Abstract:
Linear Feedback Shift Registers (LFSRs) based 2p state with p>2 or p≧2 scramblers, descramblers, sequence generators and sequence detectors in binary implementation are provided. An LFSR may apply devices implementing a binary XOR or EQUIVALENT function, a binary shift register and binary inverters and binary state generator, wherein at least an output of one shift register element in a first LFSR is connected to a device implementing a reversible binary logic function is a second LFSR. They may also apply 2p state inverters using binary combinational logic are applied. Memory based binary 2p state inverters are also applied. Non-LFSR based n-state scramblers and descramblers in binary logic are also provided. A method for simple correlation calculation is provided. Communication systems and data storage systems applying the provided LFSR devices are also disclosed.
Abstract:
Methods and apparatus for coding and decoding n-state symbols with n≧2 and n>2 and n>3 and n>4 are provided wherein at least one implementation of an addition over an alternate finite field GF(n) and an inverter defined by a multiplication over the alternate finite field GF(n) are provided. Encoders and decoders implementing a single n-state truth table that is a truth table of an addition over an alternate finite field GF(n) modified in accordance with at least one inverter defined by a multiplication over the alternate finite field GF(n) are also provided. Encoders include scramblers, Linear Feedback Shift Register (LFSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders. Systems applying encoders and decoders also are provided.
Abstract:
Apparatus and method for performing multi-value arithmetic operations are disclosed. Multi-value signals can be added, subtracted and multiplied using a first truth table to generate a residue and a second truth table to generate a carry. Additionally, method and apparatus to efficiently perform the function a0b1+a1b0 on multi-value signals are disclosed. Also an efficient method of processing large binary signals is disclosed.
Abstract:
Methods for storing on a storage or memory medium, and retrieving, and displaying of multiple images in a registered manner, the images have been recorded concurrently. The images may comprise at least 2 video programs. A camera system for recording multiple concurrent images is also disclosed. Lenses and corresponding image sensors are calibrated to have calibrated and associated settings for recording multiple images that are substantially registered images. A registered image may be displayed on a single display. It may also be displayed on multiple displays. A camera for recording and displaying registered multiple images may be part of a mobile phone.
Abstract:
Methods and apparatus to create and display screen stereoscopic and panoramic images are disclosed. Methods and apparatus are provided to generate multiple images that are combined into a stereoscopic or a panoramic image. An image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a stereoscopic or a panoramic image from the correct settings provided by the controller. A plurality of lens/sensor units is placed on a carrier. Lens/sensor units are rotationally aligned. A controller rotationally aligns images of lens/sensor units that are rotationally misaligned. The camera is enabled to communicate via a wired or via a wireless connection, with a separate, mobile, ultrathin, ultralight, display with a large display screen not smaller than 25 by 20 cm in a first embodiment of the present invention and not smaller than 20 by 15 cm in a second embodiment of the present invention to provide color images including video images in real-time. A compact controllable platform to hold and rotate a device with a lens/sensor unit is also provided.
Abstract:
Methods and systems for error detection and error correction in n-valued with n>2 data symbols are disclosed. N-valued check symbols are generated from data symbols in n-valued logic expressions using n-valued logic functions. N-valued Hamming codes are disclosed. Also disclosed is the generation of check symbols from data symbols in an n-valued expression wherein at least one check symbol is multiplied by a factor not equal to 0 or 1 in GF(n). Identifying n-valued symbols in error by check symbols and error correction by solving sets of independent n-valued equations are also disclosed. A method for introducing and removing annoyance errors is provided. Systems for error corrections in communication and data storage are also provided.
Abstract:
Methods and apparatus reducing the number of multipliers in Galois Field arithmetic are disclosed. Methods and apparatus for implementing n-valued Linear Feedback Shift Register (LFSR) based applications with a reduced number of multipliers are also disclosed. N-valued LFSRs with reduced numbers of multipliers in Fibonacci and in Galois configuration are demonstrated. Multiplier reduction methods are extended to n-valued functions with more than 2 inputs. Methods to create multiplier reduced multi-input n-valued function truth tables are disclosed. Methods and apparatus to implement these truth tables with a limited number of n-valued inverters are also disclosed. Scrambler/descrambler combinations with adders and multipliers over GF(2p) are provided. Communication, data storage and digital rights management systems using multiplier reduction methods and apparatus or the disclosed scrambler/descrambler combination are also provided.
Abstract:
A method for coding a message of a plurality of m-state symbols into a coded message of n-state symbols wherein n>m is disclosed. A method to make the distribution of states of n-state symbols a uniform distribution is also disclosed. A coding rule is initiated based on a distribution of states of m-state symbols. A method of coding the coding rule by transposition is also provided. In one embodiment a coded message of n-state symbols has symbols that each have a unique state. A system for executing the coding and decoding methods is also disclosed.
Abstract:
Ternary (3-value) and higher, multi-value digital scramblers/descramblers in digital communications. The method and apparatus of the present invention includes the creation of ternary (3-value) and higher value truth tables that establish ternary and higher value scrambling functions which are its own descrambling functions. The invention directly codes by scrambling ternary and higher-value digital signals and directly decodes by descrambling with the same function. A disclosed application of the invention is the creation of composite ternary and higher-value scrambling devices and methods consisting of single scrambling devices or functions combined with ternary or higher value shift registers. Another disclosed application is the creation of ternary and higher-value spread spectrum digital signals. Another disclosed application is a composite ternary or higher value scrambling system, comprising an odd number of scrambling functions and the ability to be its own descrambler.
Abstract:
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.