К вопросу синтеза генераторов модифицированных кодов с суммированием взвешенных информационных разрядов с последовательностью весовых коэффициентов, образующей натуральный ряд чисел

Излагаются результаты, полученные автором в области синтеза генераторов контрольных векторов модифицированных кодов Бергера. Данные коды принадлежат к классу модифицированных модульно взвешенных кодов с суммированием. Приводятся общие структуры генераторов таких кодов, а также алгоритм построения генератора, позволяющий оптимизировать его структуру, сократив количество используемых функциональных элементов. Выводится формула подсчета общего количества двухвходовых логических элементов, необходимых для технической реализации генератора. Предложенный алгоритм синтеза генераторов является универсальным и может быть использован для построения генераторов любых модифицированных модульно взвешенных кодов с суммированием.
Different codes with summation (most of which are Berger code modifications) are often used in reliable discrete devices design. Modified code with summation of weighted data bits refers to such modifications. It is systematic code (the same as Berger code) and has k = |~log2 (m +1)| check bits (m data vector length). This code formation involves attribution of natural numbers weight indexes, calculation of total active bits weight and its least nonnegative residue by modulo M = 2log2 (m+1) 1. This value is placed in low bits of check vector. High bit is calculated as modulo two sum of data bits with even positions (that have even weight indexes). This code has better data bits error detection properties comparing with Berger code. Also it is the code with minimum total number of undetectable data bits errors for given length of data and check vectors. The paper describes the method of modified Berger code generator synthesis. Component base list contains standard circuits of modulo two, half and full adders. They compose functional blocks of M = 2log2 (m+1) 1 sum. Generator itself is formed by cascade connection of such blocks. Two structural diagrams of modified Berger code generators are given; also the generator synthesis algorithm is described that optimizes its structure by separation of weight indexes by groups of summed numbers without transfers. These numbers are sent on inputs of counters of M = 2 logl (m+1)V1 sum. High bit of check vector is formed on the output of the block that calculate modulo two sum of data bits with even positions. The algorithm is illustrated on the example synthesis of the generator for modified Berger code with m = 8. -1 functional blocks of sum by M = 2log2 (m+1)_|' modulo and block of high bit formation that consists of The paper shows that of modified Berger code includes -1 modulo two adders. Dependence between complexity and data vector length is stated. It is shown that number of two-input gates in generator structure is calculated with the following expression: 7[log2 (m +1)) m -1|-12 m m + 3 2 ) 2 _ 2 _ + 9. The described way of generator synthesis is universal and could be used for the formation of generators for codes with summation of weighted data bits and for codes with summation of weighted transitions between adjacent bits as well.