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     

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     

Analysis of MFSK frequency-hopped spread-spectrum multiple-accessover a Rayleigh fading channel

An explicit expression for the symbol error probability for a system using frequency-hopped spread-spectrum multiple-access with M-ary frequency shift keying (M-ary FSK) is given when the channel is undergoing Rayleigh fading. Using this expression, the performance of binary BCH codes, nonbinary BCH codes and RS codes are compared, and the best choices of code and modulation format are determined for different channel conditions. Depending on the required codeword error probability, different choices of code and modulation format are found to give the best result. Some attention is also paid to the sometimes used assumption of a noiseless channel, which in many cases is found to give inaccurate results     

The performance of rate-compatible punctured convolutional codesfor digital mobile radio

The unequal error protection capabilities of convolutional codes belonging to the family of rate-compatible punctured convolutional codes (RCPC codes) are studied. The performance of these codes is analyzed and simulated for the first fading Rice and Rayleigh channels with differentially coherent four-phase modulation (4-DPSK). To mitigate the effect of fading, interleavers are designed for these unequal error protection codes, with the interleaving performed over one or two blocks of 256 channel bits. These codes are decoded by means of the Viterbi algorithm using both soft symbol decisions and channel state information. For reference, the performance of these codes on a Gaussian channel with coherent binary phase-shift keying (2-CPSK) is presented. A number of examples are provided to show that it is possible to accommodate widely different error protection levels within short information blocks. Unequal error protection codes for a subband speech coder are studied in detail. A detailed study of the effect of the code and channel parameters such as the encoder memory, the code rate, interleaver depth, fading bandwidth, and the contrasting performance of hard and soft decisions on the received symbols is provided     

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.     

Performance of trellis-coded CPM with iterative demodulation anddecoding

Interleaved trellis-coded systems with full response continuous-phase modulation (CPM) are considered. Upper bounds on the bit-error rate performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver, and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide good bit error performance. Finally, a noncoherent iterative receiver is proposed and is shown to perform close to the coherent iterative receiver     

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     

RS（16,12）缩短码编译码原理及性能分析

在各类数字通信系统以及计算机存储和运算系统经常利用差错控制编码降低误码率,提高通信质量,满足对数据传输通道可靠性的要求。RS码是一种性能优良的前向纠错码,具有同时纠正随机错误和突发错误的能力,它的构造特点决定了其非常适合于纠正突发性错误。文中在阐述RS系统码编译码原理的基础上,提出了RS（16,12）缩短码的编译码方法,利用MATLAB对R S（16,12）缩短码在高斯信道和瑞利信道条件下的纠错能力进行仿真,并分析其纠错性能。     

On the probability of symbol error in Viterbi decoders

An upper bound is derived on the probability that at least one of a sequence of B consecutive bits at the output of a Viterbi (1979) decoder is in error. Such a bound is useful for the analysis of concatenated coding schemes employing an outer block code over GF(2^B) (typically a Reed-Solomon (RS) code), an inner convolutional code, and a symbol (GF(2^B)) interleaver separating the two codes. The bound demonstrates that in such coding schemes a symbol interleaver is preferable to a bit interleaver. It also suggests a new criterion for good inner convolutional codes     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

Optimal detection of digital data over the nonselective Rayleighfading channel with diversity reception

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference     

Unified analysis of error performance for binary signalling over Rayleigh fading channels

Using the unified expression as devised by Wojner, an analytical framework is presented to determine error performance of all binary modulation schemes employing coherent or non-coherent detection and operating over a slow flat Rayleigh fading channel with different diversity combining. A class of generalised expressions for the bit error probability has been obtained following the probability density function or the cumulative distribution function approach.     

Experimental evaluation of combined postdetection diversity andconcatenated channel coding

The combined effects of postdetection diversity reception and concatenated channel coding are experimentally evaluated for π/4-shift QDPSK signal transmission over a Rayleigh fading channel. Two-branch postdetection diversity reception using maximal ratio combining (MRC) and selection combining (SC) are considered. The concatenated channel coding uses the Reed-Solomon (15,k) code of GP(2 ⁴) as the outer code and the BCH (7,4) code as the inner code (k=9,11,13). Measured bit error rate (BER) performance results are presented under cochannel interference (CCI) and multipath channel delay spread, as well as additive white Gaussian noise (AWGN)     

Decision feedback detection of minimum shift keying

A new decision feedback (DF) receiver for minimum shift keying (MSK) is derived, which uses the previously detected symbols to estimate the initial phase in the current symbol for optimum coherent detection. Some of theoretical and simulated bit error rate (BER) performance results are presented. The results show that the DF detection provides good bit error performance in the AWGN channel, and is also an efficient detection method for MSK in a fast Rayleigh fading mobile channel     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

Errors and erasures decoding of BCH and Reed-Solomon codes for reduced M-ary orthogonal signaling

The paper presents a comparison of communication systems using different signal constellation sizes and Reed-Solomon or Bose-Chaudhuri-Hocquengem codes with different rates so that the overall required bandwidth is the same for each system. In these comparisons, the channel symbol size is smaller than the code symbol size, so that a code symbol contains parts of multiple channel symbols. Thus, the normal assumption of independent code symbols does not apply. Instead, consideration must be taken to obtain the best arrangement of channel symbols in each code symbol. Analytical expressions are developed to compare the bit error probability performance of comparable systems, based on individual codewords using errors-only decoding and errors and erasures decoding with transmission over a Rayleigh fading channel.     

Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

RS-MPSK编码调制在传输压缩图像的Rayleigh衰落信道中的性能

本文研究了两种结构的ＲＳ－ＭＰＳＫ编码调制方案在传输压缩图像的Ｒａｙｌｅｉｇｈ衰落信道中的性能。采用计算机仿真的方法得到了该方案在Ｒａｙｌｅｉｇｈ衰落信道中的误比特率,并与理论上限进行了比较,将方案用于传输压缩图像时,可大大提高系统的性能,具有较高的理论意义和衫价值。     

Design of trellis coded QAM for flat fading and AWGN channels

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated     

Simplified eIRA code design and performance analysis for correlated Rayleigh fading channels

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for Rayleigh fading channels, instead of implementing the complex design procedures targeted, specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also show that eIRA codes designed for the BuEC enjoy the advantage of efficient encodability and a lower error-rate floor. Finally, we demonstrate that it is the distribution of the number of faded bits per codeword which determines the difference between correlated and uncorrelated fading channel performance. Perfect channel state information is assumed in this paper.