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.     

Generalized type II hybrid ARQ scheme using punctured convolutionalcoding

A method is presented to construct rate-compatible convolutional (RCC) codes from known high-rate punctured convolutional codes, obtained from best-rate 1/2 codes. The construction method is rather simple and straightforward, and still yields good codes. Moreover, low-rate codes can be obtained without any limit on the lowest achievable code rate. Based on the RCC codes, a generalized type-II hybrid ARQ scheme, which combines the benefits of the modified type-II hybrid ARQ strategy of J. Hagenauer (1988) with the code-combining ARQ strategy of D. Chase (1985), is proposed and analyzed. With the proposed generalized type-II hybrid ARQ strategy, the throughput increases as the starting coding rage increases, and as the channel degrades, it tends to merge with the throughput of rate 1/2 type-II hybrid ARQ schemes with code combining, thus allowing the system to be flexible and adaptive to channel conditions, even under wide noise variations and severe degradations     

Variable-rate hybrid ARQ for meteor-burst communications

The authors introduce a form of automatic repeat request (ARQ), referred to as variable-rate type-I hybrid ARQ, in which the code rate varies in response to the fluctuations in the power received from a meteor trail. For one implementation, the source or the destination periodically obtains estimates of the signal power at the destination, and the source uses these estimates to select the rate of the code. For an alternative approach, the code rate is determined completely by the decoding successes and failures during previous transmissions. The performance measure is the throughput per trail, which is defined as the expected number of information bits received correctly for a given 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 both implementations of variable-rate type-I hybrid ARQ than for fixed-rate type-I hybrid ARQ and ARQ without forward error correction     

Hybrid ARQ schemes for point-to-multipoint communication overnonstationary broadcast channels

Hybrid automatic-repeat-request (ARQ) error control schemes make use of both error detection and error correction in order to achieve high throughput and low undetected error probabilities on two way channels. Two hybrid ARQ schemes, termed hybrid go-back-N (HGB- N) and hybrid selective-repeat (HSR), are proposed for point-to-multipoint communications over broadcast channels. Both schemes incorporate a concatenated code for error correction and error detection. The performance study of the hybrid schemes is based on a two-state Markov model of a burst noise channel. An analytic solution is derived for the throughput efficiency of the HSR scheme, while approximations and computer simulation are used to evaluate the throughput efficiency of the HGB-N scheme. It is shown that the schemes perform considerably better than the corresponding pure ARQ schemes in which a block code is used for error detection only, especially in environments with a large number of receivers and large channel roundtrip delays, such as satellite broadcast links     

An Adaptive Hybrid ARQ Scheme

A hybrid ARQ in which the transmitter adaptively selects an FEC code according to the channel condition is presented and analyzed. The code is selected according to the past transmissions and acknowledgements by an algorithm which is a generalization of that in [1]. The throughput is obtained as a function of the frame error rate for a general system employing the adaptive hybrid ARQ with acknowledgements that arrive instantly on an error-free return channel. The throughput is obtained as a function of the signal-to-noise ratio for an example quad rate system employing convolutional codes with non-coherent frequency shift keying over the uncorrelated Rayleigh fading channel. This allows the best choice for the parameters of the algorithm to be made. In the case that the channel bit errors are independent, the generalization offers performance improvement of less than 10% over that in [1]. But when the channel errors are bursty, as in the case of Rayleigh fading with finite bit interleaving, the generalization offers throughput improvement as high as 24%. We go on to consider incorporating code combining with the adaptive scheme to form an adaptive memory hybrid ARQ. Simulation of a system using complementary punctured convolutional codes with 4 code rates shows that 2-level code combining can extend the adaptive scheme's useful throughput into the low SNR region by approximately 4 dB.     

Throughput analysis method for hybrid ARQ schemes over burst errorchannels

A definition of a burst error channel using a Markov model was presented by T. Sato et al. in a previous paper (1991). A throughput analysis method of hybrid automatic repeat request (ARQ) under the burst error channel using the three-state Markov model is described. The hybrid ARQ is studied for the random and burst error correction codes as the forward error correction (FEC) code, and multiframe rejection (MREJ) as the ARQ. The throughput efficiency is obtained with both an infinite buffer memory and a finite buffer memory. The applicable range of the burst error channel is clarified for the hybrid ARQ using random and burst error correction codes     

Optimum subpacket transmission for hybrid ARQ systems

Hybrid automatic-repeat-request (ARQ) is a flexible and efficient technique for data transmissions. In hybrid ARQ, subpacket schemes are more attractive for systems with burst errors than complete packet schemes. Although subpacket schemes were proposed in ARQ systems, optimum subpacket transmission is more effective to maximize throughput in a dynamic channel. Since convolutional codes have properties of burst errors in decoding, the optimum subpacket can be applied to convolutional codes. This paper investigates the performance of subpacket transmission for convolutionally coded systems. An efficient method is proposed to estimate the optimum number of subpackets, and adaptive subpacket schemes, i.e., schemes that enable a system to employ different optimum numbers of subpackets under various conditions, are suggested to achieve the maximum throughput of the system. Numerical and simulation results show that the adaptive subpacket scheme is very effective for the convolutionally coded hybrid ARQ system, and it can provide higher throughput, smaller delay,and lower dropping rate than complete packet schemes. Moreover, the adaptive subpacket scheme can be flexibly used with packet combining techniques to further improve the system throughput.     

Performance of truncated type-II hybrid ARQ schemes with noisyfeedback over block fading channels

This paper considers truncated type-II hybrid automatic repeat-request (ARQ) schemes with noisy feedback over block fading channels. With these ARQ techniques, the number of retransmissions is limited, and, similar to forward error correction (FEC), error-free delivery of data packets cannot be guaranteed. Bounds on the average number of transmissions, the average coding rate as well as the reliability of the schemes are derived using random coding techniques, and the performance is compared with FEC. The random coding bounds reveal the achievable performance with block codes and maximum-likelihood soft-decision decoding. Union upper bounds and simulation results show that over block fading channels, these bounds can be closely approached with simple terminated convolutional codes and soft-decision Viterbi decoding. Truncated type-II hybrid ARQ and the corresponding FEC schemes have the same probability of packet erasure; however, the truncated ARQ schemes offer a trade-off between the average coding rate and the probability of undetected error. Truncated ARQ schemes have significantly higher average coding rates than FEC at high and medium signal-to-noise ratio even with noisy feedback. Truncated ARQ can be viewed as adaptive FEC that adapts to the instantaneous channel conditions     

Rate-compatible punctured convolutional codes (RCPC codes) andtheir applications

The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P+l), where l can be varied between 1 and (N-1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. the application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimise throughput     

Parity retransmission hybrid ARQ using rate 1/2 convolutional codeson a nonstationary channel

A parity retransmission hybrid automatic repeat request (ARQ) scheme is proposed which uses rate 1/2 convolutional codes and Viterbi decoding. A protocol is described which is capable of achieving higher throughputs than previously proposed parity retransmission schemes. The performance analysis is based on a two-state Markov model of a nonstationary channel. This model constitutes a first approximation to a nonstationary channel. The two-state channel model is used to analyze the throughput and undetected error probability of the protocol presented when the receiver has both an infinite and a finite buffer size. It is shown that the throughput improves as the channel becomes more bursty     

On the performance of hybrid FEC/ARQ systems using rate compatiblepunctured turbo (RCPT) codes

This paper introduces a hybrid forward-error correction/automatic repeat-request (ARQ) system that employs rate compatible punctured turbo (RCPT) codes to achieve enhanced throughput performance over a nonstationary Gaussian channel. The proposed RCPT-ARQ system combines the performance of turbo codes with the frugal use of incremental redundancy inherent in the rate compatible punctured convolutional codes of Hagenauer (1988). Moreover, this paper introduces the notion of puncturing the systematic code symbols of a turbo code to maximize throughput at signal-to-noise ratios (SNRs) of interest. The resulting system provides both an efficient family of achievable code rates at middle to high SNR and powerful low-rate error correction capability at low SNR     

A new method for the integration of modulation and channel codingin an ARQ protocol

A method for the integration of the modulation operation in an automatic-repeat-request (ARQ) scheme is described. This method uses a memory for the successive transmissions of a codeword and, through a suitable encoding operation, the Euclidean distances among the codewords are significantly increased with the number of transmissions. The application of the described method to some different modulation schemes, such as M-ary PSK with M>2 and continuous-phase frequency shift keying modulation, is described. The optimum combination of the modulation and channel coding operations for some short block codes is also presented. The results of the theoretical analysis show that the method described permits improving both the error probability and the throughput of an ARQ protocol with respect to similar schemes     

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.     

Adaptive type II hybrid ARQ scheme using zigzag code

The authors propose a new hybrid type II ARQ scheme based on the simple multidimensional concatenated zigzag code. Owing to the fact that the error-correcting capability of zigzag codes is far better than that of conventional convolutional codes, the throughput of our scheme is better than existing hybrid ARQ schemes     

The performance of incremental redundancy schemes based on convolutional codes in the block-fading Gaussian collision channel

The throughput performance of incremental redundancy (INR) schemes, based on short constraint length convolutional codes, is evaluated for the block-fading Gaussian collision channel. Results based on simulations and union bound computations are compared to estimates of the achievable throughput performance with random binary and Gaussian coding in the limit of large block lengths, obtained through information outage considerations. For low channel loads, it is observed that INR schemes with binary convolutional codes and limited block length may provide throughput close to the achievable performance for binary random coding. However, for these low loads, compared to binary random coding, Gaussian random coding may provide significantly better throughput performance, which prompts the use of larger modulation constellations. For high channel loads, a relatively large gap in throughput performance between binary convolutional codes and binary random codes indicates a potential for extensive performance improvement by alternative coding strategies. Only small improvements of the throughput have been observed by increasing the complexity through increased state convolutional coding.     

Complementary punctured convolutional (CPC) codes and theirapplications

Presents a new class of punctured convolutional codes that are complementary (CPC codes). A set of punctured convolutional codes derived from the same original low rate code are said to be complementary if they are equivalent (in terms of their distance properties) and if when combined yield at least the original low rate code. Based on these CPC codes the author proposes and analyzes a variation of the type II hybrid ARQ scheme which is called a type III hybrid ARQ scheme. With the type III hybrid ARQ scheme, the starting code rate can be chosen to match the channel noise requirements, and as with the type II scheme, packets that are detected in error are not discarded, but are combined with complementary transmissions provided by the transmitter to help recover the transmitted message. The main advantage is that any complementary sequence sent for a packet that is detected with errors is self decodable. That is the decoder does not have to rely on previously received sequences for the same data packet for decoding, as is generally the case with incremental redundancy ARQ schemes. This feature is desirable especially in situations where a transmitted packet can be lost or severely damaged as a result of interference. CPC codes can find applications in diversity transmission systems. A novel complementary diversity scheme which makes use of CPC codes is briefly discussed     

Performance of H.263 video transmission over wireless channelsusing hybrid ARQ

This paper proposes a hybrid ARQ error control scheme based on the concatenation of a Reed-Solomon (RS) code and a rate compatible punctured convolutional (RCPC) code for low-bit-rate video transmission over wireless channels. The concatenated hybrid ARQ scheme we propose combines the advantages of both type-I and type-II hybrid ARQ schemes. Certain error correction capability is provided in each (re)transmitted packet, and the information can be recovered from each transmission or retransmission alone if the errors are within the error correction capability (similar to type-I hybrid ARQ). The retransmitted packet contains redundancy bits which, when combined with the previous transmission, result in a more powerful RS/convolutional concatenated code to recover information if error correction fails for the individual transmissions (similar to type-II hybrid ARQ). Bit-error rate (BER) or signal-to-noise ratio (SNR) of a radio channel changes over time due to mobile movement and fading. The channel quality at any instant depends on the previous channel conditions. For the accurate analysis of the performance of the hybrid ARQ scheme, we use a multistate Markov chain (MSMC) to model the radio channel at the data packet level. We propose a method to partition the range of the received SNR into a set of states for constructing the model so that the difference between the error rate of the real radio channel and that of the MSMC model is minimized. Based on the model, we analyze the performance of the concatenated hybrid ARQ scheme. The results give valuable insight into the effects of the error protection capability in each packet, the mobile speed, and the number of retransmissions. Finally, the transmission of H.263 coded video over a wireless channel with error protection provided by the concatenated hybrid ARQ scheme is studied by means of simulations     

An effective go-back-N ARQ scheme for variable-error-rate channels

In nonstationary channels, error rates vary considerably. The author proposes an effective go-back-N ARQ scheme which estimates the channel state in a simple manner, and adaptively switches its operation mode in a channel where error rates vary slowly. It provides higher throughput than other comparable ARQ schemes under a wide variety of error rate conditions     

Energy Efficient Coded Communication for IEEE 802.15.4 Compliant Wireless Sensor Networks

The multipath nature of the wireless environment does not provide reliable links for robust communication in wireless senor networks (WSNs). These unreliable links increase the error level to a greater extent and therefore, reduces battery life. Hence, there arises a need for developing energy efficient forward error correction code that avoids more energy consuming Automatic Repeat request (ARQ) scheme used in WSNs to improve link reliability. In this paper, we consider a simple block error correction codes such as cyclic and Bose Chaudhuri Hocquenghem (BCH) codes to be used in IEEE 802.15.4 RF transceiver based sensor nodes. The simulations are performed to measure network parameters such as bit error rate, and energy spent per bit under Rayleigh fading channel environment. It is found that BCH code with code rate of 0.8 provides coding gain of 1.6 dB when compared with cyclic and ARQ schemes and proves to be an energy efficient code among the codes considered.     

Improving Wireless TCP Throughput by a Novel TCM-Based Hybrid ARQ

A novel hybrid ARQ (HARQ) scheme using a concatenated two-state trellis-coded modulation (CT-TCM) code is proposed for improving wireless TCP throughput. A distinguished feature of the proposed scheme is that the heavily punctured TCM codes are used for retransmissions of the corrupted data block, which are combined at the receiver with the previously received sequences of the same data block for decoding. By this method, significantly improved coding gain and efficient spectrum utilization can be achieved with very low complexity. A Markov model is developed to evaluate TCP throughput over the proposed HARQ in wireless link. By both analysis and simulation, we demonstrate that compared with other existing TCM-based ARQ schemes, significant improvement of TCP throughput over wireless links is achieved by the proposed CT-TCM HARQ while smaller buffer size is required at the access point.