バースト誤り訂正2進巡回AN符号の符号点分布と性能評価

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Binary cyclic AN codes are useful for correcting errors in both arithmetic operationsand digital data transmission. This paper is concerned with code-point-distribution of binarycyclic AN codes for burst-error-correction. The goal is evaluation of these codes.An arithmetic AN code is a set of the form AN, where A is a specific constant called acode generator and N is an integer to be coded into a code word AN. When every code wordis expressed in binary representation, this code is called a binary arithmetic AN code. If thebinary arithmetic AN code is closed under cyclic shift, the code is called a binary cyclic ANcode.Let a code generator A be relatively prime to the radix 2, that is, an odd integer. Then,it is the smallest natural number n satisfying the equation2n-1 = AB,where B is called the number of code words and n is called code-length.Suppose that we have a received word V for a transmitting code word AN of a binarycyclic AN code. Then, an arithmetic burst-error E is defined as arithmetic differencebetween V and AN modulo 2n-1. The smallest value among all the cyclic shifts of the bursterrorE is called a basic burst, denoted by E0. Burst-length b is defined as the number ofdigits of the basic burst E0.The residue S of a received word V modulo A is called a syndrome of V. The syndromeis equal to a residue of the arithmetic burst-error E modulo A, that is, the syndrome of E. Ifand only if every arithmetic burst E of length b or smaller has a distinct syndrome, the codehas burst-error-correcting ability b.The code-rate of a binary cyclic AN code is obtained by the following equation.The code-rate r and normalized burst-error-correcting ability b/n have the relation oftrade-off. Then, a new parameter g, defined asis presented, and is called normalized burst-error-correcting ability rate g. For binary cyclicAN codes with every burst-error-correcting ability b, the maximum value rup of the coderateis given by Many codes generated by odd integers in the range of 5≦A≦131069 are actually generatedby means of computer programs. We present the code-point distribution on a (g, r)plane. These codes are with burst-error-correcting ability in the range of 1≦b≦8. Manycodes with burst-error-correcting ability b = 1,2, and 3 can be found on each of the upperboundcurves.
徳島文理大学の論文

バースト誤り訂正2進巡回AN符号の符号点分布と性能評価

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