摘要:
A sequence generator implemented on a processor that generates a sequence of signals applies a feedback shift register with feedback. A feedback loop connects at least a first and a second shift register element to last shift register element to a first shift register element of the shift register and includes at least one two-input n-state switching functions that is characterized by non-associative switching functions or switching tables. The sequence generator may be part of a scrambler, an autonomous sequence generator, a hash code generator, a communication device, and a data storage device.
摘要:
A sequence generator implemented on a receiver is synchronized with a sequence generator at a transmitter. The receiver receives k n-state symbols, with k>1 and n>1 wherein each of the k n-state symbols is associated with a generating state of the sequence generator at the transmitter. A processor in the receiver evaluates an n-state expression that generates an n-state symbol that is associated with a synchronized state of the receiver. Coefficients related to the n-state expression are stored on a memory and are retrieved by the processor. The synchronized state in one embodiment is part of a code hop. The sequence generator in the receiver may be part of a descrambler, of a communication device, of a data storage device and/or of an opening mechanism.
摘要:
An encoder creates an (p,k,n) n-state codeword with p n-state symbols of which k n-state symbols are data symbols, an n-state symbol being represented by a signal with n>2, p>2 and k>(p−k). Intermediate states of an encoder in forward and in reverse direction are provided in a comparative n-state expression and implemented on a processor. A plurality of signals representing a codeword with at least one n-state symbol in error is processed by the processor by evaluating the comparative n-state expression. A partial result of an expression is determined after a symbol has been received. An error location and an error magnitude or error value are determined. The error is corrected by the processor.
摘要:
Symbol reconstruction methods by applying Galois Field arithmetic to Reed Solomon codewords have been disclosed. Reconstruction methods by applying n-valued reversing logic functions are also provided. A correct codeword can be selected from calculated codewords by comparing a calculated codeword with the Reed-Solomon codeword in error. A correct codeword can also be found by comparing a codeword in error with possible (p,k) codewords. Non Galois Field Reed Solomon coders are disclosed. Methods for correcting symbols in errors that have been identified as being in error are provided. Apparatus that implement the error correction methods are disclosed. Systems, including communication and storage systems that use the disclosed methods are also provided.
摘要:
Methods for transposing elements of a sequence according to a rule, wherein the rule is derived from pseudo-noise or pseudo-noise like binary and non-binary sequences are disclosed. Sequences of transposed symbols can be recovered by applying a reversing rule. Sets of orthogonal hopping and transposition rules are created by applying transposition rules upon themselves. Sets of orthogonal hopping and transposition rules are also created from binary and non-binary Gold sequences.
摘要:
Method and apparatus for writing scrambled multi-value data to a physical media and for reading scrambled multi-value data from a physical media, are disclosed. The physical media can be an optical disk. The scrambling can be performed by a multi-valued LFSR scrambler and the descrambling can be performed by a multi-valued LFSR descrambler. Further, the multi-valued data that is scrambled can include synchronization data and/or user data. Error correction coding can be used during the writing process and processing to correct for errors can be used during the reading process. Also, methods and apparatus for synchronizing multi-valued data written to and read from physical media are disclosed. Multi-value correlation methods and apparatus are also disclosed.
摘要:
Methods and apparatus create codewords of n-state symbols having one of 3 or more states with n-state check symbols. Check symbols are created from independent expressions. Codewords are associated with a matrix for detection of one or more symbols in error and the location of such symbols in error. Symbols in error are reconstructed from symbols not in error, error syndromes and check symbols not in error. Deliberately created errors that can be corrected are used as nuisance errors.
摘要:
Gates or switches for use in circuits implementing ternary and multi-value functions are disclosed. The gates can be optical, mechanical or electrical. The gates can conduct or not conduct when a control input assumes one of multiple states, or when a control input assumes two or more of multiple states. Circuits and methods for implementing ternary and multi-value functions are also disclosed. Corrective design techniques that can be used when a logic expression is incorrectly realized are also disclosed. Circuits that use inverters and gates to realize logic expressions are also provided.
摘要:
A sequence generator implemented on a receiver is synchronized with a sequence generator at a transmitter. The receiver receives k n-state symbols, with k>1 and n>1 wherein each of the k n-state symbols is associated with a generating state of the sequence generator at the transmitter. A processor in the receiver evaluates an n-state expression that generates an n-state symbol that is associated with a synchronized state of the receiver. Coefficients related to the n-state expression are stored on a memory and are retrieved by the processor. The synchronized state in one embodiment is part of a code hop. The sequence generator in the receiver may be part of a descrambler, of a communication device, of a data storage device and/or of an opening mechanism.
摘要:
An encoder creates an (p,k,n) n-state codeword with p n-state symbols of which k n-state symbols are data symbols, an n-state symbol being represented by a signal with n>2, p>2 and k>(p-k). Intermediate states of an encoder in forward and in reverse direction are provided in a comparative n-state expression and implemented on a processor. A plurality of signals representing a codeword with at least one n-state symbol in error is processed by the processor by evaluating the comparative n-state expression. A partial result of an expression is determined after a symbol has been received. An error location and an error magnitude are determined. The error is corrected by the processor.