Error detection/correction and fault detection/recovery – Pulse or data error handling – Digital data error correction
Reexamination Certificate
1998-06-18
2001-10-02
Tu, Christine T. (Department: 2133)
Error detection/correction and fault detection/recovery
Pulse or data error handling
Digital data error correction
C714S701000, C370S335000
Reexamination Certificate
active
06298462
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to data transmission systems and methods for diversity systems used to combat multipath fading in mobile radio communications and, more particularly, to data transmission methods for dual diversity systems with M-ary orthogonal signaling in “Rayleigh” fading channels.
BACKGROUND OF THE INVENTION
Diversity systems are used for fading compensation (See, D. G. Brennan, “Linear diversity combining techniques”, Proc. of IRE, Vol. 47, pp. 1075-1102, June 1959.). In a dual diversity system, one symbol is transmitted over two channels and respective signals are combined at a receiver. There are several types of diversity combining techniques in practical use: selection combining (SC), equal gain combining (EGC), and maximal ratio combining (MRC). In the SC technique, a channel with the largest signal to noise ratio is selected. SC is simply implemented with orthogonal signaling and noncoherent demodulation which are frequently used in fading channels (G. Chyi, J. G. Proakis, and C. M. Keller, “On the symbol error probability of maximum selection diversity reception schemes over a Rayleigh fading channel”, IEEE Trans. Commun. Vol. 37, No. 1, pp. 78-83, January 1989.). The most efficient communication system design for M-ary orthogonal channels with noncoherent demodulation would employ low rate codes over a Galois field GF(q) with M=q (W. E. Ryan and S. G. Wilson, “Two classes convolutional codes over GF(q) for q-ary orthogonal signaling”, IEEE Trans. Commun. Vol. 39, No. 1, pp 30-40, January 1991.).
There are two kinds of coding techniques for dual diversity systems: one has each code symbol transmitted twice over each channel and the other has transmitted symbols that are made to differ from channel to channel through a special channel coding operation (G. Benelli, “Two coding techniques for diversity communications systems”, IEEE Trans. Commun. Vol. 38, No. 9, pp. 1530-1538, September 1990.). In the second technique, it is generally required to use multi-level coding operations.
When a codeword {overscore (c)} is transmitted over a communication channel, channel noise may corrupt the transmitted signals. As a result, a receiver receives the corrupted version of the transmitted codeword {overscore (c)}+{overscore (e)}, where {overscore (e)} is an error pattern of some weight u. The result of bounded distance decoding is categorized into three types: correct decoding, decoding failure, and decoding error. If u≦t, then a bounded distance decoder on the receiver'send detects and corrects the error {overscore (e)} and recovers {overscore (c)}. If u>t, then the decoder fails and either detects the presence of the error pattern but is unable to correct it, or miscorrects the received pattern {overscore (c)}+{overscore (e)} for some other codeword {overscore (c
l
+L )} if the received pattern falls into the radius l Hamming sphere of {overscore (c
l
+L )}. Miscorrection is more serious than error detection. This can occur when an error pattern {overscore (e)} is of weight u>t+1. Assuming that all error patterns of weight u are equally probable, decoding failure occurs when a received word is not contained in a decoding sphere of any codeword. Decoding failure is a kind of error detection. The conditional probability of decoding failure and undetected error are related with the geometry of code in a vector space GF(q)
n
. Let P
E
(u) denote the decoder error probability given that an error pattern of weight u occurs. P
E
(u) is given by the ratio of the number of decodable words of weight u to the number of words of weight u in the whole vector space. Let Q be the probability that a completely random error pattern will cause a decoder error. Then Q is the ratio of the number of decodable words to the cardinality of the whole vector. It is given by
Q
=
(
q
k
-
1
)
∑
i
=
0
t
(
n
i
)
(
q
-
1
)
i
q
n
(
1
)
It is known that P
E
(u) is less than or approximately equal to Q which is independent of u for Reed-Solomom codes (K. M. Cheung, “More on the decoder error probability for Reed-Solomon codes”, IEEE Trans. Inform Theory, Vol. 35, No. 4, pp. 895-900, July 1989.).
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to provide systems and methods for effectively transmitting data in dual diversity systems with M-ary orthogonal signaling in Rayleigh fading channels by utilizing Reed-Solomon coding.
To attain the above object, according to an aspect of the present invention, there is provided a method for transmitting data in dual diversity systems, comprising the steps of coding k information symbols into n symbols, and transmitting each of the coded symbols over each of channels simultaneously.
In this method, for k information symbols, one codeword with a rate of k
is needed, and each symbol is transmitted twice over two independent channels, that is, it has a channel diversity order of 2.
According to another aspect of the present invention, there is provided a method for transmitting data in dual diversity systems, comprising the steps of dividing k information symbols into two groups each having k/2 symbols, coding each k/2 symbols into n symbols, and transmitting the two groups of symbols over two channels, respectively.
In this method, for k information symbols, two codewords with a rate of k/2n are needed, and each symbol is transmitted once over one of two channels, that is, it has a channel diversity order of 1.
The above methods use the same number of channels during the same interval for k information symbols. These coding methods improve the error probability performance. The design rule of these data transmission methods are determined by using the after-decoding property of Reed-Solomon code.
A dual diversity system for transmitting data in accordance with the present invention includes coding means for coding k information symbols into n symbols, and transmitting means for transmitting the coded symbols over channels simultaneously. The coding means preferably includes a Reed-Solomon encoder for coding the information symbols into Reed-Solomon codes. The channels are preferably two independent channels and the transmitting means transmits the coded symbols twice over the two independent channels.
Another dual diversity system for transmitting data in accordance with the present invention includes dividing means for separating k information symbols into two groups each having k/2 symbols, coding means for coding each group of k/2 symbols into n symbols, and transmitting means for sending the two groups of symbols over two independent channels, respectively. The coding means preferably includes a Reed-Solomon encoder and the information symbols are preferably coded into Reed-Solomon codes. The transmitting means preferably transmits the coded symbols once over one of the two channels. The dividing means may includes a codeword divider.
The present invention will be better understood from the following detailed description of the exemplary embodiments thereof taken in conjunction with the accompanying drawings, and its scope will be pointed out in the appended claims.
REFERENCES:
patent: 5465267 (1995-11-01), Todoroki
patent: 5719875 (1998-02-01), Wei
patent: 5754563 (1998-05-01), White
patent: 5799010 (1998-08-01), Lomp et al.
patent: 5841794 (1998-11-01), Inoue et al.
F. Chau & Associates LLP
Samsung Electronics Co,. Ltd.
Tu Christine T.
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