A method compares text strings having Unicode encoding. The method receives a first string S=s.sub.1s.sub.2 . . . s.sub.n and a second string T=t.sub.1t.sub.2 . . . t.sub.m, where s.sub.1, s.sub.2, . . . , s.sub.n and t.sub.1, t.sub.2, . . . , t.sub.m are Unicode characters. The method computes a first string weight for the first string S according to a weight function . When S consists of ASCII characters, (S)=S. When S consists of ASCII characters and some accented ASCII characters that are replaceable by ASCII characters, (S)=g(s.sub.1)g(s.sub.2) . . . g(s.sub.n), where g(s.sub.i)=s.sub.i when s.sub.i is an ASCII character and g(s.sub.i)=s.sub.i when s.sub.i is an accented ASCII character that is replaceable by the corresponding ASCII character s.sub.i. The method also computes a second string weight for the second text string T. Equality of the strings is tested using the string weights.

A method compares text strings having Unicode encoding. The method receives a first string S=s.sub.1s.sub.2 . . . s.sub.n and a second string T=t.sub.1t.sub.2 . . . t.sub.m, where s.sub.1, s.sub.2, . . . , s.sub.n and t.sub.1, t.sub.2, . . . , t.sub.m are Unicode characters. The method computes a first string weight for the first string S according to a weight function . When S consists of ASCII characters, (S)=S. When S consists of ASCII characters and some accented ASCII characters that are replaceable by ASCII characters, (S)=g(s.sub.1)g(s.sub.2) . . . g(s.sub.n), where g(s.sub.i)=s.sub.i when s.sub.i is an ASCII character and g(s.sub.i)=s.sub.i when s.sub.i is an accented ASCII character that is replaceable by the corresponding ASCII character s.sub.i. The method also computes a second string weight for the second text string T. Equality of the strings is tested using the string weights.

A computer program product, an apparatus, a functionally safe programmable controller and a method for processing data, wherein an uncoded real number x is converted into a logarithmic number system (LNS) coded integer x.sub.LNS via a predetermined conversion rule for a logarithmic number system (LNS) in accordance with the relationship: x.sub.LNS=sgn(x).Math.2.sup.m+Id|x|.Math.2.sup.n, where sgn(x) denotes a sign function of the uncoded real number x, Id|x| denotes a binary logarithm of the uncoded real number x, m denotes a first exponent and n denotes a second exponent, and the LNS-coded integer x.sub.LNS is coded into an arithmetically coded integer x.sub.c via arithmetic coding such that the required integer operations is reduced.

A method and structure for probabilistic shaping and compensation techniques in coherent optical receivers. According to an example, the present invention provides a method and structure for an implementation of distribution matcher encoders and decoders for probabilistic shaping applications. The techniques involved avoid the traditional implementations based on arithmetic coding, which requires intensive multiplication functions. Furthermore, these probabilistic shaping techniques can be used in combination with LDPC codes through reverse concatenation techniques.

A communication system receives a binary sequence from a sensor, identifies a power consuming characteristic of the binary sequence, and determines an error component configured to reduce the power consuming characteristic of the binary sequence. The system compares the error component to an error tolerance deviation, and if the error component is below the error tolerance deviation, combines the error component with the binary sequence to produce an output sequence and transmits the output sequence via a serial interface to a receiver configured to receive the output sequence. The error threshold is based in part on an error tolerance characteristic of the receiver.

A communication system receives a binary sequence from a sensor, identifies a power consuming characteristic of the binary sequence, and determines an error component configured to reduce the power consuming characteristic of the binary sequence. The system compares the error component to an error tolerance deviation, and if the error component is below the error tolerance deviation, combines the error component with the binary sequence to produce an output sequence and transmits the output sequence via a serial interface to a receiver configured to receive the output sequence. The error threshold is based in part on an error tolerance characteristic of the receiver.

Encoding and decoding apparatuses and methods for implementing multi-mode coding are provided. The apparatus includes a transmitter and a receiver connected to a data bus. When data bursts are converted by the transmitter into codewords each including a plurality of symbols and/or a codeword received by the receiver is recovered as data bursts, maximum transition avoidance (MTA) codeword mappings in which no maximum transition (MT) event occurs between the plurality of symbols and minimum DC current (MDC) codeword mappings related to minimum power consumption of the plurality of symbols are used.

Encoding and decoding apparatuses and methods for implementing multi-mode coding are provided. The apparatus includes a transmitter and a receiver connected to a data bus. When data bursts are converted by the transmitter into codewords each including a plurality of symbols and/or a codeword received by the receiver is recovered as data bursts, maximum transition avoidance (MTA) codeword mappings in which no maximum transition (MT) event occurs between the plurality of symbols and minimum DC current (MDC) codeword mappings related to minimum power consumption of the plurality of symbols are used.

Systems and methods are provided for encoding a multi-pixel caching scheme for lossless encoders. The systems and methods can include obtaining a sequence of pixels, determining repeating sub-sequences of the sequence of pixels consisting of a single repeated pixel and non-repeating sub-sequences of the sequence of pixels, responsive to the determination, encoding the repeating sub-sequences using a run-length of the repeated pixel and encoding the non-repeating sub-sequences using a multi-pixel cache, wherein the encoding using a multi-pixel cache comprises, encoding non-repeating sub-sequences stored in the multi-pixel cache as the location of the non-repeating sub-sequences in the multi-pixel cache, and encoding non-repeating sub-sequences not stored in the multi-pixel cache using the value of the pixels in the non-repeating sub-sequences.

Systems and methods are provided for encoding a multi-pixel caching scheme for lossless encoders. The systems and methods can include obtaining a sequence of pixels, determining repeating sub-sequences of the sequence of pixels consisting of a single repeated pixel and non-repeating sub-sequences of the sequence of pixels, responsive to the determination, encoding the repeating sub-sequences using a run-length of the repeated pixel and encoding the non-repeating sub-sequences using a multi-pixel cache, wherein the encoding using a multi-pixel cache comprises, encoding non-repeating sub-sequences stored in the multi-pixel cache as the location of the non-repeating sub-sequences in the multi-pixel cache, and encoding non-repeating sub-sequences not stored in the multi-pixel cache using the value of the pixels in the non-repeating sub-sequences.