Performance of Hybrid ARQ Schemes with ML Code Combining over a Block-Fading Rayleigh Channel

This paper considers two well-known selective-repeat retransmission schemes, namely, hybrid type-I ARQ and hybrid type-II ARQ, using convolutional coding, in conjunction with maximum-likelihood code combining. Our theoretical analysis, based upon the concept of generalized weight distribution, shows that the use of code combining yields a significant throughput at very high channel error rates not only in constant AWGN channels but also in fading channels. To demonstrate this, we consider a widely-used block-fading Rayleigh channel model, in which the channel is assumed to be constant during each block of data and the fading is assumed to be independent from block to block. A key parameter in designing retransmission protocols for delay-limited applications in such channels is the minimum number of retransmissions, needed to achieve error-free decoding at almost all channel conditions (low outage probability). This number can be reduced significantly when code combining is employed.     

Delay and coding gain analysis of a truncated type-II hybrid ARQprotocol

Time delay of a truncated type-II hybrid ARQ protocol with one retransmission is analyzed by using queueing theory. The truncated protocol uses rate 1/2 error correcting codes. Parity bits for error correction are transmitted only when they are needed. It is shown that the truncated type-II hybrid protocol has a bounded delay and bounded queue length under typical communication traffic conditions. The error performance of the truncated protocol is further analyzed for a normalized Nakagami-m fading channel and compared with the performance of a conventional (untruncated) protocol. The results show that the truncated protocol provides coding gain improvement over the untruncated type-II hybrid ARQ protocol. Thus, it is suggested that the truncated protocol is best suited to power- and delay-limited mobile applications     

Multistage decoding of multilevel block M-PSK modulationcodes and its performance analysis

Multistage decoding of multilevel block multilevel phase-shift keying (M-PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10^-6     

Performance comparison of different decoding strategies for abandwidth-efficient block-coded scheme on mobile radio channels

The performance of bandwidth-efficient Reed-Solomon (RS)-coded MPSK schemes is evaluated on a shadowed Rician fading channel using different decoding strategies, namely, errors-only, errors-and-erasures, and soft-decision decoding. The lower bounds of the bit error probability are found for errors-only and for errors-and-erasures decoding. For the soft-decision decoding the upper bound of the bit error rate is derived. The error bounds are calculated and examined by simulation for some RS-coded MPSK schemes on a shadowed Rician channel. It is shown that their performance is significantly improved compared to uncoded QPSK. The amount of improvement depends on the signal-to-noise ratio (SNR), the decoding strategy, and the degree of shadowing. A comparison between different decoding techniques, for one of the RS-coded schemes, for different degrees of shadowing shows that the use of channel measurement information in the decoding process is more effective for heavy shadowed channels     

Policy allocation for transmission of embedded bit streams over noisy channels with feedback - [Transactions letters]

An efficient policy allocation algorithm for the transmission of embedded bit streams over noisy channels with feedback is proposed. The transmission is based on the type- II hybrid ARQ/FEC protocol and uses a nested sequence C of channel codes to protect the packets. There are also constraints on the total bit budget and on the allowed number of retransmissions per packet. The allocation algorithm assigns different protection policies, each policy being a subset of C, to different packets to maximize the average number of correctly received source bits. We study the performance and the complexity of the proposed scheme through the transmission of images encoded by JPEG2000 over mobile channels with correlated Rayleigh fading. We demonstrate by simulations that the proposed multiplepolicy scheme provides significant improvements over a purely FEC scheme with no feedback and also the existing fixed-policy schemes. Our results show that feedback is particularly helpful for poor channel conditions and that the proposed scheme is very robust against changes in the channel signal-to-noise ratio (SNR) and the mobile speed.     

Bandwidth efficient communication via a Rayleigh fading channelusing RS coded multiphase signaling

The idea of combining RS (Reed-Solomon) codes with multiphase signaling schemes on fading channels is introduced. The performance of these schemes over a Rayleigh fading channel is evaluated for different decoding strategies, i.e., errors-only, errors-and-erasures, and soft-decision decoding techniques. Both analytical and simulation results show that substantial coding gains are obtained compared to the uncoded reference system     

Reliability/energy trade-off in Bluetooth error control schemes

Two important objectives in wireless sensor networks are reliability and reducing energy consumption. Hence, overcoming energy constraints and utilizing error control schemes such as Automatic Repeat Request (ARQ) and Forward Error Correction (FEC) are necessary to improve the energy efficiency and reliability. However, these two concerns are at odds, so there is a trade-off between them. Considering this point, the impact of various error control schemes on these objectives and the trade-off between them has been considered in Bluetooth networks recently. However, all these works consider ideal assumptions (e.g., perfect error detection) only. This work evaluates the energy-efficiency of Bluetooth error control schemes in Rayleigh fading channels taking into consideration both ideal assumptions and residual error probability of the CRC code in ARQ schemes. A comparative analysis of coding techniques using different BCH codes on the AUX1 packet is provided. In addition, the impact of variations in number of hops and SNR on the effectiveness of proposed coding techniques is analyzed through simulation. This analysis provides information that help network designers to choose suitable packet types and coding techniques for Bluetooth networks depending on the network situation.     

Joint iterative decoding of serially concatenated error controlcoded CDMA

Joint iterative decoding of multiple forward error control (FEC) encoded data streams is studied for linear multiple access channels, such as code-division multiple access (CDMA). It is shown that such systems can be viewed as serially concatenated coding systems, and that iterative soft-decision decoding can be performed successfully To improve power efficiency, powerful FEC codes are used. These FEC codes are themselves serially concatenated. The overall transmission system can be viewed as the concatenation of two error control codes with the linear multiple access channel, and soft-decision decoders are used at each stage. A variance transfer function approach applied to the analysis of this system captures the role of the component decoders in an overall iterative decoding system. We show that this approach forms a methodology to study the effects of the component codes as well as that of the iteration schedule. Analysis and simulation examples are presented for transmission systems that operate close to the Shannon limit and illustrate the accuracy of the analysis     

Coding for Parallel Channels: Gallager Bounds and Applications to Turbo-Like Codes

The transmission of coded communication systems is widely modeled to take place over a set of parallel channels. This model is used for transmission over block-fading channels, rate-compatible puncturing of turbo-like codes, multicarrier signaling, multilevel coding, etc. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived in the parallel-channel setting. We focus on the generalization of the Gallager-type bounds and discuss the connections between some versions of these bounds. The tightness of these bounds for parallel channels is exemplified for structured ensembles of turbo codes, repeat-accumulate (RA) codes, and some of their recent variations (e.g., punctured accumulate-repeat-accumulate codes). The bounds on the decoding error probability of an ML decoder are compared to computer simulations of iterative decoding. The new bounds show a remarkable improvement over the union bound and some other previously reported bounds for independent parallel channels. This improvement is exemplified for relatively short block lengths, and it is pronounced when the block length is increased. In the asymptotic case, where we let the block length tend to infinity, inner bounds on the attainable channel regions of modern coding techniques under ML decoding are obtained, based solely on the asymptotic growth rates of the average distance spectra of these code ensembles.     

Hybrid Error Control Using Retransmission and Generalized Burst-Trapping Codes

On most real channels hybrid error control schemes are expected to provide a throughput higher than that of automatic repeatrequest (ARQ) systems and a reliability better than forward error correction (FEC) systems. On compound channels, channels with a mixture of random and burst errors, generalized burst-trapping (GBT) codes seem to be quite effective for FEC. In this paper, a hybrid scheme with Go BackNARQ as the retransmission component and GBT code as the FEC component, is described. Its performance is analyzed in terms of throughput efficiency and undetected error probability and is compared with that of a forward-acting GBT code. Numerical calculations of the parameters are presented to illustrate the performance.     

A Comparison of Block and Convolutional Codes in ARQ Error Control Schemes

ARQ methods of error control can considerably improve the reliablity of data transmission in such areas as satellite communications, computer networks, etc. A number of ARQ schemes using both block and convolutional codes have appeared in the literature. In this paper, the following problem is addressed. Given two different implementations of an ARQ scheme, one using a block code and the other using a convolutional code, such that the bit error probability of both implementations does not exceed some specific value, which implementation has the higher throughput and under what conditions will it be attained? The comparison is made for three basic retransmission schemes using both hybrid and pure ARQ: stop-and-wait, go-back-N, and selective repeat. Numerical estimates of the throughput were obtained using approximate theoretical expressions for BCH codes and simulation results for sequential decoding of rate 1/2 convolutional codes. Parameters optimizing the performance of both block and convolutional codes for different channel conditions and round trip delays were found and were used to obtain these numerical estimates. Comparison of the quantitative results indicates a trend toward preferring convolutional codes as delay and/or block length increases. A binary symmetric channel with noiseless feedback was assumed. Possible implications for the Gaussian channel are also discussed.     

Forward Error Correction Coding for Fading Compensation in Mobile Satellite Channels

Fading in mobile satellite communications severely degrades the performance of data transmission. The channel is modeled with nonfrequency selective Rice and Rayleigh fading. Also, stored channel simulation is used for hardware data transmission. FEC coding with Viterbi decoding of convolutional codes, and Berlekamp-Massey decoding of Reed-Solomon codes, are used to compensate for the fading. In addition to interleaving, channel state and erasure information improve the performance of the decoder. The BER after decoding is calculated for specific codes on several channels and for different transmission schemes. Using very simple channel state and erasure information gives 2-7 dB additional coding gain. These gains have been verified by hardware data transmission on synthetic fading channels and stored mobile satellite channels.     

Performance Analysis of Wireless Multimedia DS/CDMA Communications with Power Control and Hybrid ARQ

In this paper, we present aperformance analysis of a wireless multimedia direct-sequence code-divisionmultiple-access(DS/CDMA) system based on different error control schemes and an optimal power control algorithm over multipath Rayleigh fading channels.The error control schemes consist of Forward Error Correction (FEC), diversity, and Automatic Repeat reQuest (ARQ). The concatenated codes with a Reed–Solomon outer code andconvolutional inner code are used as FEC. Since a multimedia system is required to support services with different rates and Quality of Services (QoS), different error control schemes are used to satisfy the requirements of different media. In particular, a power control algorithm which can optimize the capacityperformance of the integrated system is presented. Numerical results will show that power optimization can increase the capacity and decrease the total transmission power. By incorporating diversity and hybrid ARQ along with appropriate code ratesin the optimal power controlled system, dramatic increase in system capacitycan also be achieved.     

Hybrid ARQ with selective combining for fading channels

We propose and analyze a hybrid automatic repeat request (ARQ) with a selective combining scheme using rate-compatible punctured convolutional (RCPC) codes for fading channels. A finite-state Markov channel model is used to represent the Rayleigh fading channels. We show that the hybrid ARQ with selective combining yields better performance than the generalized type-II ARQ scheme for fading channels. Furthermore, simulation results of real-time video time division multiple access (TDMA) transmission system are given. Better video quality can be obtained by our proposed scheme, with a bounded delay. Analytical results of throughput and packet error rate (PER) are compared to the simulated results. Our analysis based on a finite-state Markov channel model, is shown to give good agreement with simulations     

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     

On improved bounds on the decoding error probability of block codesover interleaved fading channels, with applications to turbo-like codes

We derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved Rician fading channels, coherently detected and maximum-likelihood (ML) decoded. We assume that the fading coefficients during each symbol are statistically independent (due to a perfect channel interleaver), and that perfect estimates of these fading coefficients are provided to the receiver. The improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity, and are found by generalizing some previously introduced upper bounds for the binary-input additive white Gaussian nose (AWGN) channel. The advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low-density parity-check (LDPC) codes, and it is especially pronounced in a portion of the rate region exceeding the cutoff rate. Our generalization of the Duman and Salehi bound (Duman and Salehi 1998, Duman 1998) which is based on certain variations of Gallager's (1965) bounding technique, is demonstrated to be the tightest reported upper bound. We therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo-like codes, referring to the optimal ML decoding. For certain ensembles of uniformly interleaved turbo codes, the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms     

A novel adaptive hybrid ARQ scheme for wireless ATM networks

This paper describes the design and performance of a novel adaptive hybrid ARQ scheme using concatenated FEC codes for error control over wireless ATM networks. The wireless links are characterized by higher, time‐varying error rates and burstier error patterns in comparison with the fiber‐based links for which ATM was designed. The purpose of the hybrid ARQ scheme is to provide a capability to dynamically support reliable ATM‐based transport over wireless channels by using a combination of our ARQ scheme (called SDLP) and the concatenated FEC scheme. The key ideas in the proposed hybrid ARQ scheme are to adapt the code rate to the channel conditions using incremental redundancy and to increase the starting code rate as much as possible with the concatenated FEC, maximizing the throughput efficiency. The numerical results show that our proposed scheme outperforms other ARQ schemes for all SNR values. This revised version was published online in July 2006 with corrections to the Cover Date.     

Performance evaluation of the generalized type-II hybrid ARQ schemewith noisy feedback on Markov channels

The generalized type-II hybrid automatic repeat request (ARQ) scheme on Markov channels is examined in order to study the effect of feedback channel errors on the performance of ARQ systems. It is shown that it is possible to derive expressions for certain critical performance parameters, such as the throughput efficiency, the probabilities of packet loss, undetected error, and correct delivery. To provide a means of comparison, a parallel set of expressions is provided under the usual assumption of an error-free feedback channel. By use of simulations, the ARQ system performance is examined under noiseless feedback and noisy feedback. It is found that feedback channel noise can result in the loss of packets, an increase in the number of undetected errors, and the occurrence of unnecessary transmissions. To enhance the performance of the GH-II ARQ scheme, a predictor is used and found to lower the probability of undetected error, reduce the number of unnecessary transmissions, and increase the throughput efficiency     

Performance of Hybrid Error Control Schemes of Satellite Channels

The effectiveness of hybrid error control schemes involving forward error correction (FEC) and automatic repeat request (ARQ) is examined for satellite channels. The principal features of the channel are: large round-trip transmission delay due to the satellite link, and burst errors introduced by the terrestrial links that connect the users to the satellite link. The performance is estimated for two channels described by Fritchman's simple partitioned finite-state Markov model, and is compared to that obtainable if the channel is considered as a binary symmetric channel of the same bit error probability. Results show that the hybrid schemes offer substantial improvement over ARQ and FEC, and that an optimum exists for the number of errors corrected to obtain maximum throughput efficiency.     

Incremental-redundancy transmission for meteor-burst communications

The performance of type-II hybrid automatic repeat request (ARQ) is compared to that of fixed-rate type-I hybrid ARQ for meteor-burst communications. Maximum throughput is obtained for meteor-burst communications by using a transmission scheme for which the information rate of the code, varies in response to the fluctuations in the power received from a meteor trail. For type-II hybrid ARQ, a variation in the code rate is inherent in the coding scheme. On the first transmission that is made for a data block, a code of relatively high rate is used, but if an additional transmission is required, only redundant symbols are sent, and this reduces the overall rate of the code. The performance measure is the throughput per trail, which is defined as the expected number of successfully received information bits for a given meteor trail. The authors also develop an approximation for the average value of the throughput, averaged over the parameters of the meteor trail. Numerical results for Reed-Solomon codes are included to illustrate the relative performance of the various schemes. It is shown that the throughput is larger for type-II hybrid ARQ than for either fixed-rate type-I hybrid ARQ or ARQ without forward-error-correction