Performance of coding-spreading tradeoff in DS-CDMA systems using RCPT and RCPC codes

The use of rate-compatible punctured turbo and rate-compatible punctured convolutional (RCPT/RCPC) codes as channel codes in a direct-sequence code-division multiple-access system where the system bandwidth expansion is fixed is investigated. The best RCPC and RCPT code rate in terms of maximizing the system spectral efficiency and minimizing the optimal power allocation where the receiver is either a matched filter (MF) or a minimum mean-square error (MMSE) device is assessed. It is shown that for the MF receiver, the coding-spreading tradeoff favors a code-rate reduction. In the case of the MMSE receiver, when the E/sub b//N/sub 0/ value and the system load are increased, the best code rate also increases. By examining the slope of the performance curves, it is deduced that, under similar operating conditions, the best code rate of the RCPT codes is lower than that of the RCPC codes. Also, the best code rate for a Rayleigh fading channel is lower than that for an additive white Gaussian noise channel.     

Coded modulation for a coherent DS-CDMA system employing an MMSE receiver in a fading channel

Previous results have shown that high rate codes tend to yield a lower average bit-error rate than low rate codes when employing a minimum mean-square error (MMSE) receiver for a direct-sequence code-division multiple-access (CDMA) system in either an additive white Gaussian noise channel or a flat Rayleigh fading channel. we consider the use of larger signal constellations with both trellis-coded modulation and bit-interleaved coded modulation (BICM) to determine if further gains can be achieved in either the Rayleigh or Ricean fading channel. The average bit-error probability is derived for both coding schemes using the general Ricean fading channel model, based upon the common assumptions of infinite interleaving, perfect channel state information, and optimal MMSE receiver coefficients. New bounds are presented for BICM with 8-PSK and 16-QAM symbols, which take advantage of the symmetries inherent in the signal constellations with Gray code mapping. In addition, simulation results are presented which show the important effect a finite interleaving delay constraint has on the comparison of various codes. The results show that there are cases when coded modulation does yield a significant improvement in performance for a CDMA system using an MMSE receiver, compared to standard convolutional coding. However, the best coding strategy depends upon several factors, including the nature of the fading process (Rayleigh or Ricean), the operating signal-to-noise ratio, the interleaving delay constraint, the time-variability of the channel, the number of users in the system, and the severity of the near-far problem.     

Coding for a coherent DS-CDMA system employing an MMSE receiver ina Rayleigh fading channel

This paper analyzes the performance of a convolutionally coded code-division multiple-access system, which employs a linear, minimum mean-square error (MMSE) receiver for interference suppression. A flat, Rayleigh fading channel is considered, where convolutional encoding and interleaving are employed in order to combat the effects of the fading. Theoretical results are derived for the average bit-error probability of the MMSE receiver, where the optimum tap weights for the adaptive filter are determined by the solution of the Wiener-Hopf equations. Simulation results showing the average bit-error rate of the MMSE receiver are also presented, which incorporate the effects of recursive least squares adaptation, channel estimation using pilot symbol-assisted modulation, and finite interleaving. Results show that the MMSE receiver with coding can provide a substantial gain over the matched-filter receiver in a rapidly varying, Rayleigh fading channel. The results also reiterate the fact that lower rate codes are not necessarily the best choice when used with the MMSE receiver     

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Variable-bit-rate speech transmission using punctured convolutionalcodes

Rate (n-1)/n punctured convolutional codes are very effective in conjunction with embedded differential pulse code modulation (EDPCM) in variable-bit-rate speech transmission. The authors investigate the performance of this variable-bit-rate EDPCM system in terms of probability of bit error and audio signal-to-noise ratio (SNR) versus channel SNR in an additive white Gaussian noise and Rayleigh fading channel using soft-decision decoding for specific sets of code generators of punctured convolutional codes. The results show that different sets of code generators affect the performance in terms of both the probability of bit error and the audio SNR. Improvements were obtained in the cases of Gaussian nonfading and Rayleigh fading channels using soft-decision decoding     

Multilevel trellis MPSK modulation codes for the Rayleigh fadingchannel

The multilevel coding technique is used for constructing multilevel trellis M-ary phase-shift-keying (MPSK) modulation codes for the Rayleigh fading channel. In the construction of a code, all the factors which affect the code performance and its decoding complexity are considered. The error performance of some of these codes based on both one-stage optimum decoding and multistage suboptimum decoding has been simulated. The simulation results show that these codes achieve good error performance with small decoding complexity     

Some block- and trellis-coded modulations for the Rayleigh fadingchannel

The error performance of a modulation code over a channel depends on several distance parameters and the path multiplicity of the code. For the AWGN channel, the error performance of a modulation code depends mainly on its minimum squared Euclidean distance and path multiplicity. For the Rayleigh fading channel, however, the error performance of a modulation code depends strongly on its minimum symbol distance, minimum product distance, and path multiplicity. It depends on the minimum squared Euclidean distance in a lesser degree. This paper is concerned with the construction of block and trellis MPSK modulation codes for the Rayleigh fading channel. In each construction, the distance parameters are chosen to achieve good error performance with reduced decoding complexity     

Exact error performance of square orthogonal space- time block coding with channel estimation

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N/spl times/1 code vectors are transmitted over L symbol intervals, resulting in an N/spl times/L code matrix. A least-squares estimate (LSE) as well as a minimum mean-square estimate (MMSE) of the M/spl times/N channel matrix is obtained from a sequence of pilot code vectors. For the case of linear square (i.e., with N=L) orthogonal codes over constant envelope constellations, we obtain an expression for the exact decoding error probability (DEP) for coherent maximum-likelihood decoding. We also find the coding gain for high average signal-to-noise ratio (SNR) per diversity branch in the case of Rayleigh fading. A comparison between both channel-estimation techniques is done in terms of the average pilot-power-to-signal-power ratio (APPSPR). It is found that MMSE requires lower pilot power than LSE for the same DEP and the same average SNR per diversity branch. In addition, the error performance with LSE approaches that with MMSE, with an increase of average SNR per branch or an increase of APPSPR.     

SVD iterative detection of turbo-coded multiantenna unitary differential modulation

A new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced. Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas, where no channel state information is available at the receiver is investigated. Codes achieving bit-error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 1.6-1.9 dB from code restricted capacity limit were found. At higher data rates, computation of code restricted capacity is impractical. Therefore, the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used. The codes achieve BER lower than 10/sup -4/ at E/sub b//N/sub 0/ of 3.2-6 dB from this bound, with coding rates of 1.125-5.06 bits per channel use, and different modulation decoding complexities. The codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code. The receiver employs the high-performance coupled iterative decoding of the turbo code and the modulation code. Information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Performance evaluation of superorthogonal turbo codes in AWGN andflat Rayleigh fading channels

Turbo codes are parallel concatenated codes whose performance in the additive white Gaussian noise (AWGN) channel has been shown to be near the theoretical limit. In this paper, we describe a low-rate superorthogonal turbo code that combines the principles of low-rate convolutional coding and that of parallel concatenation. Due to the bandwidth expansion, this code outperforms the ordinary turbo code both in AWGN and especially in fading channels. Thus, superorthogonal turbo codes are suited mainly for spread-spectrum applications. For the purposes of iterative decoding, we concisely describe the connection between the optimal maximum a posteriori symbol estimation and suboptimal soft-output decoding based on sequence estimation. The suboptimal decoder produces outputs that can directly be used as additive metrics at successive decoding iterations, without the need for estimating channel noise variance. Simulation results in AWGN and flat Rayleigh fading channels are also presented, along with analytical upper bounds of bit- and frame-error probabilities     

Efficiently decoded full-rate space-time block codes

Space-time block codes with orthogonal structures typically provide full-diversity reception and simple receiver processing. However, rate-1 orthogonal codes for complex constellations have not been found for more than two transmit antennas. By using a genetic algorithm, rate-1 space-time block codes that accommodate very simple receiver processing at the cost of reduced diversity are designed in this paper for more than two transmit antennas. Simulation results show that evolved codes combined with efficient outer codes provide better performance over fading channels than minimum-decoding-complexity quasiorthogonal codes at typical operating signal-to-noise ratios. When the fading is more severe than Rayleigh fading, the spectral efficiency is specified, and an efficient outer code is used, evolved codes outperform orthogonal space-time block codes.     

Leveraging coherent space-time codes for noncoherent communication via training

Training codes are introduced for the multiple-antenna, noncoherent, multiple block-Rayleigh-fading channel in which the fading coefficients, which are constant over a fixed number of dimensions (coherence interval) for each block and then change independently to a new realization, are known neither at the transmitter nor at the receiver. Each codeword of a training code consists of a part known to the receiver-used to form a minimum mean-squared error (MMSE) estimate of the channel-and a part that contains codeword(s) of a space-time block or trellis code designed for the coherent channel (in which the receiver has perfect knowledge of the channel). The channel estimate is used as if it were error-free for decoding the information-bearing part of the training codeword. Training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable. Conditions for which the estimator-detector (E-D) receiver is equivalent to the optimal noncoherent receiver are established. A key performance analysis result of this paper is that the training codes when decoded with the E-D receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code. In some cases, the performance of training codes can be measured relative to coherent reception via "training efficiency," which is then optimized over the energy allocation between the training and data phases. In the limit of increasing block lengths, training codes always achieve the performance of coherent reception. The examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available, even though the latter require exponential decoding complexity.     

短波FH/DQPSK系统中分组turbo码的性能分析

本文基于短波跳频（FH）系统的特点，对短波FH/DQPSK系统中分组trubo码的性能进行了分析，并给出了平均误码上限的数学表达式。数值模拟的结果表明，采用分组turbo码编码的FH/DQPSK系统，在短波慢瑞利衰落的信道下，当译码迭代数为4次，SNR=6.8dB时，可使系统的误码率降到10^-5左右。     

Joint iterative channel estimation and decoding in flat correlatedRayleigh fading

This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds     

Performance bounds of rate-? convolutional codes with QPSK on Rayleigh fading channel

An analytic expression for the bit error probability upper bounds of rate-? convolutional codes in conjunction with QPSK modulation and maximum-likelihood Viterbi decoding on the fully interleaved Rayleigh fading channel is presented. The given expression is evaluated numerically for selected rate-? optimum convolutional codes together with QPSK.     

Soft decision decoding of block codes using received signalenvelope in digital mobile radio

The codeword error rate (WER) performance of noncoherent frequency-shift keying with soft decision decoding of block codes using Chase's second algorithm (1972) is investigated in a Rayleigh fading channel. The received signal envelope is sampled and used as channel measurement information. The theoretical upper and lower bounds of the WER are derived, assuming independent Rayleigh envelope samples in a received block. When the Golay (23, 12, 7) code is used, soft decision decoding with 6-bit error correction capability (3-bit error and 3-bit erasure) requires an average signal-to-noise power ratio about 5 dB lower than that for minimum distance decoding with 3-bit error correction to obtain a WER=10^-3. The effects of bit interleaving on the WER performance when fading envelope variation is slow compared to the bit rate are investigated through computer simulations     

Multiple serial and parallel concatenated single parity-check codes

Single parity-check (SPC) codes are applied in both parallel and serial concatenated structures to produce high-performance coding schemes. The number of concatenations or stages, M, is increased to improve system performance at moderate-to-low bit-error rates without changing the overall code parameters (namely, code rate and code block length). Analytical bounds are presented to estimate the performance at high signal-to-noise ratios. The SPC concatenated codes are considered with binary phase-shift keying and with 16-quadrature amplitude modulation bit-interleaved coded modulation on the additive white Gaussian noise channel and the independent Rayleigh fading channel. Simulations show that the four-stage serial or parallel concatenated SPC codes can, respectively, outperform or perform as well as 16-state turbo codes. Furthermore, decoding complexity is approximately 9-10 times less complex than that of 16-state turbo codes. The convergence behavior of both serial and parallel concatenated SPC codes is also discussed.     

瑞利衰落信道下的Turbo均衡

Turbo均衡是一种将Turbo原理和均衡技术结合起来的技术。他通过反复均衡和信道译码来提高接收机性能。针时瑞利衰落信道，采用基于线性滤波器的软输入／软输出均衡器来消除码间干扰，其系数由最小均方误差准则确定。译码器采用最大后验概率算法时卷积码译码。考虑到瑞利衰落信道为随机信道，用非相干检测时信道进行估计。接收机通过联合均衡和译码以充分利用已经获得的信息，实现信道估计及信道均衡与信道译码的迭代更新。仿真结果表明其性能不仅远远优于非迭代系统．而且在信噪比高于4dB时几乎可以完全消除符号间干扰的影响，与MAPSE相比其复杂度大大降低。     

Product accumulate codes: a class of codes with near-capacity performance and low decoding complexity

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.     

Turbo乘积码在衰落信道中的应用

基于Turbo乘积码的编译码原理,利用Matlab仿真工具,对以(64,57,4)扩展汉明码为子码的Turbo乘积码进行迭代次数、量化比特数等不同参数的性能仿真,根据仿真结果选取最佳的设计参数,同时通过仿真给出了Turbo乘积码在衰落信道中的应用效果。结合Matlab仿真,在Quartus环境中完成编译码算法的硬件设计与调试,并将其应用到无线通信调制解调器中。测试结果表明,Turbo乘积码显著改善了调制解调器在衰落信道中的误码性能。