Design and performance of block-coded modulation for digitalmicrowave radio systems

Two block-coded modulation (BCM) families particularly suited for high-capacity digital microwave radio systems are presented. The first family is based on one-step partitioning, and the second family is based on two-step partitioning of the signal constellation. The alphabet expansion is a decreasing function of the block length, and the constellation is constructed in such a way as to minimize both the average and peak signal powers. Using short block lengths, specific modulation schemes are described that transmit 4, 6, and 8 information bits per symbol. The asymptotic coding gain is only on the order of 2 dB in the first family, and of 3 dB in the second family, but their detection simplicity makes the presented BCM schemes particularly attractive for high-speed applications where trellis-coded modulation (TCM) decoders may be difficult to implement     

Six-dimensional trellis-coding with QAM signal sets

A family of 6-D trellis-coded modulation (TCM) schemes which involve a 2-step partitioning of the constituent QAM signal alphabet is presented. With infinite constellations without shaping, the asymptotic coding gain is 3 dB for the 2-state code, 4 dB for the 4- and 8-state codes, and 5 dB for the 16- and 32-state codes which involve a smaller alphabet expansion. The authors also describe a rotationally invariant 16-state code that achieves the same asymptotic gain as its linear counterpart. Practical signal constellations are described for 6-D TCM with the spectral efficiency of uncoded 64-QAM, and the performance of these schemes is studied by means of computer simulations. It was found that they achieve an additional coding gain of 0.2-0.3 dB over infinite hypercube-type constellations. The performance of the presented schemes at practical signal-to-noise ratio values is evaluated using transfer function techniques     

Multidimensional constellations. I. Introduction, figures of merit,and generalized cross constellations

The authors discuss the major attributes desired in signal constellations, such as signal-to-noise ratio (SNR) efficiency, simplicity of mapping bits to points and vice versa, compatibility with coded modulation schemes, and compatibility with quadrature amplitude modulation (QAM). The capability of supporting a so-called opportunistic secondary channel, often used for internal control signaling, is considered. The gain in SNR efficiency of a multidimensional constellation (lattice code) consisting of the points from a lattice Λ within a region R compared to a cubic constellation is shown to be approximately separable into the coding gain of Λ and the shape gain of R, for large constellations. Similarly, the expansion of the associated constituent 2-D constellation is shown to be approximately separable into a constellation expansion ratio (CER) coding component CER_c(Λ) and a shaping component CER _s(R). The N sphere is the region R with the best shape gain, but N also has large constellation expansion. Bounds for the best possible shape gain versus CER_s(R) or peak-to-average-power ratio (PAR) are given. Generalized cross constellations are discussed. These constellations yield a modest shape gain with very low CER_s(R) or PAR, are easily implemented, are well suited for use with coded QAM modems, and can be readily adapted to support an opportunistic secondary channel     

Block versus trellis: an introduction to coded modulation

Coded modulation has had a very significant impact on the communications scene in the decade or so since its introduction, finding practical applications from voice-band modems for telephone lines to deep-space communications. The paper introduces the principles of coded modulation and describes the two main schemes: block coded modulation (BCM) and trellis coded modulation (TCM). In particular it considers the argument between the proponents of BCM and TCM, and points out some pitfalls in the use of performance measures such as asymptotic coding gain for these schemes. It concludes that in terms of performance versus decoder complexity the schemes seem to be quite close, and the choice of the system designer may be determined by other factors     

Nonequiprobable signaling on the Gaussian channel

Signaling schemes for the Gaussian channel based on finite-dimensional lattices are considered. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. Spherical signal constellations minimize average signal power, and in the limit as N →∞, the shape gain of the N-sphere over the N-cube approaches πe/6≈1.53 dB. A nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension. A signal constellation, Ω is partitioned into T subconstellations Ω₀ , . . ., Ω_τ-1 of equal size by scaling a basic region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellation Ω_i with frequency f_i. Shaping codes make it possible to achieve any desired fractional bit rate. The schemes presented are compared with equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. For comparable shape gain and constellation expansion ratio, the peak to average power ratio of the schemes presented is superior. Furthermore, a simple table lookup is all that is required to address points in the constellations. It is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework     

Near-capacity coding in multicarrier modulation systems

We apply irregular low-density parity-check (LDPC) codes to the design of multilevel coded quadrature amplitude modulation (QAM) schemes for application in discrete multitone systems in frequency-selective channels. A combined Gray/Ungerboeck scheme is used to label each QAM constellation. The Gray-labeled bits are protected using an irregular LDPC code with iterative soft-decision decoding, while other bits are protected using a high-rate Reed-Solomon code with hard-decision decoding (or are left uncoded). The rate of the LDPC code is selected by analyzing the capacity of the channel seen by the Gray-labeled bits and is made adaptive by selective concatenation with an inner repetition code. Using a practical bit-loading algorithm, we apply this coding scheme to an ensemble of frequency-selective channels with Gaussian noise. Over a large number of channel realizations, this coding scheme provides an average effective coding gain of more than 7.5 dB at a bit-error rate of 10/sup -7/ and a block length of approximately 10/sup 5/ b. This represents a gap of approximately 2.3 dB from the Shannon limit of the additive white Gaussian noise channel, which could be closed to within 0.8-1.2 dB using constellation shaping.     

基于非编码信息匹配的自适应Turbo TCM编码调制方案

本文提出了一种通过调整非编码信息量,并与信号映射相结合来改变编码、调制模式的自适应Turbo TCM编码调制方案,称之为基于非编码信息匹配的自适应Turbo TCM编码调制方案.由于将Turbo码和TCM编码调制技术相结合得到的Turbo TCM编码调制方案的带宽效率高,所以,在慢时变无线衰落信道中,自适应Turbo TCM编码调制的平均频谱效率也将很高.给出了该方案的工作原理、设计方法,并通过蒙特卡洛(Monte Carlo)仿真研究了该方案的性能.与现有编码调制方案相比,该方案具有频谱效率高、易于设计和实现的优点.     

Lattice codes for amplified direct-detection optical systems

Theories of shaping for lattice codes have been developed for systems (optical or non-optical) using coherent detection with additive white Gaussian noise (AWGN) and for direct-detection optical systems with AWGN. This paper considers shaping for amplified direct-detection optical systems in which signal-spontaneous beat noise, a form of signal-dependent noise, is dominant. An A-dimensional (A-D) signal is formed by modulating the intensities(squares of field magnitudes) of a sequence of N time-disjoint pulses. In field magnitude coordinates, signal energy is represented by a L² norm, and the optimal constellation bounding region is the nonnegative orthant bounded by an N-sphere. Under a continuous approximation, as Nrarrinfin, the ultimate shape gain is 1.53 dB and the induced signaling distribution on the constituent 1-D constellation becomes half- Gaussian. In practice, the ultimate shape gain can be approached when the 1-D constellation follows a truncated half-Gaussian distribution. We investigate the tradeoffs between shape gain and increases in constellation expansion ratio or peak-to-average power ratio. We compare our shaping results with those for coherent detection systems and direct-detection optical systems with AWGN.     

一种新颖的两天线差分空时分组编码方案

传统的差分空时分组编码（DSTBC）在QPSK调制时存在着信号星座扩展．文中提出了一种在QPSK调制下新颖的两发射天线差分空时分组编码方案，此方案提供了一定的编码增益，同时也解决了星座扩展问题．在新方案中，改进了从信息块到系数矢量的映射，从而使其性能与相干空时分组编码相比大约只差1dB。同时新方案编码相对简单，在接收端也具有低的解码复杂度．     

An eight-dimensional 64-state trellis code for transmitting 4 bitsper 2-D symbol

An eight-dimensional, 64-state, 90° rotationally invariant trellis code for transmitting 4 bits/baud over a bandlimited channel is described. The 2-D constellation contains 20 points. The code achieves a 5.23-dB coding gain over the uncoded 4×4 QAM (quadrature amplitude modulation) constellation and a 1.23-dB gain over the standard CCITT V32 trellis code. Simulation results are presented that verify these coding gains. Simulation results showing symbol error probability versus signal/noise ratio and trellis depth are also presented     

Bit-interleaved coded modulation with iterative decoding using constellation shaping over Rayleigh fading channels

We propose to investigate the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) over Rayleigh fading channel by using constellation shaping (CS). The (CS) is implemented by inserting shaping block codes between mapping and channel coding functions, in order to generate non-equiprobable distribution of a 16-ary QAM signal constellation. Simulation results carried out on 2-bit/s/Hz 16-QAM BICM-ID indicate that is possible to obtain a gain of 1.2 dB at a BER of 10^-3 compared to the equiprobable 16-QAM BICM-ID schemes. It is also shown that, the error floor level can reduced by applying the signal space diversity technique.     

Performance analysis of stack decoding on block coded modulation schemes using tree diagram

The channel encoder adds redundancy in a structured way to provide error control capability. Modulator converts the symbol sequences from the channel encoder into waveforms which are then transmitted over the channel. Usually channel coder and modulator are implemented independently one after the other. But in a band limited channel better coding gains without sacrificing signal power are achieved when coding is combined with modulation. Block Coded Modulation (BCM) is such a scheme that results from the combination of linear block codes and modulation. In this paper we are proposing a stack decoding of rate 2/3 and rate 1/2 BCM schemes using tree structure and performance is compared with the Viterbi decoding that uses trellis representation. Simulation result shows that at reasonable bit error rate stack decoder performance is just 0.2 to 0.5 dB inferior to that of Viterbi decoding. Since stack decoding is a near optimum decoding scheme and whose decoding procedure is adaptable to noise level, we can consider this method in place of Viterbi decoding which is optimum and its decoding complexity grows exponentially with large code lengths.     

On block-coded modulation with interblock memory

Block-coded modulation with interblock memory (BCMIM) is a variation of block-coded modulation (BCM) which is designed for multilevel coding. By providing interblock memory between adjacent blocks, the coding rate of a BCMIM scheme can be increased without decreasing the minimum squared Euclidean distance (MSED) as compared to the original BCM. In an early version of BCMIM, interblock coding is provided only between the first two coding levels of adjacent blocks. In this paper, we design BCMIM with a more general form for which interblock coding can be introduced among many coding levels. In this way, we can further increase the coding rate of BCMIM without decreasing the MSED. We provide many examples to show the advantages of BCMIM with the general form. Most of the examples are designed based on multidimensional signal sets, since a multidimensional signal set can provide more coding levels than a two-dimensional (2-D) signal set     

一种用于BICM-ID系统的新颖8APSK映射方案

为了能够通过高阶调制信号增加信道容量,提高编码增益和频谱效率,对8阶振幅移相键控(APSK)星座映射方案进行优化.基于欧氏距离设计准则提出一种新颖(2,6)-scheme 8APSK映射方案,并应用于联合准循环构造法构造的低密度奇偶校验(LDPC)(4599,4307)码的比特交织编码调制迭代译码(BICM-ID)系统中.信道容量仿真表明,所提方案在高、低信噪比区域都具有非常优越的互信息性能.误码率(BER)性能仿真表明,在BER为10-7时,联合LDPC(4599,4307)码的(2,6)-scheme 8APSK映射方案较(4,4)-scheme 8APSK映射方案、8PSK调制的格雷(Gray)映射、集分割(SP)映射、半集分割(SSP)映射分别提高了约0.45 dB、1.10 dB、1.62 dB、2.13 dB的编码增益.外附信息转移(EXIT)图仿真说明,所提方案能够更早地打开译码通道,从而更早地通过迭代来实现无错译码.     

TCM schemes with partially overlapped signal constellations

In conventional TCM schemes, for a rate of n bits per channel symbol, a 2ⁿ⁺¹-point constellation is used. It is shown that using constellations with less than 2ⁿ⁺¹-points, one can achieve a considerable coding gain in comparison to the traditional 2ⁿ⁺¹-point constellation. The increase in coding gain is due to a reduction in transmitted signal energy as a result of deleting some high-power signals from the original constellation and reusing of some of the low-power signals instead     

Error Performance of Rotated Phase Shift Keying Modulation over Fading Channels

In this paper, the modulation diversity is used to improve the performance of M-PSK modulation over fading channels. Modulation diversity can be achieved by rotating the signal constellation and using component interleaving. We derive symbol error probability expressions for rotated uncoded M-PSK over Ricean fading channels and obtain optimal rotation angles for M-PSK (M = 2, 4, 8). We show that rotated signal constellations with component interleaving improve the performance of M-PSK significantly as compared to the unrotated one over Rayleigh and Ricean fading channels. For example, when the ratio of the direct path power to the multipath signal power, K is 0 and 10, 8 and 1.5 dB gains are obtained, respectively, at a symbol error probability of 10⁻³ for 8PSK modulation. We also show that as K gets larger, the gain obtained by the rotation rapidly decreases. We develop a new asymmetric 8PSK signal constellation obtained from two QPSK signal constellations that are optimally rotated by different angles. This asymmetric 8PSK and also the rotated 8PSK signal constellation together with component interleaving are applied to four-state trellis-coded schemes. Simulation results show that these new schemes provide good performance improvements over the original TCM schemes and previous relevant works over Rayleigh and Ricean fading channels.     

Sequence MAP decoding of trellis codes for Gaussian and Rayleighchannels

This paper considers the use of sequence maximum a posteriori (MAP) decoding of trellis codes. A MAP receiver can exploit any “residual redundancy” that may exist in the channel encoded signal in the form of memory and/or a nonuniform distribution, thereby providing enhanced performance over very noisy channels, relative to maximum likelihood (ML) decoding. The paper begins with a first-order two-state Markov model for the channel encoder input. A variety of different systems with different source parameters, different modulation schemes, and different encoder complexities are simulated. Sequence MAP decoding is shown to substantially improve performance under very noisy channel conditions for systems with low-to-moderate redundancy, with relative gain increasing as the rate increases. As a result, coding schemes with multidimensional constellations are shown to have higher MAP gains than comparable schemes with two-dimensional (2-D) constellations. The second part of the paper considers trellis encoding of the code-excited linear predictive (CELP) speech coder's line spectral parameters (LSPs) with four-dimensional (4-D) QPSK modulation. Two source LSP models are used. One assumes only intraframe correlation of LSPs while the second one models both intraframe and interframe correlation. MAP decoding gains (over ML decoding) as much as 4 dB are achieved. Also, a comparison between the conventionally designed codes and an I-Q QPSK scheme shows that the I-Q scheme achieves better performance even though the first (sampler) LSP model is used     

Optimal nonuniform signaling for Gaussian channels

Variable-rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied. When the criterion is one of minimizing the average transmitted energy for a given average bit rate, the best possible distribution with which to select constellations points is a Maxwell-Boltzmann distribution. In principle, when constellation points are selected according to a Maxwell-Boltzmann distribution, the ultimate shaping gain (πe/6 or 1.53 dB) can be achieved in any dimension. Nonuniform signaling schemes can be designed by mapping simple variable-length prefix codes onto the constellation. Using the Huffman procedure, prefix codes can be designed that approach the optimal performance. These schemes provide a fixed-rate primary channel and a variable-rate secondary channel, and are easily incorporated into standard lattice-type coded modulation schemes     

Variable-rate variable-power MQAM for fading channels

We propose a variable-rate and variable-power MQAM modulation scheme for high-speed data transmission over fading channels. We first review results for the Shannon capacity of fading channels with channel side information, where capacity is achieved using adaptive transmission techniques. We then derive the spectral efficiency of our proposed modulation. We show that there is a constant power gap between the spectral efficiency of our proposed technique and the channel capacity, and this gap is a simple function of the required bit-error rate (BER). In addition, using just five or six different signal constellations, we achieve within 1-2 dB of the maximum efficiency using unrestricted constellation sets. We compute the rate at which the transmitter needs to update its power and rate as a function of the channel Doppler frequency for these constellation sets. We also obtain the exact efficiency loss for smaller constellation sets, which may be required if the transmitter adaptation rate is constrained by hardware limitations. Our modulation scheme exhibits a 5-10-dB power gain relative to variable-power fixed-rate transmission, and up to 20 dB of gain relative to nonadaptive transmission. We also determine the effect of channel estimation error and delay on the BER performance of our adaptive scheme. We conclude with a discussion of coding techniques and the relationship between our proposed modulation and Shannon capacity     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.