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.     

Performance of Error-Correcting Codes on Channels with Memory

Most magnetic recording and many other digital communication channels exhibit statistical dependencies among errors. The design of error-control schemes for such channels .requires proper models and tools that can be used to evaluate error performance after decoding. In this paper a simplified partitioned model of a channel with memory suggested by B. D. Fritchman is considered. This model is used to derive expressions for block and bit error probability bounds for major block burst-error-correcting codes: interleaved, single burst-correcting, and nonbiuary codes. The model-based bounds are compared to the experimental ones using the data obtained for helical scan magnetic tape recorders. The comparison showed an agreement between experimental and analytical data within one order of magnitude, with the average difference being as small as 16 percent in some cases. A simple and effective implementation of a multiple burst-error-correcting scheme based on the majority-logic decoding of interleaved binary codes is suggested. The scheme requires about ten off-the-shelf IC's for both encoder and decoder with the interleaving degree up to 512.     

Beam transformation techinques for ultrasonic medical imaging

Data acquisition rates in pulsed ultrasound scanners are limited by the speed of sound in the human body. This poses severe limitations to the design of future ultrasound equipment, such as 3-D imaging scanners. The authors describe a technique for higher data acquisition rates based on the simultaneous transmission of multiple beams. By using a linear combination of the received beams, interbeam interference due to the sidelobe energy of the transmitting beams can be significantly reduced. The transformation coefficients are found by using a least squares minimization criterion. A simulation environment used for the evaluation of the authors' methodologies and various simulation results are presented.