Extending a repetition period of a random sequence
First Claim
1. A method for extending a sequence repetition period of a random number generator in a communications system based on the availability of a random sequence, comprising:
- performing, by a ring generator circuit, a plurality of residue number system (RNS) arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values;
converting, by said ring generator circuit, each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit;
generating, by said ring generator circuit, an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and
combining, by said communication system, said plurality of output sequence numbers having said arbitrary permutation ordering with respective output sequence bits defining information to be transmitted from said communications system.
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Abstract
A method is provided for extending a sequence repetition period of a random number generator in systems based on the availability of random sequences. The method includes performing RNS arithmetic operations to express a random number in a sequence as RNS residue values. Each generated random number has a value between zero and n!−1. The method also includes converting each of the RNS residue values to a relatively prime base number system so that each of the RNS residue values includes at least one digit. The method further includes generating an arbitrary permutation ordering of output sequence numbers using a select combination of digits associated with each of the RNS residue values. The arbitrary permutation ordering is applied to a cyclic structure having n elements. Each of the n elements has an associated output sequence number.
91 Citations
27 Claims
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1. A method for extending a sequence repetition period of a random number generator in a communications system based on the availability of a random sequence, comprising:
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performing, by a ring generator circuit, a plurality of residue number system (RNS) arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values; converting, by said ring generator circuit, each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; generating, by said ring generator circuit, an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and combining, by said communication system, said plurality of output sequence numbers having said arbitrary permutation ordering with respective output sequence bits defining information to be transmitted from said communications system. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A ring generator, comprising:
at least one electronic circuit configured for; performing a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values; converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and combining said plurality of output sequence numbers in said arbitrary permutation ordering with a plurality of output sequence bits defining information to be transmitted from a communications system. - View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18, 19)
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20. A device comprising a machine-readable storage medium having stored thereon instructions, which when executed by said device, cause the device to perform the following operations comprising:
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performing a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values; converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and combining said plurality of output sequence numbers in said arbitrary permutation ordering with a plurality of output sequence bits defining information to be communicated from said device. - View Dependent Claims (21, 22, 23, 24, 25, 26, 27)
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Specification