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Browse Prior Art Database

Waterpouring Recipe for Prescribed Reliability

IP.com Disclosure Number: IPCOM000122665D
Original Publication Date: 1991-Dec-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 3 page(s) / 78K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR

Abstract

The classical waterpouring recipe (1,2) is designed for input power allocation to transmit at capacity rates. In real life one would like to transmit at rates optimized for prescribed reliability criteria. With this in mind, a waterpouring recipe for the input power allocation as a function of frequency to meet prescribed error rates is introduced.

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Waterpouring Recipe for Prescribed Reliability

      The classical waterpouring recipe (1,2) is designed for
input power allocation to transmit at capacity rates.  In real life
one would like to transmit at rates optimized for prescribed
reliability criteria.  With this in mind, a waterpouring recipe for
the input power allocation as a function of frequency to meet
prescribed error rates is introduced.  The recipe is given by the
formula
                              1       12        N(w)
                    |S(w)|2 = __ _   _____  ____________
                              g       p2       |H(w)|2
where H(w) denotes the channel response function as a function of
frequency, N(w) denotes the noise power spectrum, and g is determined
by the power constraint
                               I   |S(w)|2dw = E2
                                R
where E2 is a constant, and is a function of the physics of the
channel, and R is the open set (union of intervals) over which |S(w)|
is defined (positive).  It is readily seen that this formula is an
extension of the classical waterpouring recipe; the latter is the
special case where p = 12.

      The recipe is motivated by the following argument.  The channel
is viewed as a union of independent subchannels indexed by frequency
j.  Along each subchannel Cj we transmit 2mj levels, equally spaced
from -(2mj-1) sj|2 to (2mj-1)sj|2.  A uniform separation criteria is
given:
                                   sj
                              p = ____
                                   Nj
This is equivalent to prescribing uniform reliability across the
subchannels.  Data is encoded randomly and uniformly among the
levels, so that the average output power in subchannel Cj is
                                   (4m2j-1)s2j
                  |Hj|2|Sj|2 =   _________________
                       ...