快速跳頻/MFSK通訊系統於多音頻干擾下的位元交錯二位元碼的EXIT chart分析

It has been demonstrated that turbo codes substantially outperform other codes, e.g., convolutional codes, both in the non-fading additive white Gaussian noise (AWGN) channel as well as multiple-transmit and multiple-receive antenna fading channels. Moreover, it has also been reported that turbo codes perform very well in fast fading channels, but perform somewhat poorly on slow and block fading channels of which the broadband fixed wireless access (FWA) channel is an example. In this paper, we thoroughly compare the performance of turbo-coded and convolutional-coded broadband FWA systems both with and without antenna diversity under the condition of identical complexity for a variety of decoding algorithms. In particular, we derive mathematical expressions to characterize the complexity of turbo decoding based on state-of-the-art Log-MAP and Max-Log-MAP algorithms as well as convolutional decoding based on the Viterbi algorithm in terms of the number of equivalent addition operations. Simulation results show that turbo codes do not offer any performance advantage over convolutional codes in FWA systems without antenna diversity or FWA systems with limited antenna diversity. Indeed, turbo codes only outperform convolutional codes in FWA systems having significant antenna diversity.

EXtrinsic Information Transfer (EXIT) chart is a graphical tool for analysis of low density parity check (LDPC) and other codes with iterative decoding. In this paper, we propose the design of LDPC codes for coded modulation schemes by application of linear programming with conditions derived from EXIT charts. Points on the EXIT curve for bit and check node operations are first computed either using analysis or by simulation. The entire EXIT curve is then obtained by linear interpolation. Finally, the EXIT curves are optimized to obtain the maximum possible rate for the code under a given threshold condition. To demonstrate the design procedure, we consider the cases of M-PAM and 8-PSK over the additive white Gaussian noise (AWGN) channel. The optimization method presented is versatile, and can be extended to other constellations and situations easily.

It is well known that binary error-correcting codes with iterative decoders can achieve near Shannon-limit performance on the additive white Gaussian noise (AWGN) channel, but their performance on more realistic wireless channels can become degraded due to the presence of burst errors or impulsive noise due to interference. A better performing coding scheme is the class of non-binary codes, which are known to be more effective in correcting burst errors, but interestingly there is no research reported in the literature investigating non-binary codes on impulsive noise channels. In this paper, we investigate the performance of non-binary turbo codes defined in a finite field GF(4) on symmetric alpha-stable impulsive noise channels and compare with comparable binary turbo codes. A Cauchy receiver is also employed to mitigate the effects of the channel to assist the turbo decoding. Our simulation results show that although the non-binary turbo code performs similarly to the binary turbo code on the AWGN channel, it achieves a significant coding gain over the binary turbo code as impulsiveness increases.

This paper studies the performance of ultra-wideband (UWB) radio communications systems employing phase shift keying (PSK) modulation and fully saturated power amplifiers through additive white Gaussian noise (AWGN) channel or Rayleigh fading channel. An impulse response method is provided to analyze the signal-to-noise ratio (SNR) degradation. Both convolutional code and turbo code are employed with the Viterbi decoding and the iterative decoding, respectively. The decoding algorithms are modified for the Rayleigh fading channel. Near optimal bit error rate (BER) performance is achieved when employing either convolutional code or turbo code. The simulation results match the derivation. Therefore, fully saturated power amplifiers can be employed in UWB PSK systems to significantly reduce radio cost, simplify radio circuit, and increase battery life for portable terminals.

Turbo codes (TC) is a powerful branch of error-control coding that has exhibited performances close to the Shannon limit, whilst offering a reasonable level of computational complexity. Repeat-punctured turbo codes (RPTCs) exploit the fact that the use of larger interleavers correspond to better bit-error rate (BER) performances for the conventional turbo code, and makes use of repetition and puncturing to improve the performance of the conventional turbo code for moderate to high signal-to-noise ratios (SNRs). Motivated by turbo codes and repeat-punctured turbo codes, we study the use of a new scheme, dual-repeat-punctured turbo codes (DRPTC) in the additive white Gaussian noise (AWGN) channel. DRPTCs primarily make use of repetition and puncturing and the structure of the conventional turbo code to yield a more superior performance. The decoding in principle follows the technique of turbo decoding but needs some changes to yield the performance improvement. Simulation results for the AWGN channel is presented together with the analytical union bounds derived from transfer-function bounding techniques, and the codeword distance-spectrum for the proposed scheme is presented and evaluated.

Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

Motivated by recent results in Joint Source/ Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

The performance of turbo codes has been shown to be near the theoretical limit in the additive while Gaussian noise channel. By using orthogonal signaling, which allows for bandwidth expansion, the performance of the turbo coding scheme can be improved even further. Since this is a low-rate code, the code is mainly suitable for spread-spectrum modulation applications. In classical turbo codes the frame length is set equal to the interleaver size, however, the codeword distance spectrum of turbo codes improves with an increasing interleaver size. It has been reported that by using repetition and puncturing the performance of turbo codes can be improved. Repeat-Punctured Turbo Codes has shown a significant increase in performance at moderate to high signal-to-noise ratios. In this paper, we study the use of orthogonal signaling and parallel concatenation together with repetition and puncturing to improve the performance of superorthogonal convolutional turbo codes for reliable and effective communications. Simulation results for the additive white Gaussian noise channel are presented together with analytical upper bounds, which have been derived using transfer function bounding techniques.

In previous works, density evolution schemes have been used to design an irregular low-density parity-check (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.

In this paper, we address the design of Cooperative communication with coding schemes for the 3-node relay channel with half-duplex constraint. Based on an analysis of the extrinsic information transfer characteristics (EXIT) chart of the component codes we investigate the potential of Turbo codes which are employed by the source node in order to increase the reliability of the system. The source node transmits coded symbols to both the relay and the destination nodes during the first transmission period. The relay performs parallel concatenated codes decoding. It then re-encodes the information bits using a Recursive Systematic Convolutional (RSC) code during the second transmission period. The resultant symbols transmitted from the source and relay nodes can be viewed as the coded symbols of a three-component parallel-concatenated encoder. Thus the EXIT chart is used for iterative decoding and it is helpful to find the best constituent coding schemes for creating parallel concatenated codes for cooperative communication. Thus by considering the interleaver size, code rate and code polynomial we can design a system for cooperative communication using Turbo codes.

Recently, an efficient error performance scheme named as labeling diversity has been proposed in the literature for wireless local area network (WLAN). This paper proposes labeling diversity for 8-phase shift keying (8-PSK) modulation named as boosted space-time scheme. A pair of labeling map is opted for this scheme by maximizing the utility function in asymptotic coding gain under the supposition of error-free feedback. Furthermore, labeling diversity is employed with the space-time forward error correction (FEC) codes like convolution and turbo codes for point to point communication scenarios. Since non-line of sight (NLOS) point to point communication scenario is assumed therefore Rayleigh distributed channel model is selected which remains constant for single space-time block code (STBC). The STBC used in boosted space-time scheme is non-orthogonal therefore maximum likelihood (ML) soft de-mapper is employed at the receiver. The convergence of iterative decoding between soft de-mapper and decoder is analyzed by the extrinsic information transfer (EXIT) chart. The validity of the convergence of iterative decoding is also verified by Monte Carlo simulation. It is evident from the simulation results that bit error rate (BER) performance of boosted space-time scheme is superior to the conventional spacetime scheme under identical conditions. Moreover, the boosted space-time scheme with convolution code performs better for low signal-to-noise ratio (SNR) regime in comparison to boosted space-time scheme with turbo code. However, for high SNR regime, turbo coding scheme outperforms the convolution scheme. In addition, turbo coding scheme provides better BER performance to the convolution scheme under non-iterative decoding.

Recently, the differential detection scheme has attracted considerable attention as a demodulated scheme for digital mobile communications because of its robustness in the frequency nonselective fading channel. A problem of the differential detection scheme is that its bit error rate (BER) performance in the additive white Gaussian noise (AWGN) channel is inferior to that of the coherent detection scheme. To solve this problem, many methods to improve BER performance of the differential detection in the AWGN channel have been proposed. However, those methods require complex signal processings.This paper proposes a novel differential detection scheme as a simpler improvement method which estimates the differential phase of the transmitted signal by a sequence estimation scheme using the Viterbi algorithm. The proposed scheme is simplified in a manner such that its signal processing is composed of only additions and subtractions on the phase information of the received signal. Results of computer simulation show that BER performance of the proposed scheme is close to that of the ideal coherent detection in the AWGN channel. In addition, the trellis diagram of the Viterbi algorithm can be reduced without performance degradation introducing the signal processing similar to the Scarece State Transition (SST) type Viterbi decoding. The proposed scheme also is useful in the case of the fast Rician fading channel and the slow Rayleigh fading channel.

In digital communications, 90 or 180 degree phase ambiguity between the receiver and transmitter carrier is a serious problem for the coherent demodulation. To remove their phase ambiguity, differential quadrature phase shift keying (DQPSK) was proposed with the cost of a remarkable 2.4 dB performance degradation. Based on the iterative decoding (ID) scheme, an efficient joint convolutional code (CC)-coded DQPSK method is proposed to close the gap between quadrature phase shift keying (QPSK) and DQPSK. Using the extrinsic information transfer (EXIT) chart technique, we unveil that the low-complexity convolutional codes outperform the high-complexity Turbo codes for the ID scheme. Simulation results turn out that the proposed scheme can overcome the error-floor effect, and achieve almost 3.54 dB and 0.9 dB signal-to-noise ratio (SNR) gain compared with the non-iterative CC at 10−5 Bit Error Rate (BER)and iterative Turbo schemes at 10−7 BER, respectively.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. This paper first introduces a low-complexity regular mapping optimization for BICM-ID and 8PSK, for the purpose of finding the optimal mapping. Furthermore, the irregular mapping optimization is proposed for a closer approach to the channel capacity. The extrinsic information transfer (EXIT) chart analysis is aided for the proposed optimization algorithms to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping outperforms the other mappings used for comparison, and yields about 0.5dB away from the channel capacity over the additive white Gaussian noise (AWGN) channel.