ERROR DETECTION incorporated with automatic-repeatrequest (ARQ) is widely used for error control in data communications systems. This method of error control is simple and provides high system reliability. If a properly chosen code is used for error detection, virtually error-free data transmission can be attained. This paper surveys various types of ARQ and hybrid ARQ schemes, and error detection using linear block codes.

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Automatic-repeat-request error-control schemes

The hybrid ARQ scheme with parity retransmission for error control, recently proposed by Lin and Yu [1], [2], is quite robust. This scheme provides both high system throughput and high system reliability. In this paper, a modified Lin-Yu hybrid ARQ scheme is presented. The modified scheme provides a slightly better throughput performance than the original Lin-Yu scheme; however, it is more flexible in utilizing the error-correction power of a code. The modified scheme can be incorporated with a rate 1/2 convolutional code using Viterbi decoding. Furthermore, the pure selectiverepeat ARQ is a degenerated case of the modified scheme in selective mode. Lin and Yu analyzed their scheme only for a receiver buffer of size N where N is the number of data blocks that can be transmitted in a round-trip delay interval. No analysis for other buffer sizes was given. In this paper, the throughput performance of the modified Lin-Yu scheme is analyzed for any size of receiver buffer. Consequently, the throughput efficiency of the pure selective-repeat ARQ for any receiver buffer size can be obtained. We also show that the modified scheme achieves the same order of reliability as a pure ARQ scheme.

A Modified Selective-Repeat Type-II Hybrid ARQ System and Its Performance Analysis

The method developed by T. Fujiwara et al. (1985) for efficiently computing the minimum distance of shortened Hamming codes using the weight distribution of their dual codes is extended to treat arbitrary shortened cyclic codes. Using this method implemented on a high-speed special-purpose processor, several classes of cyclic redundancy-check (CRC) codes with 24 and 32 parity bits are investigated. The CRC codes of each class are known to have the same minimum distance d/sub min.L/ in a certain range L of block lengths n, and within each class that CRC code has been determined the minimum distance of which exceeds d/sub min.L/ up to the largest block length. The d/sub min/ profiles of the resulting codes are presented and compared with the d/sub min/ profiles of recent suggestions of P. Merkey and E. C. Posner (1984), as well as with the d/sub min/ profile of the widely used 32 parity-bit standard code recommended in IEEE-802. >

Optimization of cyclic redundancy-check codes with 24 and 32 parity bits

The problem of computing the probability of undetected error is considered for linear block codes used for error detection. The recent literature is first reviewed and several results are extended. It is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual. Using the dual code formulation, the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes. Several bounds on the undetected error probability are then presented. We conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained. An efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results.

On the Probability of Undetected Error for Linear Block Codes

In this paper we investigate the performance of maximum-distance-separable codes with symbols from GF(q) when they are used for pure error detection or for simultaneous error correction and detection over a q -input and q -output discret memoryless channel with symbol error probability e. First we show that the probability of undetected error for an MDS code used for pure error detection is upper bounded by q^{-r} and decreases monotonically as edecreases from (q - 1)/q to 0, where r is the number of parity-check symbols of the code. Then we show that the probability of undetected error for an MDS code used for correcting t or fewer symbol errors is upper bounded by q^{-r} \Sum\min{i=0}\max{t}(\min{i} \max{n})(q - 1)^{i} and decreases monotonically as e decreases from (q - 1)/q to 0. These results show that the MDS codes are effective for both pure error detection and simultaneous error correction and detection.

https://ntrs.nasa.gov/api/citations/19840003761/downloads/19840003761.pdf

On the Probability of Undetected Error for the Maximum Distance Separable Codes

A recent paper [1] discussed the 2^{-p} bound (where p = n- k ) for the probability of undetected error P(\epsilon) for an (n,k) block code used for error detection on a binary symmetric channel. This investigation is continued and extended and dual codes are studied. The dual and extension of a perfect code obey the 2^{-p} bound, but this is not necessarily true for arbitrary codes that obey the bound. Double-error-correcting BCH codes are shown to obey the bound. Finally the problem of constructing uniformly good codes is examined.

On some properties of the undetected error probability of linear codes (Corresp.)

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On some properties of the undetected error probability of linear codes (Corresp.)