Multiple symbol trellis coding of CPFSK

This paper describes a technique related to the design of a trellis encoder, combined with the full response M-ary continuous phase frequency shift keying (CPFSK) with modulation index 1/M. A new representation of CPFSK waveforms in N signaling intervals, is proposed as a function of an (N+1)-D vector. We also decompose the generation of the proposed CPFSK waveform into two stages, an N-consecutive continuous phase encoder (NCPE) and a memoryless modulator (MM). This decomposition makes it possible to design binary convolutional encoders with various code rates, cascaded to the NCPE. Specific optimal outer convolutional encoders of two and three-consecutive full response four-ary CPFSK with modulation index 1/4 are designed following Ungerboeck's (1982) set partitioning approach. These codes achieve asymptotic coding gains up to 4.77 dB for the two consecutive case with code rate 3/4, and asymptotic coding gains up to 5.45 dB for the three-consecutive case with code rate 5/6     

QAM调制下基于卷积码与累加编码调制级联的纠错码性能研究

基于卷积码与累加编码的PPM调制级联码(SCPPM)在泊松信道光PPM调制下具有极优异的性能。文章将这种累加编码结构引入到QAM调制中,分析其性能。将卷积码+累加编码+QAM调制串行级联(SCAQAM)纠错方案与常规基于卷积码、并行级联卷积码(Turbo)以及低密度奇偶校验码(LDPC)的比特交织编码调制迭代译码(BICM-ID)系统进行比较,并进一步比较了SCAQAM系统的自然、格雷、反格雷星座映射方式。结果表明,在高阶QAM调制下,这种纠错结构具有极优异的误码性能。对于16QAM及64QAM调制,SCAQAM相对于另外几种纠错码结构的BICM-ID系统分别有约0.3和0.5 dB的性能提升,只有卷积码与累加码结合才更具性能优势。并且SCAQAM将累加后的比特流以反格雷方式映射具有更优异的性能。     

Coded continuous phase modulation using ring convolutional codes

Rate 1/2 convolutional codes over the ring of integers modulo M are combined with M-ary continuous phase modulation (CPM) schemes whose modulation indices are of the form h=1/M. An M-ary CPM scheme with h=1/M can be modeled by a continuous-phase encoder (CPE) followed by a memoryless modulator (MM), where the CPE is linear over the ring of integers modulo M. The fact that the convolutional code and the CPE are over the same algebra allows the state of the CPE to be fed back and used by the convolutional encoder. A modified Euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes. Numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity     

Practical coding for QAM transmission of HDTV

It is demonstrated how modulation schemes based on QPSK can be directly incorporated into QAM-based systems. It is argued that this leads directly to an easily implementable structure that is both efficient in bandwidth and data reliability. It is contended that the correct solution to the concatenated coding problem for HDTV transmission is to simply extend the modulation codes developed for QPSK-to-QAM modulation. In nonconcatenated situations, a trellis code based on a binary code at rate 2/3 is usually best. However, this is not the case for higher error rates at the output of the trellis decoder (e.g., when a symbol error correcting decoder follows as a concatenated code). The reason for this follows from an analysis of the effect of the number of nearest neighbors on the error rate. A four-way partition of QAM is a natural extension of QPSK modulation; it is a simple matter to incorporate any good QPSK code into a trellis coding scheme for QAM modulation. A concatenated coding scheme based on QPSK trellis codes and symbol error correcting coding is proposed. An example is presented to show the advantages of this approach     

Performance analysis of Viterbi decoding for 64-DAPSK and 64-QAMmodulated OFDM signals

The multilevel modulation techniques of 64-quadrature amplitude modulation (QAM) and 64-differential amplitude and phase-shift keying (DAPSK) have been proposed in combination with the orthogonal frequency-division multiplexing (OFDM) scheme for digital terrestrial video broadcasting (DTVB). With this system a data rate of 34 Mb/s can be transmitted over an 8-MHz radio channel. A comparison of these modulation methods in the uncoded case has been presented by Engels and Rohling (see European Trans. Telecommun., vol.6, p.633-40, 1995). The channel coding scheme proposed for DTVB by Schafer (see Proc. Int. Broadcasting Convention, Amsterdam, The Netherlands, p.79-84, 1995) consists of an inner convolutional code concatenated with an outer Reed-Solomon (RS) code. In this paper the performance of the convolutional codes is analyzed for the two modulation techniques. This analysis includes soft decision Viterbi (1971) decoding of the convolutional code. For soft decision decoding of DAPSK modulated signals a new metric is developed     

Iterative demodulation, demapping, and decoding of coded non-square QAM

It is shown that a non-square (NS) 2/sup 2n+1/-ary quadrature amplitude modulation (QAM) can be decomposed into a single parity-check (SPC) block encoder and a memoryless modulator in such a way that the inherent block encoder has a recursive nature. When concatenated with a forward-error-correcting (FEC) code, iterative demodulation, demapping, and decoding of the FEC code and the inherent SPC code of NS-2/sup 2n+1/-QAM is then possible. Simulation results show that coded NS-8QAM performs nearly 2 dB better than standard 8QAM and star-8QAM, and nearly 1 dB better than 8-ary phase-shift keying when the FEC code is a rate-1/2, 16-state convolutional code, while coded NS-32QAM performs 0.75 dB better than standard 32QAM.     

Joint noncoherent demodulation and decoding for the block fading channel: a practical framework for approaching Shannon capacity

The paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels, guided by explicit comparisons with information-theoretic benchmarks. Noncoherent reception is interpreted as joint data and channel estimation, assuming that the channel is time varying and a priori unknown. We consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection. For an information rate of about 1/2 bit per channel use, the proposed scheme, using a quaternary phase-shift keying (QPSK) alphabet, provides performance within 1.6-1.7 dB of Shannon capacity for the block fading channel, and is about 2.5-3 dB superior to standard differential demodulation in conjunction with an outer channel code. We also provide capacity computations for noncoherent communication using standard phase-shift keying (PSK) and quadrature amplitude modulation (QAM) alphabets; comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal-to-noise ratio. These results imply that QPSK suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations, but that QAM is superior to PSK for higher information or fading rates, motivating further research into efficient noncoherent coded modulation with QAM alphabets.     

5G通信中的极化码在高阶调制下的应用

极化码作为信道编码领域的一类新型编码方案,已经被确定为5G移动通信系统中增强移动宽带(Enhanced Mobile Broadband,eMBB)场景下控制信道的编码方案。为了提高5G通信中的频带利用率和信息传输速率,提出将极化码与高阶调制技术相结合,针对16QAM和256QAM两种调制方式,建立和仿真了基于极化码的高阶调制通信系统。在加性高斯白噪声(Additive White Gaussian Noise,AWGN)信道模型下采用逐次消除(Successive Cancellation,SC)译码算法对不同参数的极化码进行仿真比较。仿真结果表明,在现有5G标准控制信道的16QAM模型下,码长N=1024,码率R=1/3,信噪比Eb/N0=6 dB时,极化码误码率可以达到10^-5。未来极化码的应用将推广到数据信道,在256QAM调制方式下,也体现出较好的纠错性能;在16QAM调制方式下,将极化码与同等速率的LDPC码及卷积码相比较,性能增益也有良好的体现。     

Quadrature amplitude modulation in modulating retroreflector system

It has been shown that the data throughput of an optical modulating retroreflector (MRR) system can be enhanced by use of spectrally efficient M-ary quadrature amplitude modulation (M-ary QAM). It has been demonstrated that this MRR system has sufficient dynamic range to support up to 64-QAM at 30 Mbit/s in a 6.75 MHz channel bandwidth.     

M-ary amplitude shift keying OFDM system

Coherent M-ary amplitude-shift keying (MASK) is proposed for use in orthogonal frequency-division multiplexing (OFDM) systems. The frequency separation between subcarriers is only 1/2T instead of 1/T. With a slightly wider bandwidth, an /spl radic/M-ary ASK OFDM can achieve the same bit-error rate (BER) of M-ary quadrature amplitude modulation (QAM) OFDM and a better BER than that of M-ary phase-shift keying (MPSK) OFDM. The /spl radic/M-ary ASK OFDM has the same peak-to-average-power ratio as that of the M-ary QAM OFDM. The MASK OFDM can be implemented digitally and efficiently by fast cosine transform and demodulated by inverse fast cosine transform. Comparisons show that implementation complexity is reduced for additive white Gaussian noise channels with the use of the new scheme.     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

Asymptotic clipping noise distribution and its impact on M-ary QAMtransmission over optical fiber

Performance analysis for a hybrid subcarrier-multiplexed (SCM) AM/QAM transmission over an optical fiber is presented. It is shown that the bit-error-rate (BER) of M-ary QAM in such hybrid systems can be significantly affected due to occasional laser “clipping” of the SCM signal. Here we analytically determine the asymptotic distribution of the clipping noise by modeling it as a Poisson impulse train. The BER of M-ary QAM is then evaluated in terms of optical modulation indices of M-ary QAM and AM signals which in turn specify signal-to-noise ratio (SNR), impulsive index (clipping index) of the clipping noise, and power ratio of the Gaussian noise to the clipping noise. Numerical examples are given and compared with experimental data with reasonably good agreement for small SNR's. The results have application for estimating the BER's of digital signals for SCM analog/digital transmission over an optical fiber and for employing appropriate error correction codes and/or optimum receiver design for such environments     

Bit Error Probability of Trellis-Coded Quadrature Amplitude Modulation Over Cross-Coupled Multidimensional Channels

Convolutionally encodedM-ary quadrature amplitude modulation (M-QAM) systems operated over multidimensional channels, for example dual-polarized radio systems, are considered in this paper. We have derived upper bounds on the average bit-error probability for 4QAM (QPSK) with conventional convolutional coding by means of a truncated union bound technique and averaging over the cross-polarization interference by means of the method of moments. By modifying this technique, we have found approximate upper bounds on the average biterror probability for bandwidth efficient trellis-coded QAM systems. This is an extension of our previous work [1] that was based on one dominating error event probability as a performance measure. Our evaluations seem to indicate that bandwidth efficient trellis-codedMQAM schemes offer much larger coding gains in an interference environment, e.g., a cross-coupled interference channel, than in a Gaussian noise channel. In general, our findings point out that optimum codes for a Gaussian channel are not optimum when applied in an interference environment. We note that a rate 1/2 convolutional code for example, with a code memory greater than two, if applied to two of the bits in each signal point representation, can be utilized with a simple decoder to greatly improve the performance of a QAM signal in interference. Also, we have introduced a new concept referred to as dualchannel polarization hopping in this paper which can improve the system performance significantly for systems with nonsymmetrical interference.     

Channel coding with multilevel/phase signals

A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance. Soft maximum--likelihood (ML) decoding using the Viterbi algorithm is assumed. Following a discussion of channel capacity, simple hand-designed trellis codes are presented for 8 phase-shift keying (PSK) and 16 quadrature amplitude-shift keying (QASK) modulation. These simple codes achieve coding gains in the order of 3-4 dB. It is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals, which we call "mapping by set partitioning." Based on a new distance measure between binary code sequences which efficiently lower-bounds the Euclidean distance between the corresponding channel signal sequences, a search procedure for more powerful codes is developed. Codes with coding gains up to 6 dB are obtained for a variety of multilevel/phase modulation schemes. Simulation results are presented and an example of carrier-phase tracking is discussed.     

Adaptive coded modulation for fading channels

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB     

高阶调制解调下的低复杂度软信息求解

现代通信系统中,软译码可有效提升译码性能,高阶调制如MQAM和MPSK能够在不增加带宽的同时获得高的传输速率。但高阶调制解调模式下软信息的精确求解过于复杂,目前已有的近似算法性能损失过大。针对软输入技术,结合16QAM和32PSK 2种高阶调制方式,对软信息计算作进一步分析,提出了采用数值逼近的方法对16QAM的最小距离软信息计算公式进行修正和采用旋转坐标转换软信息量度方案的方法对32PSK的软信息计算公式进行修正的2种算法。结合LDPC码的仿真结果表明,算法在不增加计算复杂度的前提下,其性能仍能进一步逼近理论算法。     

Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel

It is shown that When Pierce's pulse-position modulation scheme with 2^Lpositions is used on a self-noise-limited directdetection optical communication channel, there results a 2^L-ary erasure channel that is equivalent to the parallel combination ofL"completely correlated" binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.     

Combined coding and precoding for PAM and QAM HDSL systems

A system is described for high-speed digital subscriber line (HDSL) applications. It uses trellis coding combined with Tomlinson (1971) precoding. Theoretical performance results are provided for uncoded pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) assuming an ideal decision feedback equalizer (DFE) that includes an optimum feedforward filter. The similarities and differences in behavior are explained. It is shown that combined coding and Tomlinson precoding can achieve the equalization performance of the DFE and full coding gain of the trellis code. Simulation results are given to show that about 3.4 dB additional margin is obtained by using a four-dimensional eight-state trellis code. The receiver complexity is increased by it is quite manageable     

Minimization of Wireless Sensor Network Energy Consumption Through Optimal Modulation Scheme and Channel Coding Strategy

Wireless sensor networks (WSNs) are composed of sensor nodes generally powered by batteries, for which recharging or replacement is difficult. Since battery technology has not progressed as rapidly as semiconductor technology, energy efficiency has become increasingly important in WSN. On the other hand, data exchanged between nodes are vulnerable to corruption by errors induced by random noise, signal fading and other factors. Therefore, improving link reliability and reducing energy consumption are prime concerns in the design of wireless sensor networks. In this context, performing optimal modulation schemes with suitable channel coding process is a crucial task at the physical layer of this class of networks. This paper investigates the best modulation strategy to minimize the total energy consumption required to send a given number of bits. Energy consumption with both uncoded and coded modulation techniques including M-ary QAM (MQAM), M-ary PSK (MPSK), M-ary FSK (MFSK) and MSK is analytically analyzed and simulated over transmission time, modulation rate and transmission distance. A comparative analysis in terms of energy consumption and probability of Bit Error Rate (BER) referring to MSK modulation with proper Error Control Codes (ECC) approach is presented in this paper. We show that the gain achieved with coded MSK scheme is very promising for obtaining optimal energy network consumption.     

Multidimensional trellis coded phase modulation using a multilevelconcatenation approach. I. Code design

The first part of this paper presents a simple and systematic technique for constructing multidimensional M-ary phase shift keying (MPSK) trellis coded modulation (TCM) codes. The construction is based on a multilevel concatenation approach. In which binary convolutional codes with good free branch distances are used as the outer codes and block MPSK modulation codes are used as the inner codes (or the signal spaces). Conditions on phase invariance of these codes are derived and a multistage decoding scheme for these codes is proposed. The proposed technique can be used to construct good codes for both the additive white Gaussian noise (AWGN) and fading channels as is shown in the second part of this paper