m-sequence
m-sequence A periodic sequence of symbols generated by a linear feedback shift register whose feedback coefficients form a primitive polynomial. A q-ary register (with q prime) whose generating polynomial is of degree n will have period qn – 1, provided that the initial state is nonzero, and its contents will proceed through all the nonzero q-ary n-tuples. The termwise modulo-q sum of two m-sequences is another m-sequence: the m-sequences (of a given generating polynomial), together with the zero sequence, form a group.
The term is short for maximum-length sequence. It is so called because the generating shift register only has qn states, and so such a register (with arbitrary feedback logic) cannot generate a sequence whose period exceeds qn. But with linear logic the zero state must stand in a loop of its own (see Good–de Bruijn diagram) and so the period of a linear feedback register cannot exceed qn – 1. This period, which can be achieved when and only when the polynomial is primitive, is therefore the maximum that can be achieved.
m-sequences have many useful properties. They are employed as pseudorandom sequences, error-correcting codes (as they stand, or shortened, or extended), and in determining the time response of linear channels (see convolution). See also simplex codes.
The term is short for maximum-length sequence. It is so called because the generating shift register only has qn states, and so such a register (with arbitrary feedback logic) cannot generate a sequence whose period exceeds qn. But with linear logic the zero state must stand in a loop of its own (see Good–de Bruijn diagram) and so the period of a linear feedback register cannot exceed qn – 1. This period, which can be achieved when and only when the polynomial is primitive, is therefore the maximum that can be achieved.
m-sequences have many useful properties. They are employed as pseudorandom sequences, error-correcting codes (as they stand, or shortened, or extended), and in determining the time response of linear channels (see convolution). See also simplex codes.
More From encyclopedia.com
Symbolic Logic , Logic, Symbolic
A modern version of formal logic, referred to variously as logistic, mathematical logic, and the algebra of logic; it may be describe… Alu , ALU Abbrev. for arithmetic and logic unit. A portion of the central processor that generally forms functions of (usually) two input values and produc… Binary notation , Gray code A binary (n, n) block code having the following properties:
(a) there are 2n codewords, each of length n bits;
(b) successive codewords dif… Coding And Decoding , Coding and Decoding
Representation of information is a fundamental aspect of all communication from bird songs to human language to modern telecommun… Flip-flop , flip-flop (bistable) An electronic circuit element that is capable of exhibiting either of two stable states and of switching between these states in… Logic Circuit , logic circuit An electric circuit concerned with logic systems. The term logic device is often used synonymously. A logic circuit is required to prod…
You Might Also Like
NEARBY TERMS
m-sequence