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Algorithms for Spectrum Shaping of Binary Codes

IP.com Disclosure Number: IPCOM000100394D
Original Publication Date: 1990-Apr-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 5 page(s) / 192K

Publishing Venue

IBM

Related People

Guerin, R: AUTHOR [+2]

Abstract

This article is concerned with the improvement of spectral performances of binary codes. It considers the problem of mapping symbols from a known source to codewords from a given codeset, so as to obtain the best possible spectral performance. The assignment takes into account the probability distribution of the source and the characteristics of the codewords. The criteria used for spectral performance depend on the type of code. Two classes of codes are considered. The first class is the general class of non-DC-constrained codes, while the second consists of DC-constrained codes, wherein the power spectrum is restricted to be zero at zero frequency.

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Algorithms for Spectrum Shaping of Binary Codes

       This article is concerned with the improvement of
spectral performances of binary codes.  It considers the problem of
mapping symbols from a known source to codewords from a given
codeset, so as to obtain the best possible spectral performance.  The
assignment takes into account the probability distribution of the
source and the characteristics of the codewords.  The criteria used
for spectral performance depend on the type of code.  Two classes of
codes are considered.  The first class is the general class of
non-DC-constrained codes, while the second consists of DC-constrained
codes, wherein the power spectrum is restricted to be zero at zero
frequency.

      Most previous work in related areas concentrates on the design
of new codes with improved spectral performance.  For example, (1,2)
propose DC-constrained codes with better cut-off rates at zero
frequency by forcing higher-order derivatives of the power spectrum
to zero at zero frequency.  Shaft (3) considers bandwidth compaction
codes which permit a decrease in bandwidth at the cost of a decrease
in signal to noise ratio.  Marcus and Siegel (4) propose codes with
spectral nulls at rational sub-multiples of the symbol frequency.

      The scope of this work is different in the sense that the
source and the code are assumed given, and the differences in source
symbol probabilities are exploited to obtain assignments of codewords
to source symbols that achieve improved spectral performance.  Most
of the references mentioned above assume sources emitting
equiprobable symbols.  However, many practical sources inherently
have non-uniform symbols distribution.  It is in such cases that the
results of this disclosure have most of their significance, although
some of them also apply to sources with uniform symbols distribution.

      The original motivation of this work was to see if non-uniform
source distributions, which, in schemes such as Huffman coding, had
been used to improve time domain performance, e.g., bit rate, could
similarly be exploited to improve spectral performance.  As mentioned
earlier, two special cases were studied.

      In the case of non-DC-constrained codes, a method is presented
that maximizes power in the main lobe of the power spectrum.  The
result holds when transmission pulses, with decreasing energy
spectrum in the main lobe, are used.  The result gives mathematical
basis to the rather intuitive argument that, to maximize the power in
the main lobe of the spectrum, codewords with less transitions must
be assigned to source symbols with higher probabilities.

      In the possibly more interesting case of DC-constrained codes,
an algorithm is presented that, for a given source and code, gives
the assignment resulting in the highest cut-off frequency.
Interestingly enough, the algorithm simply expands on the simple rule
of assigning codewords with more transitions to...