一种低复杂度双二元卷积Turbo码译码算法

双二元卷积Turbo码（ DB CTC)的非二进制编码使得译码复杂度增加,限制了其在某些实际通信工程中的使用。在最大后验概率（ MAP)译码算法的基础上,提出了一种优化算法,将译码的存储量和计算量降为原来的1/4。仿真结果表明：在不同编码长度和码率的情况下,优化算法与原算法性能相当;在误码率为10-5的条件下,两者的Eb/N0差异同样不大于0.1 dB。     

OFDM for data communication over mobile radio FM channels. I.Analysis and experimental results

The performance of OFDM/FM modulation for digital communication over Rayleigh-fading mobile radio channels is described. The use of orthogonal frequency division multiplexing (OFDM) over mobile radio channels was proposed by Cimini (1985). OFDM transmits blocks of bits in parallel and reduces the bit error rate (BER) by averaging the effects of fading over the bits in the block. OFDM/FM is a modulation technique in which the OFDM baseband signal is used to modulate an FM transmitter. OFDM/FM can be implemented simply and inexpensively by retrofitting existing FM communication systems. Expressions are derived for the BER and word error rate (WER) within a block when each subchannel is QAM-modulated. Several numerical methods are developed to evaluate the overall BER and WER. An experimental OFDM/FM system was implemented and tested using unmodified VHF FM radio equipment and a fading channel simulator. The BER and WER results obtained from the hardware measurements agree closely with the numerical results     

BER analysis of convolution coded QDPSK, in digital mobile radio

The bit error rate (BER) performance of convolutional coded quaternary differential phase-shift keying (QDPSK) with Viterbi decoding is theoretically investigated in Rayleigh fading environments. The probability density functions of the path and branch metric values of Viterbi decoding are derived. The BERs after decoding due to additive white Gaussian noise and cochannel interference are theoretically analyzed. Rate 1/2 codes and their symbol punctured high-rate codes are considered, and the symbol positions for deletion to minimize the BER after decoding are presented for the codes with a constraint length K=3-7. It is shown that Viterbi decoding considerably reduces the desired signal-to-interference power ratio as well as the signal energy per information bit-to-noise power spectrum density ratio necessary to achieve a certain BER. The spectrum efficiency of the cellular mobile radio system, achievable by the use of the symbol punctured codes, is also evaluated     

A combined soft-decision deinterleaver/decoder for the IS95 reverselink

The reverse link encoding steps of the IS95 cellular code-division multiple-access (CDMA) standard consist of convolutional encoding, block interleaving, and orthogonal Walsh function encoding. Deinterleaving individual symbol metrics obtained from the Walsh function matched filters followed by conventional Viterbi decoding produces suboptimal results, as unwanted intersymbol Walsh function correlation is introduced. We propose a combined deinterleaver/decoder with improved performance over existing decoders with little added overhead and no extra decoding delay. Applied to the IS95 reverse link, the proposed decoder has about 1.0-dB gain over soft-decision decoding with interleaved symbol metrics at a bit error rate (BER) of 10^-3     

A new performance evaluation metric for sub-optimal iterative decoders

In this letter, a new metric for fast and efficient performance comparison of iterative sub-optimal decoding algorithms is proposed. It is based on the estimation of a metric between the A-Posteriori Probability (APP) decoded symbol of optimal and suboptimal decoding algorithms. We apply the notion of entropy to evaluate this function. The metric is tested on data sets from the different sub optimal algorithms for the duo binary turbo codes used in WiMax(802.16e) application and a (251,502) Galois Field (26) low density parity check (LDPC) code. Experimental results show that the values of the proposed metric correlate well with the BER performance of the suboptimal implementation of the iterative decoding algorithm.     

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     

Performance comparison of proposed 3-d coherent spatial-phase-time coding/decoding with super structured fiber Bragg grating-based optical CDMA systems

In this paper, performance comparison in terms of bit error rate (BER) of proposed WDM compatible optical CDMA system incorporating 3-D spectral-phase-time encoding/decoding to a 7 chip-super-structured fiber Bragg grating (SSFBG)-based optical code division multiple access (OCDMA) system is investigated. Coding and decoding using binary [0, π] phase chips is demonstrated for six users at 5 Gb/s, and a single coded signal is separated with acceptable bit-error rate ≤10^?9. In our proposed optical CDMA system encoding and decoding is done by converting hadamard codes (used for conventional CDMA system) to phase codes. It is then compared with two optical pulse retiming and reshaping systems incorporating super structured fiber Bragg gratings (SSFBGs) as pulse shaping elements. Simulation results show that with all input bands having same sample rate, size data rates our proposed codes with even larger number of channels perform better in terms of eye opening & BER.     

Estimation of Bit and Frame Error Rates of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels

A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSCs) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.     

Computing the word-, symbol-, and bit-error rates for block error-correcting codes

In order to select error-correcting codes for various applications, their performances have to be determined. However, when targeting error-rate computations for block error-correcting codes, many required results are missing in the coding literature. Even in the simple case of binary codes and bounded-distance decoding, classical texts do not provide a bit-error rate (BER) expression taking into account both decoding errors and failures. In the case of nonbinary codes used to protect binary symbols, such as Reed-Solomon codes in many applications, there is no available result making realistic channel assumptions in order to derive BERs. Finally, for the more complex case of complete decoding, only some bounds are available, such as the union one. This paper presents new approximations of error rates for block error-correcting codes as a function of the channel BER (crossover probability). We extend an existing approximation in order to consider not only bounded-distance decoding, but also complete "nearest-neighbor" decoding. We also develop approximations able to deal with nonbinary codes. Combined with state-of-the-art approximations, these new results enable the computation of bit-, symbol-, and word-error rates in various decoding situations. They can consider separately errors related to erroneously decoded words and decoding failures, and they provide accurate estimates of error rates. As they do not require detailed information about the structure of codes, they are general enough to be used in simple comparisons between different codes, avoiding the need for simulations.     

An algorithmic approach to the optimization of importance samplingparameters in digital communication system simulation

Importance sampling is recognized as a potentially powerful method for reducing simulation runtimes when estimating the bit error rate (BER) of communications systems using Monte Carlo simulation. Analytically, minimizing the variance of the importance sampling (IS) estimator with respect to the biasing parameters has typically yielded solutions for systems for which the BER could be found analytically. A technique for finding an asymptotically optimal set of biasing parameter values, in the sense that as the resolution of the search and the number of runs used both approach infinity, the algorithm converges to the true optimum, is proposed. The algorithm determines the amount of biasing that minimizes a statistical measure of the variance of the BER estimate and exploits a theoretically justifiable relationship, for small sample sizes, between the BER estimate and the amount of biasing. The translation biasing scheme is considered, although the algorithm is applicable to other parametric IS techniques. Only mild assumptions are required of the noise distribution and system. Experimentally, improvement factors ranging from two to eight orders of magnitude are obtained for a number of distributions for both linear and nonlinear systems with memory     

Majority-logic-like vector symbol decoding with alternative symbolvalue lists

Majority-logic-like decoding is an outer concatenated code decoding technique using the structure of a binary majority logic code. It is shown that it is easy to adapt such a technique to handle the case where the decoder is given an ordered list of two or more prospective candidates for each inner code symbol. Large reductions in failure probability can be achieved. Simulation results are shown for both block and convolutional codes. Punctured convolutional codes allow a convenient flexibility of rate while retaining high decoding power. For example, a (856, 500) terminated convolutional code with an average of 180 random first-choice symbol errors can correct all the errors in a simple manner about 97% of the time, with the aid of second-choice values. A (856, 500) maximum-distance block code could correct only up to 178 errors based on guaranteed correction capability and would be extremely complex     

Stochastic gradient optimization of importance sampling for theefficient simulation of digital communication systems

Importance sampling (IS) techniques offer the potential for large speed-up factors for bit error rate (BER) estimation using Monte Carlo (MC) simulation. To obtain these speed-up factors, the IS parameters specifying the simulation probability density function (PDF) must be carefully chosen. With the increased complexity in communication systems, analytical optimization of the IS parameters can be virtually impossible. We present a new IS optimization algorithm based on stochastic gradient techniques. The formulation of the stochastic gradient descent (SGD) algorithm is more general and system-independent than other existing IS methodologies, and its applicability is not restricted to a specific PDF or biasing scheme. The effectiveness of the SGD algorithm is demonstrated by two examples of communication systems where the IS techniques have not been applied before. The first example is a communication system with diversity combining, slow nonselective Rayleigh fading channel, and noncoherent envelope detection. The second example is a binary baseband communication system with a static linear channel and a recursive least square (RLS) linear equalizer in the presence of additive white Gaussian noise (AWGN)     

LDPC编码的随机极性CP-EBPSK系统

随机极性的连续相位扩展二元相移键控（CP-EBPSK）是一种高频谱效率的调制技术,特殊的冲击滤波器使得门限判决解调成为可能,为了进一步改善其在低信噪比下的误码率性能,引入低密度奇偶校验（LDPC）码作为信道编码。精确的后验概率估计对于译码性能至关重要,但解调方式的特殊性给获取后验概率带来困难。本文引入并分析了贝叶斯方法和支持向量机（SVM）以及两种基于判决门限的后验概率估计法。仿真结果表明,基于SVM和贝叶斯方法较基于判决门限的后验概率估计法更加精确,解调性能可提升8dB-9dB,但在解调之前对需要对码元进行训练,因而复杂度也相对较高;而基于判决门限的后验概率估计法不需要这一过程,因而实现较为简单,性能也可提升7dB以上。所以,在随机极性的CP-EBPSK系统中利用后验概率估计法作为LDPC码译码初始化较为有效。      

Best short rate 1/2 tailbiting codes for the bit-error ratecriterion

We give a method of finding convolutional codes with minimum bit-error rate (BER) that combines ideas of importance sampling, Monte Carlo integration, and maximum a posteriori probability decoding. The method is applied to rate 1/2 tailbiting convolutional coding, both feedforward and feedback systematic. Tables of BER-minimizing encoders are given for memories 2-5 and tailbiting size 5-40, over a range of good and bad binary symmetric and additive white Gaussian noise channels. The best generators for these cases are in general all different and are not necessarily the generators that optimize distance. The best generators for bad channels are always systematic. The best when the channel quality is known are usually feedforward, but when it is unknown, they are feedback systematic. The best generators in good channels are predicted by a union bound technique     

Decoding With Expected Length and Threshold Approximated (DELTA): A Near-ML Scheme for Multiple-Input–Multiple-Output Systems

In this paper, we propose a near maximum likelihood (ML) scheme for the decoding of multiple-input–multiple-output (MIMO) systems. By employing the metric-first search method, Schnorr–Euchner enumeration, and branch-length thresholds in a single frame systematically, the proposed technique provides efficiency that is higher than those of other conventional near-ML decoding schemes. From simulation results, it is confirmed that the proposed scheme has computational complexity lower than those of other near-ML decoders while maintaining the bit error rate (BER) very close to the ML performance. The proposed scheme, in addition, possesses the capability of allowing flexible tradeoffs between the computational complexity and BER performance.      

Transmission performance analysis of a new class of line codes for optical fiber systems

A family of mB(m+1)B binary, nonalphabetic, balanced line codes is presented that is suitable for high bit rate (>or=135 Mb/s) optical fiber transmission due to its relatively simple encoding and decoding rules. Here, B represents a block of m bits, where m is an odd number. The coding, decoding, and bit error rate (BER) performance of the codes are discussed. Statistical and spectral analysis for the specific case in which the number of bits, m, equals seven, is presented. This makes possible a detailed comparison of the proposed code with conventional 7B8B codes.<>     

Physical‐layer network coding with limited feedback using orthogonal space–time block codes

This paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.     

On the computation of the performance probabilities for block codeswith a bounded-distance decoding rule

When a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance, the probability of decoding failure, the probability of erroneous decoding, and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code. For the symmetric erasure channel, numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known, and for linear maximum distance separable (MDS) codes. The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution. Numerical examples include a triple-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length 63 and a Reed-Solomon code of length 1023 and minimum distance 31     

PL approximation of DBPSK in DF-based cooperative FSO network with pointing error

In this paper, we utilize piecewise linear (PL) approximation to analyze the performance of cooperative free space optical (FSO) network employing differentially modulated binary phase shift keying (DBPSK) data with multiple decode-and-forward (DF) relays. The maximum-likelihood (ML) decoding rule at the destination is approximated by PL approximation which considers the possibility of erroneous relaying and performs very similar to the ML decoder with reduced decoding complexity. The atmospheric fading optical links are modeled by Gamma–Gamma distribution subject to both types of detection techniques, i.e., heterodyne detection and intensity modulation/direct detection (IM/DD) with pointing error. We analytically formulate the probability of error for the multiple-DF relay-based FSO network. However, the novel unified expression of average bit error rate (BER) of PL decoder with single relay and single source to destination pair is derived. Further, we also derive the asymptotic approximate BER of DF-FSO network with multiple relays at high signal-to-noise ratio (SNR) of source to relay links considering heterodyne detection with negligible pointing error. In addition, the unified closed-form expressions of outage probability with single and multiple DF relays are derived in terms of Meijer G function. The expression of outage probability is examined at high SNR in order to obtain analytical diversity order. The impact of different power distribution techniques on outage probability is determined by utilizing power distribution parameters. The derived analytical results are validated through simulation.