Compressed domain processors configured to perform operations on data compressed in a format that preserves order. The Compressed domain processors may include operations such as addition, subtraction, multiplication, division, sorting, and searching. In some cases, compression engines for compressing the data into the desired formats are provided.

Compressed domain processors configured to perform operations on data compressed in a format that preserves order. The Compressed domain processors may include operations such as addition, subtraction, multiplication, division, sorting, and searching. In some cases, compression engines for compressing the data into the desired formats are provided.

Collating text strings having Unicode encoding includes receiving two text strings S=s.sub.1s.sub.2 . . . s and T=t.sub.1t.sub.2 . . . t.sub.m. When the two text strings are not identical, there is a smallest positive integer p for which the two text strings differ. The process looks up the characters s.sub.p and t.sub.p in a predefined lookup table. If either of these characters is missing from the lookup table, the collation of the text strings is determined using the standard Unicode comparison of the text strings s.sub.ps.sub.p+1 . . . s.sub.n and t.sub.pt.sub.p+1 . . . t.sub.m. Otherwise, the lookup table assigns weights v.sub.p and w.sub.p for the characters s.sub.p and t.sub.p. When v.sub.pw.sub.p, these weights define the collation order of the strings S and T. When v.sub.p=w.sub.p, the collation of S and T is determined recursively using the suffix strings s.sub.p+1 . . . s.sub.n and t.sub.p+1 . . . t.sub.m.

Collating text strings having Unicode encoding includes receiving two text strings S=s.sub.1s.sub.2 . . . s and T=t.sub.1t.sub.2 . . . t.sub.m. When the two text strings are not identical, there is a smallest positive integer p for which the two text strings differ. The process looks up the characters s.sub.p and t.sub.p in a predefined lookup table. If either of these characters is missing from the lookup table, the collation of the text strings is determined using the standard Unicode comparison of the text strings s.sub.ps.sub.p+1 . . . s.sub.n and t.sub.pt.sub.p+1 . . . t.sub.m. Otherwise, the lookup table assigns weights v.sub.p and w.sub.p for the characters s.sub.p and t.sub.p. When v.sub.pw.sub.p, these weights define the collation order of the strings S and T. When v.sub.p=w.sub.p, the collation of S and T is determined recursively using the suffix strings s.sub.p+1 . . . s.sub.n and t.sub.p+1 . . . t.sub.m.

Systems and methods are described for generating and implementing pulse-shaping filters for efficient utilization of limited spectral resources in wireless communication systems. Wireless communication systems operating at high spectral efficiency conventionally use pulse shaping filters that rely on Nyquist waveforms for good main lobe performance with low inter-symbol interference (ISI) power. Conventional uses of non-Nyquist waveforms typically involve an orthogonalization process to convert those non-Nyquist waveforms to Nyquist waveforms for ISI free performance. Embodiments of pulse shaping filters described herein generate a non-Nyquist partial response (NNPR) transmit filter and/or matched receive filter based on applying a tunable second-weighted orthogonalization to a tunable first-weighted non-Nyquist waveform to obtain a pulse-shaping waveform with parametric control over throughput and power penalty.

Systems and methods are described for generating and implementing pulse-shaping filters for efficient utilization of limited spectral resources in wireless communication systems. Wireless communication systems operating at high spectral efficiency conventionally use pulse shaping filters that rely on Nyquist waveforms for good main lobe performance with low inter-symbol interference (ISI) power. Conventional uses of non-Nyquist waveforms typically involve an orthogonalization process to convert those non-Nyquist waveforms to Nyquist waveforms for ISI free performance. Embodiments of pulse shaping filters described herein generate a non-Nyquist partial response (NNPR) transmit filter and/or matched receive filter based on applying a tunable second-weighted orthogonalization to a tunable first-weighted non-Nyquist waveform to obtain a pulse-shaping waveform with parametric control over throughput and power penalty.

A method for protecting data in a data memory against an undetected change, wherein a functional variable x is encoded via a value, an input constant, an input signature and a timestamp D into a coded variable, where the functional variable is normalized relative to a base to form the integer value from the functional variable.

Compressed domain processors configured to perform operations on data compressed in a format that preserves order. The Compressed domain processors may include operations such as addition, subtraction, multiplication, division, sorting, and searching. In some cases, compression engines for compressing the data into the desired formats are provided.

Comparing text strings with Unicode encoding includes receiving two text strings S.sub.1 and S.sub.2. The process computes, for the first text string S.sub.1, a first weight according to a weight function that computes an ASCII prefix .sub.A(S.sub.1), computes a Unicode weight suffix .sub.U(S.sub.1), and concatenates the weights to form the first weight (S.sub.1)=.sub.A(S.sub.1)+.sub.U(S.sub.1). Computing the ASCII prefix for the first string applies bitwise operations to n-byte contiguous blocks of the first string to determine whether each block contains only ASCII characters, and replaces accented Unicode characters with equivalent unaccented ASCII characters when comparison is designated as accent-insensitive. When there is a first block containing a non-replaceable non-ASCII character, the Unicode weight suffix is computed by performing a character-by-character Unicode weight lookup beginning with the first block. The same process is applied to the second string. The text string are compared by comparing their computed weights.

Comparing text strings with Unicode encoding includes receiving two text strings S.sub.1 and S.sub.2. The process computes, for the first text string S.sub.1, a first weight according to a weight function that computes an ASCII prefix .sub.A(S.sub.1), computes a Unicode weight suffix .sub.U(S.sub.1), and concatenates the weights to form the first weight (S.sub.1)=.sub.A(S.sub.1)+.sub.U(S.sub.1). Computing the ASCII prefix for the first string applies bitwise operations to n-byte contiguous blocks of the first string to determine whether each block contains only ASCII characters, and replaces accented Unicode characters with equivalent unaccented ASCII characters when comparison is designated as accent-insensitive. When there is a first block containing a non-replaceable non-ASCII character, the Unicode weight suffix is computed by performing a character-by-character Unicode weight lookup beginning with the first block. The same process is applied to the second string. The text string are compared by comparing their computed weights.