Multidimensional mapping for bit-interleaved coded modulation with BPSK/QPSK signaling

In recent years, it has been recognized that bit-interleaved coded modulation with iterative decoding (BICM-ID) achieves excellent performance on virtually any channel, provided the signal mapping is carefully designed. In this paper, we introduce multidimensional mapping for BICM-ID, where a group of bits is mapped to a vector of symbols, rather than a single symbol. This allows for more flexibility and potential performance improvements. Our analysis shows that multidimensional mapping leads to an increase in Euclidean distance, thus boosting the performance compared to conventional mapping schemes. We derive a design criterion for optimal mappings and we provide such optimal mappings for BPSK and QPSK constellations.     

Bit-interleaved coded modulation with iterative decoding and 8 PSK signaling

We have suggested bit-interleaved coded modulation with soft decision iterative decoding (BICM-ID) for bandwidth-efficient transmission over Gaussian and fading channels. Unlike trellis coded modulation, BICM-ID has a small free Euclidean distance but large diversity order due to bit interleaving. With iterative decoding, soft bit decisions can be employed to significantly improve the conditional intersignal Euclidean distance. This leads to a large coding gain, comparable to that of turbo TCM, over both Gaussian and Rayleigh fading channels with much less system complexity. We address critical design issues to enhance the decoding performance and provide the analytical bounds on the performance with an ideal feedback assumption. We investigate the performance characteristics of BICM-ID through extensive simulations and show that at high signal to noise ratios, the performance of BICM-ID converges to the performance assuming error-free feedback.     

Trellis-coded modulation with bit interleaving and iterativedecoding

This paper considers bit-interleaved coded modulation (BICM) for bandwidth-efficient transmission using software radios. A simple iterative decoding (ID) method with hard-decision feedback is suggested to achieve better performance. The paper shows that convolutional codes with good Hamming-distance property can provide both high diversity order and large free Euclidean distance for BICM-ID. The method offers a common framework for coded modulation over channels with a variety of fading statistics. In addition, BICM-ID allows an efficient combination of punctured convolutional codes and multiphase/level modulation, and therefore provides a simple mechanism for variable-rate transmission     

Design and performance of BICM-ID systems with hypercube constellations

This paper introduces new mappings of QPSK symbols, viewed as a multi-dimensional hypercube, to improve the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID). By evaluating the upper bound of the bit error rate performance of BICM-ID, a condition to find the best mapping of a hypercube constellation in terms of the asymptotic performance under different channel models is established. A general and simple algorithm to construct the best mapping of a hypercube is then proposed. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without bandwidth or power expansion and with a very small increase in the system complexity.     

高斯信道中32阶四维星座图的标识映射设计(英文)

In the bit-interleaved coded modulation with iterative decoding,it is desired that any two Hamming neighbors,i.e..signal constellation points whose binary labels are at unit Hamming distance,be separated by a large Euclidean distance.This paper determines the mappings for the 32-ary fourdimensional generalized cross constellation(32-4D-GCC) so that the minimum squared Euclidean distance d_(min)~2 between Hamming neighbors is maximized.Among such mappings,those with minimum multiplicity N(d_(min)~2) are selected.To reduce the large search space,a set of "mapping templates," each producing a collection of mappings with the same set partitions of binary labels,is introduced.Via enumeration of mapping templates,it is shown that the optimum d_(min)~2=16and the optimum N(d_(min)~2)=16.Among thousands optimum mappings found by computer search,two of the best performance are presented.     

A new labeling search algorithm for Bit-Interleaved Coded Modulation with Iterative Decoding

Bit-Interleaved Coded Modulation with Iterative Decoding （BICM-ID） is a bandwidth efficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and the outer decoder. The choice of the symbol mapping is the crucial design parameter. This paper indicates that the Harmonic Mean of the Minimum Squared Euclidean （HMMSE） distance is the best criterion for the mapping design. Based on the design criterion of the HMMSE distance, a new search algorithm to find the optimized labeling maps for BICM-ID system is proposed. Numerical results and performance comparison show that the new labeling search method has a low complexity and outperforms other labeling schemes using other design criterion in BICM-ID system, therefore it is an optimized labeling method.     

基于Anti-Gray映射的4D-QPSK星座设计

多维映射通过增加星座的维度数而使得符号间的平均欧式距离大大增加,这可以大程度地提高数字通信系统的可靠性。然而已有的基于Gray映射的4D-QPSK星座在设计上,并没有充分利用四维星座的空间优势,对于相邻星座点的汉明距离并未达到最大。提出一种基于Anti-Gray映射的4D-QPSK星座设计方案,该方案中的比特映射方式按照相邻星座点汉明距离最大,汉明距离为1的星座点欧式距离最大的设计原则,使星座点间具有最大的分集度。仿真结果表明,该方案可以提高抵抗衰落信道的能力。     

Signal mappings of 8-ary constellations for bit interleaved coded modulation with iterative decoding

Bit interleaved coded modulation with iterative decoding (BICM-ID) is a spectral efficiency coded modulation technique. This technique is therefore very attractive for many broadcasting services where transmission bandwidth is a primary concern. It has been shown that when signal constellation, interleaver and error-control code are fixed, signal mapping has a critical influence to the error performance of a BICM-ID system. Based on the technique of mutual information, good mappings of different 8-ary constellations are presented for BICM-ID systems over an additive white Gaussian noise (AWGN) channel. It is also shown that, compared to free Euclidean distances, mutual information is a more useful technique to find the good signal mappings for BICM-ID systems.     

Rate gains in block-coded modulation systems with interblock memory

This paper examines the performance gains achievable by adding interblock memory to, and altering the mapping of coded bits to symbols in, block-coded modulation systems. The channel noise considered is additive Gaussian, and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors. In the case of the additive white Gaussian noise channel, these goals translate into the design of block codes of a given weighted or `normalized' distance whose rate is as high as possible, and whose number of codewords at minimum normalized distance is low. The effect of designing codes for normalized distance rather than Hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest, and many such best codes are given     

BICM-ID的MPSK星座映射

在分析了星座映射对比特交织编码调制迭代译码影响的基础上,给出了迭代解调和解码时,星座映射的设计准则,进而给出了一种新的迭代解码的8PSK映射方案.新方案不但满足最大平方欧氏距离(MSEW)映射,在高信噪比时具有较好的性能,而且提高了解调器软信息的输出质量,因而在低信噪比时也具有较好的性能.性能分析和仿真结果表明所给方案的有效性.     

Joint trellis coded quantization/modulation

A joint source/channel coding system constructed using trellis coded quantization (TCQ) and trellis coded modulation (TCM) is described. Identical trellises are used in the TCQ and TCM systems, and a straightforward mapping of TCQ codewords to TCM symbols is presented which guarantees that Euclidean squared distance in the channel is commensurate with quantization mean-square error (MSE). Hence, likely TCM error events of small Euclidean distance cause only a small increase in overall source coding MSE     

Design, analysis, and performance evaluation for BICM-ID withsquare QAM constellations in Rayleigh fading channels

We consider bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth-efficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a low-rate code and a new labeling technique designed specifically for fading channels. This results in a large coding gain over noniterative coded modulation and performance close to that of “turbo” coded modulation with less complexity. We also show that BICM-ID designed for fading channels usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICM-ID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10^-6 can be achieved with 16-QAM, a four-state rate 1/2 code at E_b/N₀ of about seven dB. We also derive performance bounds for BICM-ID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels     

Multidimensional Subcarrier Mapping for Bit-Interleaved Coded OFDM With Iterative Decoding

A power and bandwidth-efficient bit-interleaved coded modulation (BICM) with orthogonal frequency-division multiplexing (OFDM) and iterative decoding (BI-COFDM-ID) using combined multidimensional mapping and subcarrier grouping is proposed for broadband transmission in a frequency-selective fading environment. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence, they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multidimensional mapping for bit-interleaved coded modulation with iterative decoding (BICM-ID) in frequency-flat Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with linear constellation preceding (LCP). Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using LCP and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth, and receiver complexity.     

On Joint Source and Channel Coding Using Trellis Coded CPM: Analytical Bounds on the Channel Distortion

Joint source and channel coding (JSCC) using trellis coded quantization (TCQ) in conjunction with trellis coded continuous phase modulation (CPM) is studied. The channel is assumed to be the additive white gaussian noise (AWGN) channel. Analytical bounds on the channel distortion for the investigated systems with maximum-likelihood sequence detection (MLSD) are developed. The bounds are based on the transfer function technique, which was modified and generalized to include continuous-amplitude discrete-time signals. For a memoryless uniform source, the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal-to-noise ratio (SNR) values. For a memoryless nonuniform source, the constructed bounds are not as tight as the one for the uniform source, however, it still can be used as an indication to how the system performs. It is concluded that the minimum Euclidean distance of the system alone is not enough to evaluate the performance of the considered systems. The number of error events having minimum Euclidean distance and the total distortion caused by those error events also affect the asymptotic performance. This work provides an analysis tool for the investigated systems. The analysis method is very general. It may be applied to any trellis based JSCC schemes.     

Algorithm for mapping between information bits and channel symbolsin MTCM codes

An algorithm for mapping between information bits and channel symbols in multiple trellis-coded modulation (MTCM) codes with M-PSK signal sets is proposed. The core of the algorithm assigns information bits with a Hamming distance in proportion to the sum of the Euclidean distance to each M-PSK symbol. The analytical results show that the additional gains from applying the algorithm can be achieved with little or no loss     

Low-complexity LDPC coded BICM-ID with orthogonal modulations

A low-complexity low density parity check (LDPC) coded bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme with orthogonal modulations is proposed. With a novel mapping strategy of coded bits to symbols, the proposed scheme is equivalent to a generalised LDPC code with Hadamard constraints and thus orthogonal demodulation can be merged into the iterative LDPC decoding process, resulting in a simpler implementation and a lower computational complexity.     

16-QAM BICM-ID in fading channels with imperfect channel state information

We analyze the impact of imperfect channel state information (CSI) on the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) over fading channels. We develop a general, accurate and efficient theoretical error-free feedback bound (EF bound) to analyze the asymptotic bit-error rate (BER) of BICM-ID with imperfect CSI, and predict the BER floor due to channel estimation error. The convergence to the EF bound and the accuracy of the BER floor prediction are verified by simulation with various sets of code and channel parameters. These results are canonical, in that they apply to a variety of system configurations. Pilot symbol assisted modulation is used as a particular example for Rayleigh-fading channels.     

Euclidean distance for combinations of some Hamming codes and binary CPFSK modulation (Corresp.)

The integration of channel coding and modulation in a communication system to increase the Euclidean distance between modulated signals is analyzed. Systems using binary continuous-phase frequency-shift keying modulation and some block codes, such as Hamming codes and shortened Hamming codes, are considered. It is shown that the minimum Euclidean distance depends on the configuration of the parity-check matrixHof the code. For the examined codes the optimum configurations ofH, which give the maximum values of the minimum Euclidean distance, are determined.     

Performance Evaluation of Combined Coding and Modulation Schemes for Nonlinear Channels

The performance of combined coding and modulation schemes in channels with intersymbol interference and nonlinearities is studied using an analytical approach. The class of possible receivers is presented, and a generalization of the minimum Euclidean distance used for the asymptotic analysis of the performance of combined coding and modulation schemes on AWGN channels is introduced. Numerical results are presented for coded 16-PSK modulation.     

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.