Pulse or digital communications – Systems using alternating or pulsating current – Plural channels for transmission of a single pulse train
Reexamination Certificate
2000-04-13
2004-03-02
Tran, Khai (Department: 2631)
Pulse or digital communications
Systems using alternating or pulsating current
Plural channels for transmission of a single pulse train
C375S341000, C714S774000
Reexamination Certificate
active
06700937
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of Invention
This invention relates to iterative decoding of input sequences.
2. Description of Related Art
Maximum a posteriori (MAP) sequence decoding selects a most probable information sequence X
1
T
=(X
1
, X
2
, . . . , X
T
) that produced the received sequence Y
1
T
=(Y
1
, Y
2
, . . . , Y
T
). For transmitters and/or channels that are modeled using Hidden Markov Models (HMM), the process for obtaining the information sequence X
1
T
that corresponds to a maximum probability is difficult due to a large number of possible hidden states as well as a large number of possible information sequences X
1
T
. Thus, new technology is needed to improve MAP decoding for HMMs.
SUMMARY OF THE INVENTION
This invention provides an iterative process to maximum a posteriori (MAP) decoding. The iterative process uses an auxiliary function which is defined in terms of a complete data probability distribution. The MAP decoding is based on an expectation maximization (EM) algorithm which finds the maximum by iteratively maximizing the auxiliary function. For a special case of trellis coded modulation, the auxiliary function may be maximized by a combination of forward-backward and Viterbi algorithms. The iterative process converges monotonically and thus improves the performance of any decoding algorithm.
The MAP decoding decodes received inputs by minimizing a probability of error. A direct approach to achieve this minimization results in a complexity which grows exponentially with T, where T is the size of the input. The iterative process avoids this complexity by converging on the MAP solution through repeated use of the auxiliary function.
REFERENCES:
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patent: 6167552 (2000-12-01), Gagnon et al.
patent: 6182261 (2001-01-01), Haller et al.
patent: 6223319 (2001-04-01), Ross et al.
patent: 6343368 (2002-01-01), Lerzer
patent: 6377610 (2002-04-01), Hagenauer et al.
Georghiades, et al., “Sequence Estimation in the Presence of Random Parameters Via the EM Algorithms”, IEEE Transactions on Communications, vol. 45, No. 3, Mar. 1997.
Turin,Digital Transmission System; Performance Analysis and Modeling, pp. 126-143, pp. 227-228, 1998.
AT&T Corp.
Brendzel Henry T.
Tran Khai
Tran Khanh Cong
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