature amplitude modulated constellations are considered. An approximation to their error performance is described and compared to simulation results, which show it to be a very good estimate at moderate to high signal-to-noise ratio. The effect of parallel transitions is considered and the tradeoff between distance and the error coefficient is explored     

On the construction of group block codes

We consider the construction of group block codes, i.e., subgroups of Gⁿ, the n-fold direct product of a group G. Two concepts are introduced that make this construction similar to that of codes over gf(2). The first concept is that of an indecomposable code. The second is that of a parity-check matrix. As a result, group block codes over a decomposable Abelian group of exponent d_m can be seen as block codes over the ring of residues modulo d_m, and their minimum Hamming distance can be easily determined. We also prove that, under certain technical conditions, (n, k) systematic group block codes over non-Abelian groups are asymptotically bad, in the sense that their minimum Hamming distance cannot exceed [n/k].     

On the weight distribution of linear block codes formed fromconvolutional codes

We explain how to obtain the weight enumerator and the performance of linear block codes formed in several distinct ways from a convolutional code     

Binary multilevel coset codes based on Reed-Muller codes

We study the construction and decoding of binary multilevel coset codes. This construction, originally introduced by Blokh and Zyablov in 1974 and by Zinov'ev in 1976, shows remarkable analogies with most recent schemes of coded modulations. Basic elements of the construction are an inner code, head of a partition chain having suitable distance properties, and a set of outer codes, generally nonbinary. For each partition level there is an outer code whose alphabet has the same order of the partition: in this way it is possible to associate every partition subset to a code symbol. It is well known that these codes can be efficiently decoded by the so called “multistage decoding.” We show that good codes (in terms of performance/complexity) can be constructed using Reed-Muller (RM) codes as inner codes. To this aim RM codes are revisited in the framework of the above construction and decoding techniques. In particular we describe a family of decoders for RM codes which include Forney's (1988) and Hemmati's (1989) decoders as special cases. Finally, we present some examples of efficient binary codes based on RM codes, and assess their performance via computer simulation     

On the decoder error probability of block codes

By using coding and combinational techniques, an explicit formula is derived which enumerates the complete weight distribution of decodable words of block codes using partially known weight distributions. Also, an approximation formula for nonbinary block codes is obtained. These results give exact and approximate expressions for the decoder error probability P_E(u) of block codes