Note: Descriptions are shown in the official language in which they were submitted.
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ARRANGEMENTS AND METHODS FOR SPACE-TIME TURBO TRELLIS CODING
This invention relates to coding for communications
systems, for example for a cellular wireless communications
system, for providing space-time (ST) diversity for so-called
turbo trellis coding (TC) or trellis coded modulation (TCM).
Background of the Invention
As is well known, wireless communications channels
are subject to time-varying multipath fading, and it is
relatively difficult to increase the quality, or decrease the
effective error rate, of a multipath fading channel. One',
technique which has been found to be advantageous is antenna
diversity, using two or more antennas (or signal polarizations)
at a transmitter and/or at a receiver of the system.
In a cellular wireless communications system, each
base station typically serves many remote (fixed or mobile)
units and its characteristics (e. g. size and location) are more
conducive to antenna diversity, so that it is desirable to
implement antenna diversity at least at a base station, with or
without antenna diversity at remote units. At least for
communications from the base station in this case, this results
in transmit diversity, i.e. a signal is transmitted from two or
more transmit antennas.
S. M. Alamouti, "A Simple Transmit Diversity
Technique for Wireless Communications", IEEE Journal on
Selected Areas in Communications, Vol. 16, No. 8, pages 1451-
1458, October 1998 describes a simple transmit diversity scheme
using space-time block coding (STBC). For the case of two
transmit antennas, complex symbols s0 and -s1* are successively
transmitted from one antenna and simultaneously complex symbols
s1 and s0* are successively transmitted from the other antenna,
where * represents the complex conjugate. These transmitted
symbols constitute what is referred to as a space-time block.
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It is also known to use various coding schemes in
order to enhance communications. Among such schemes, it has
been recognised that so-called turbo coding (parallel
concatenated convolutional coding) enables iterative decoding
methods to achieve results which are close to the Shannon limit
for AWGN (additive white Gaussian noise) communication
channels. A turbo coder uses two, typically identical,
recursive systematic convolutional (RSC) component coders,
signals to be transmitted being supplied directly to one of the
component coders and via an interleaver to the other of the
component coders. Accordingly, it would be desirable o
combine turbo and space-time coding techniques in the same
transmitter.
V. Tarokh et al., "Space-Time Codes for High Data
Rate Wireless Communication: Performance Criterion and Code
Construction'°, IEEE Transactions on Information Theory, Vol.
44, No. 2, pages 744-765, March 1998 describes various
convolutional, or trellis, codes which can be used with two or
more transmit antennas to provide the advantages of trellis
e(convolutional) coding and space-time coding. Although these
codes are considered optimal for maximum diversity gain, they
are not necessarily optimal for coding gain. Furthermore,
these codes are non-recursive. In contrast, it is well
established that the best efficiency for turbo coding is
achieved using recursive codes. Consequently, the codes
described by Tarokh et al. are not particularly suitable for
use in a-turbo coding arrangement.
P. Robertson et al., "Bandwidth-Efficient Turbo
Trellis-Coded Modulation Using Punctured Component Codes", IEEE
Journal on Selected Areas in Communications, Vol. 16, No. 2,
pages 206-218, February 1998 describes a turbo coder using
Ungerboeck and multidimensional TCM component codes, in which
the interleaver operates on groups each of m information bits.
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For each step corresponding to a group o~f m information bits, a
signal mapper associated with each component coder produces n
symbols, where n=D/2 and D is the signal set dimensionality;
for example D=2 or 4 and n=1 or 2. An n-symbol de-interleaver
de-interleaves output symbols from the second component coder,
and a selector alternately for successive steps selects symbols
output from the first component coder and symbols from the de-
interleaver and supplies them to a single output path. This
arrangement does not provide transmit diversity and this
document is not concerned with space-time coding.
G. Bauch, "Concatenation of Space-Time Block Codes
and "Turbo"-TCM", Proceedings of the International Conference
on Communications, ICC'99, pages 1202-1206, June 1999 describes
two types of turbo trellis coded modulation (TCM) coder, whose
output is supplied to a space-time block coder, so that the
turbo-TCM and STBC arrangements are simply concatenated with
one another. One of these two types of turbo TCM coder is as
described by Robertson et.al_ (to which reference is made for
details) as discussed above using Ungerboeck codes and
providing one symbol at the output of the mapping function, but
the Bauch illustration of this does not show the symbol de
interleaver. This Bauch publication does not discuss
multidimensional component codes.
A continuing need exists to provide further
improvements through coding in wireless communications.
Summary of the Invention
According to one aspect, this invention provides a
coding arrangement comprising: first and second recursive
STTCM (space-time trellis coded modulation) coders each
arranged to produce, in each of a.plurality of successive
symbol intervals, a plurality of T M-PSK (M-ary phase shift
keying, where M is a plural integer) symbols from b bits
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supplied thereto, where b is an integer; an interleaves
arranged to interleave groups each of b input bits within an
interleaving block with a mapping of even-to-even and odd-to- '
odd, or even-to-odd and odd-to-even, positions; input bits
supplied to the first codes and to the interleaves, and
interleaved bits supplied from the interleaves to the second
codes; a symbol de-interleaves arranged.to de-interleave, in a
manner converse to the interleaving by the interleaves, groups
of T symbols produced by the second STTCM codes; and a selector
arranged to supply T symbols produced by the first STTCM codes
and T symbols from the de-interleaves in alternating symbol
intervals to respective ones of T output paths.
Preferably each coder,is arranged to produce, in each
wsymbol interval, T modulo-M sums of linear combinations of
current and one or more preceding groups of the~b bits supplied
to the codes to constitute the T symbols produced by the codes
in the respective symbol interval. Conveniently, for each
codes, M=2b and b is at least 2; for example b=2 or 3.
The T output paths typically lead to T antennas of a
transmitter thereby providing space-time diversity for turbo
coded TCM symbols, and for example T=2, 3, or 4.
The invention also provides a method of coding for
providing space-time diversity for information to be
transmitted from a plurality T of antennas, comprising the
steps of: in each of a plurality of successive symbol
intervals, producing T symbols at outputs of each of first and
second recursive STTCM (space-time trellis coded modulation)
coders, to the first of which coders input bits are supplied
directly and to the second of which coders said information
bits are supplied after interleaving of bit groups for
respective symbol intervals in an interleaving block with a
mapping of even-to-even and odd-to-odd, or even-to-odd and odd-
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to-even, positions; de-interleaving, in a manner converse to
the interleaving, groups of T symbols produced by the second
STTCM coder; and selecting the T symbols produced by the first
coder and the T symbols from the de-interleaving step in
respective first and second alternating symbol intervals for
supply to paths to the T antennas.
The preferred features may be combined as appropriate, as would
be apparent to a skilled person, and may be combined with any
of the aspects of the invention.
Brief Description of the Drawings
The invention will be further understood from the
following description with reference to the accompanying
drawings, in which by way of example:
Fig. 1 illustrates parts of a known space-time block
code (STBC) transmitter;
Fig. 2 illustrates a known turbo coder;
Fig. 3 illustrates parts of a turbo space-time
trellis coded modulation (STTCM) coding arrangement for a
transmitter using two transmit antennas, in accordance with an
embodiment of this invention;
Fig. 4 illustrates a 16-state recursive trellis coder
which can be used in the arrangement of Fig. 3; and
Fig. 5 illustrates a decoding arrangement for use
with the coding arrangement of Fig. 3.
Detailed Description
Referring to the drawings; Fig. 1 illustrates parts
of a known space-time block code (STBC) transmitter. For
simplicity and clarity in this and other figures of the
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drawings, only those parts are shown which are necessary for a
full understanding of the prior art and embodiments of this
invention.
The transmitter of Fig. 1 includes a serial-to-
parallel (S-P) converter 10, an M-PSK mapping function 12, and
a space-time block codex (STBC) 14 providing outputs, via
transmitter functions such as up-converters and power
amplifiers not shown but represented in Fig. 1 by dashed lines,
to at least two antennas 16 and 18 which provide transmit
diversity. The S-P converter 10 is supplied with input bits of
information to be communicated and produces output bits on two
or more parallel lines to the M-PSK mapping function 12, which
produces..from the parallel bits sequential symbols x1, x~, ... of
an equal-energy signal constellation.
For example, as shown in Fig. 1 the mapping function
12 may provide a Gray code mapping of in each case 2 input bits
from the S-P converter 10 to respective ones of M=4 signal
points of a QPSK (quadrature phase shift keying) signal point
constellation. It can be appreciated that the mapping function
12 can provide any desired mapping to a signal point
constellation with any desired number M of phase states; for
example M=2 (for which the S-P converter 10 is not required),
4, or 8.
The QPSK symbols x1, x2, ..., represented by complex
numbers, are supplied to the STBC 14, which for simplicity is
shown in Fig. 1 as having two outputs for the respective
transmit antennas 16 and 18, but may instead have more than two
outputs for a corresponding larger number of transmit antennas.
For the case of two antennas as shown, the STBC 14 forms a
space-time block of symbols, as represented in Fig. 1, from
each successive pair of symbols x1 and x~ supplied to its input.
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More particularly, the STBC function is represented
by a T-by-T orthogonal matrix HX, where T is the number of
transmit antennas and hence symbol outputs of the STBC 14. For
the case of T=2 as represented in Fig. 1,
Hx lxl , xz ~ -_ x~ xz
l -x * x
z
In accordance with this~matrix HX, for each pair of PSK symbols
x1 and x2 supplied to the input of the STBC 14, in a first
symbol interval the antenna 16 is supplied with the symbol x1
and the second antenna 18 is supplied with the symbol x2, and in
a second symbol interval the first antenna 16 is supplied with
the symbol -x2* and the second antenna 18 is supplied with the
symbol xl*, where * denotes the complex conjugate. Thus both
QPSK symbols in each pair are transmitted twice in different
forms, from different antennas and at different times to
provide both space and time diversity. It can be seen that
each column of the matrix HX indicates the symbols transmitted
in successive intervals from a respective antenna, and each row
represents a respective symbol transmission interval.
Referring to Fig. 2, a known turbo (parallel
concatenated convolutional) coder comprises two recursive
systematic convolutional (RSC) coders 20 and 22 which are
referred to as the constituent or component coders of the turbo
coder, an interleaver 24, and a selector 26. Input bits are
supplied to the input of one coder 20, which produces at its
outputs both systematic bits S1, which are the same as the
input bits, and parity bits P1. The input bits are also
supplied to and interleaved by the interleaver 24, and the
interleaved bits are supplied to the input of the other coder
22, which produces at its outputs both systematic bits S2,
which are the same as the interleaved input bits, and parity
bits P2. The outputs of the two coders 20 and 22 are supplied
to inputs of the selector 26, except that typically and as
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shown in Fig. 3 the systematic bit output of the codes 22 is
not connected because the interleaved bits at this output are
never selected by the selector 26.
The selector 26 selects all of the systematic bits
S1, and some or all of the parity bits P1 and P2 from the
coders 20 and 22 respectively, and supplies them to an output
of the turbo codes as output bits. The selection of parity
bits depends upon the rate of the codes. For example, for a
rate 1/3 (3 output bits for each input bit) codes, the selector
26 can select all of the parity bits P1 and P2. For a rate 1/2
(2 output bits for each input bit) codes, the selector 26 can
alternately select the parity bits P1 and P2, so that only half
of,the parity bits P1 and half of the parity bits P2 are
output, this process being referred to as puncturing.
In the turbo-TCM arrangement (Robertson et al.)
referred to in the Background of the Invention, the interleaves
24 operates on groups each of m bits which are mapped at the
output of each component codes into a PSK symbol combining the
systematic and parity information. The symbols from the second
component codes are de-interleaved by a symbol de-interleaves,
and the output selector alternately selects the symbols output
from the first component codes (and the de-interleaves. The
interleaves (and consequently also the de-interleaves) in this
case must provide an even-to-even and odd-to-odd (or even-to-
odd and odd-to-even) position mapping.
In the concatenated SBTC and turbo code (Bauch)
arrangements referred to in the Background of the Invention, in
essence the output bits of a turbo codes such as that of Fig. 3
are supplied as input bits to a space-time block codes such as
that of Fig. 1, or the output symbols from a turbo-TCM codes as
described by Robertson et al. are supplied as input ymbols to
an STBC codes 14 as described above with reference to Fig. 1.
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Fig. 3 illustrates parts of a turbo space-time
trellis coded modulation (STTCM) coding arrangement for a
transmitter using two transmit antennas, in accordance with an
embodiment of this invention. As in the case of Fig. 1, the
two antennas are referenced 16 and 18, and input bits of
information to be communicated are supplied to the S-P
converter 10, which has b outputs for groups each of b
linformation bits. The remainder of Fig. 3 represents the turbo
STTCM coding arrangement, which comprises first and second
recursive STTCM component coders 30 and 32, an interleaves 34,
a symbol de-interleaves 36, and a selector 38 having two
outputs for the respective transmit paths to the two antennas
16 and 18. The coders 30 and 32 and the interleaves 34 each
have b inputs for the groups of information bits.
The groups of b bits supplied from the S-P converter
10 are interleaved in these groups by the interleaves 34. The
non-interleaved bit groups supplied to the codes 30, and the
interleaved bit groups supplied to the codes 32, are coded and
mapped into symbols by these functions as described further
below. For the case of two output paths corresponding to the
two transmit antennas as shown in Fig. 3, each of the coders 30
and 32 produces two M-PSK symbols in respect of each bit group,
where M=2b. The symbols produced in each symbol interval by the
first codes 30 from the non-interleaved bit groups are
identified as x11 and x12 as shown in Fig. 3. The symbols
produced by the second codes 32 are de-interleaved by the de-
interleaver 36, which operates conversely to the interleaves
34, to produce symbols in each symbol interval which are
identified as x21 and x22 as shown in Fig. 3. It is assumed
here for convenience and simplicity that the coders 30 and 32
are identical, but as for known turbo coders this need not
necessarily be the case and the coders 30 and 32 could instead
differ from one another.
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The selector 38 is controlled by a control signal of
alternating ones and zeros (1010... as illustrated) at the bit
group rate, and performs selection and puncturing functions as
represented in Fig. 3 by switches within the selector 38. In a
first state of the control signal, for example when the control
signal is a binary 1, the switches of the selector 38 have the
states illustrated in Fig. 3 in which the symbols x11 and x12
from the coder 30 are supplied as symbols x1 and x2 respectively
to the output paths to the transmit antennas 16 and 18
respectively, and the symbols x21 and x2z.from the symbol de-
interleaver 36 are not used. In a second state of the control
signal, for example when the control signal is a binary 0, the
switches of the selector 38 have their opposite states in which
the symbols x21 and x22 from the symbol de-interleaver 36 are
supplied as the symbols x1 and x~ respectively to the output
paths to the transmit antennas 16 and 18 respectively, and the
symbols x11 and x12 from the coder 30 are not used.
It can be appreciated that, with the selector 38
alternately selecting non-interleaved symbols from the coder 30
and de-interleaved symbols from the de-interleaver 36 as
described above, it is necessary (for decoding reasons as
explained in the Robertson et al. publication referred to
above) for the interleaver 34 to map even positions at its
input to even positions at its output, and odd positions at its
input to odd positions at its output (or, alternatively, even-
to-odd and odd-to-even position mapping), as in the case of the
Robertson et al. arrangement discussed above. The interleaver
34 is arranged to provide such mapping accordingly, and the de-
interleaver 36 provides a converse mapping as described above.
The coding arrangement of Fig. 3 is further described
below in terms of a simple example, in which the component
coders-30 and 32 are assumed to be identical 8-state recursive
QPSK (i.e. M=4) STTCM coders, with two output paths for two
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transmit antennas, and an interleaving block size of 6 groups
each of b=2 bits. The coder states are numbered 0 to 7, and
each QPSK symbol has one of four states numbered 0 to 3. Each
of the coders 30 and 32 operates in accordance with the
following Table 1, in which the next state of the coder and the
two output QPSK symbols are dependent upon the current state of
the coder and the b=2 input bits of the current group. These
are represented in the table in the form p/qr, where p denotes
the next state of the coder and q and r represent the two
output QPSK symbols, e.g. the symbols x11 and x12 respectively
for the coder 30:
Current Input
Bits
State 00 01 10 11
0 0/00 1/22 4/02 5/20
1 1/30 0/12 5/32 4/10
2 4/22 5/00 0/20 1/02
3 5/12 4/30 1110 0/32
4 6/11 7133 2113 3/31
5 7/01 6/23 3/03 2/21
6 2/33 3/11 6/31 7/13
7 3/23 2/01 7121 6/03
Table 1
For example, if an input bit sequence to this coding
arrangement is c=(10,00,11,10,01,01), then from Table 1 it can
be seen that, starting from state 0, the coder 30 generates the
symbol sequence (x11,x12)=x(0,2), (1,1), (1,3), (2,1), (0,1), (0,0)}
with its next states being successively 4, 6, 7, 7, 2, and 5.
If the interleaver 34 interleaves the sequence c to form the
interleaved sequence ci=(01,10,10,01,11,00), i.e. if the
interleaver moves 2-bit groups in positions numbered 0 to 5 in
the interleaving block to positions 2, 5, 4, 1, 0, and 3
respectively, then the coder 32 generates the symbol sequence
~(2,2),(3,2),(0,3),(3,0),(3,1),(1,2)} from an initial state of
0 with its next states being successively 1, 5, 3, 4, 3, and 5.
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The de-interleaver 34 de-interleaves this sequence to produce
the sequence (x21,x22)={(0,3), (1,2), (3,1), (3,2), (2,2), (3,0)}.
Consequently, the selector 38 produces the symbol sequence
x1=(0,1,1,3,0,3) on the output path to the antenna 16 and the
symbol sequence x2=(2,2,3,2,1,0) on the output path to the
antenna 18.
From the above description and from Fig. 3 it can be
appreciated that the units 30, 32, 34, 36, and 38 provide a
turbo coding arrangement for space-time trellis coded
20 modulation, thereby enabling advantages of coding gain and
diversity gain of these coding functions to be combined.
While the above simple example serves to assist in
providing a full understanding of the coding arrangement of
Fig. 3 and its operation, it can be appreciated that selection
of the particular STTCM codes to be used can have a significant
affect on the performance of the coding arrangement. For
example, the STTCM codes known from the Tarokh et al.
publication referred to above are not recursive as is important
to obtain the full advantages of a turbo coding arrangement,
and are not necessarily optimal for coding gain. STTCM codes
can be found through systematic code searching techniques
(where this is computationally feasible) to provide a
theoretically maximal diversity gain and an improved coding
gain, as described by S. Baro et al, in "Improved Codes for
Space-Time Trellis Coded Modulation", IEEE Communications
Letters, Vol. 4, No. 1, pages 20-22, January 2000. Desirable
STTCM codes (and consequently forms of the STTCM coders 30 and
32) can be determined in other ways either known or yet to be
devised. The particular codes described below are given by way
of example of recursive STTCM codes which are considered to
provide advantageous performance in particular situations.
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Fig. 4 illustrates a 16-state QPSK recursive feedback
STTCM codes which can be used to constitute each of the
component coders 30 and 32 in the coding arrangement described
above with reference to Fig. 3.
Referring to Fig. 4, the recursive feedback STTCM
codes comprises four delay elements 41 to 44 each providing a
delay T corresponding to each group of b=2 (for QPSK) input
bits c° and ct to the-codes at a time t, the delay elements
thereby providing the codes with 24=l6 states. In addition, the
codes comprises adding elements 45 and 46, multiplication
functions 47 to 52, and a summing function 53 which is supplied
with the outputs of the multiplication functions 47 to 52 and
which produces two output symbols (for two transmit antennas)
xt and xt at the time t, corresponding for example to the
output symbols x11 and x1~ respectively of the codes 30 as
described above.
The input bit ct is supplied to one input, and the
outputs of the delay elements 41 and 42 are supplied to other
inputs, of the adding element 45, whose output is supplied to
the input of the delay element 41. The output of the delay
element 41 is also supplied to the input of the delay element
42. The outputs of the adding element 45 and of the delay
elements 41 and 42 are also supplied to inputs of the
multiplication functions 47 to 49 respectively, which are also
supplied with multiplication coefficients (ao,ao), (al,ai), and
( a~ , a2 ) respectively.
Similarly, the input bit ct is supplied to one input,
and the outputs of the delay elements 43 and 44 are supplied to
other inputs, of the adding element 46, whose output is
supplied to the input of the delay element 43. The output of
the delay element 43 is also supplied to the input of the delay
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element 44. The outputs of the adding element 46 and of the
delay elements 43 and 44 are also supplied to inputs of the
multiplication functions 50 to 52 respectively, which are also
supplied with multiplication coefficients ( bo , bo ) , ( bi , bi ) , and
( b2 , b2 ) respectively.
The coder of Fig. 4 provides a modulo-4 sum of the
linear combinations of the current and delayed binary inputs,
represented algebraically by the Equation:
Vp V1
xn = ~c° an + ~cl bn mod 4 ( 1 )
t t-7o 7p t-ji h
jo=0 j1'~°
where n E{1,2~ identifies the two output symbols, the memory
order v of the coder is given by v=v° +v~ , a~i, bpi E {0,1, 2, 3~ for
QPSK, ji E ~0 ,1, ..., vi ~ , and a variable ct is def fined as
~i
ct = ct + ~ct-ji mod ~ with i E {0 ,1~ .
7i-1
The performance of STTCM coding on fast fading
channels (channels for which the fading coefficient changes
from one symbol interval to the next) is determined by the
minimum symbol Hamming distance 8~"in and the minimum product
distance pdmin. Table 2 lists recursive QPSK STTCM codes, in
terms of their multiplication coefficients for various values v
of memory order, which have been found to best satisfy these
criteria and accordingly are presently preferred., using the
structure exemplified by Fig. 4 as described above (contracted
or expanded if appropriate for the respective memory order):
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Memory
Order
v
2 3 4 5
~1n 2 2 3 3
pdmin 24 . 48 . 48 . 144 ,
0 0 0 0
(ao,ao) (3,1) (0,2) (0,2) (0.1)
(.ai ~ ai (2, 1) (1, 3) (0, 1) (2, 0)
)
(a2 ~ a2 - (2, 0) (2, 3) (3, 0)
)
( ) - _ _ (1~2)
(bo,bo) (2,2) (2,2) (2,3) (1,3)-
(b1~ b1) (0,2) (1,2) (1,3) (1,2)
(b2~bz) ~ - ~ ~ ~ (0,2) (2~1)
~
Table 2
Similarly, an 8-PSK STTCM coder for a transmitter
with two transmit antennas and for fast fading channels
provides a modulo-8 sum of the linear combinations of the
current and delayed binary inputs, ct,ct,and cc at a time t,
can be represented algebraically by the Equation:
vv v1 v2
xn = ~c° an + ~c1 bn + ~c2 do mod 8 ( 2 )
t t-jo Jo t-ji h t-jz Jz
ja=° j1-0 jz=_0
where again n Efl,2~ identifies the two output symbols, the
memory order v of the coder is given by v=v°+v1+v2, for 8-PSK
a~i,b~i,d~~ E f0,1,2,...,7~, ji E f0,1,...,v~~, and a variable cr is
defined as ct = ct + ~cr_j~ mod 2 with i E f 0 ,1, 2~ . Table 3 , having
j~-1
a similar form to Table 2 above, lists multiplication
coefficients for presently preferred 8-PSK STTCM codes:
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Number
of States
8 16 32
SHmin 2 2 2
pdmin 15 . 2 4 . 2 9 .
51 0 6 6
( ao , ao (2, 1) (0, 4) (3, 4)
)
(ai~ai) (2,4) (4,2) (0,4)
(bo,bo) (0,4) (1,0) (1,0)
(bi,bi) (4.0) (2,1) (0.1)
(ba. bz) _ ' (0.1) (60 0),
(do,do) (4,6) (3,1) (1,1)
(dl,di) (2,1) (6.4) (3,1)
(dz,dz) _ - (1,1)
Table 3
For slow fading channels (channels for which the
fading coefficient is constant over the symbols of an
interleaving block), recursive feedback STTCM codes can be
derived from feedforward codes by rearranging the order of
outputs of the trellis. The following Table 4 represents, for
the feedforward code and the derived recursive feedback code
and in a similar manner to that of Table 1 above, the next
state of the coder and the two output symbols of a 4-state QPSK
STTCM coder for a coding arrangement for two transmit antennas:
Current Feedforward Recursive
Feedback
Input Input
Bits Bits
State
00 01 10 11 00 01 10 11
0 0/00 1/23 2/02 3/21 0/00 1/23 2/02 3/21
1 0/20 1/03 2/22 3/01 3/00 0/21 1/02 2/23
2 0/12 1/31 2/10 3/33 2/02 3/23 0/00 1/21
3 0/32 1/11 2/30 3/13 1/00 2/23 3/02 0121
Table 4
Similarly, the following Table 5 represents, for the
feedforward code and the derived recursive feedback code, the
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next state of the coder and the two output symbols of an
8-state QPSK STTCM coder for a coding arrangement for two
transmit antennas:
Current Feedforward Recursive
Feedback
Input Input
Bits Bits
State
00 01 10 11 00 01 10 11
0 0/00 1/20 2,/02 3/22 0/00 1/20 2/02 3/22
1 0/11 1/31 2/13 3/33 4/13 5/31 6/11 7/33
2 0/21 1/01 2/23 3/03 3/03 0/21 1/01 2/23
3 0/32 1/12 2/30 3/10 7/10 4/12 5/32 6/30
4 0/03 1/23 2/01 3/21 2/01 3/21 0/03 1/23
0/10 1/30 2/12 3/32 6/12 7/32 4/10 5/30
6 0/20 1/00 2/22 3/02 1/20 2/22 3/02 0/00
7 0/31 1/11 2/33 3/13 5/31 6/33 7/13 4/11
Table 5
5 Similarly, the following Table 6 represents, for the
derived recursive feedback code only, the next state of the
coder and the two output symbols of an 8-state 8-PSK STTCM
coder for a coding arrangement for two transmit antennas:
Current Input
Bits
State 000 001 010 011 100 101 110 111
0 0/00 1/04 2/46 3/42 4/21 5/25 6/67 7/63
1 7/40 0/44 1/06 2/02 3/61 4/65 5/27 6/23
2 6/20 7/24 0/45 1/62 2/41 3/66 4/07 5/03
3 5/60 6/64 7143 0/22 1/01 2/05 3/47 4/26
4 4134 5/30 6/72 7/76 0/55 1/51 2/13 3/17
5 3/74 4170 5/32 6/36 7/15 0/11 1/53 2/57
6 2/54 3/33 4/12 5/16 6/75 7/71 0/50 1/37
7 1/14 2/10 3/52 4/56 5/35 6/31 7/73 0/77
Table 6
The recursive feedback STTCM codes defined in Tables
4, 5, and 6 can be used with advantage for a transmitter with
two transmit antennas for slow fading channels.
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The above examples relate to recursive STTCM codes
that provide two output symbols for each group of b input bits,
for supply to two antennas in an alternating manner from the
two component coders 30 and 32 of the turbo coding arrangement
of Fig. 3. It can be appreciated that the same principles can
be applied to a coding arrangement for use with a greater
number of transmit antennas by using recursive STTCM component
codes that provide a correspondingly greater number of output
symbols for each group of b input bits. Considered generally,
if the transmitter has a plurality of T transmit antennas, then
each of the two component coders is chosen to be a recursive
STTCM coder providing T output symbols for each group of b
input bits, and the selector alternately selects the T symbols
o~f the two component coders for supply to T output paths for
the T transmit antennas.
By way of example, the following Table 7 lists, in a
similar manner to Table 2 above, multiplication coefficients
for various values v of memory order for recursive gPSK STTCM
codes for three output symbols, i.e. for three transmit
antennas:
Memory
Order
v
2 3 4
SHmin 2 2 3
pdmin 64.0 120.0 384.0
(ao,aa,ao) (0,2,2) (0,2,0) (0,2,2)
(ai,a~,ai) (1,1,2) (1,3,0) (0,1,2)
(a2,a2,a2) - (2Ø1) (2.2,0)
(bo,bo,bo) (2r0,2) (2,2,2) (2,0,2)
(bi,bz,bi) (2,2,0) (1,2,2) (1,2,0)
(b2, b2, b2 - - (0~2~2)
)
Table 7
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For QPSK symbols for three transmit antennas for fast
fading channels, the recursive STTCM coders are represented by
Equation (1) given above but with n E~1,2,3~ corresponding to
the three output paths.
By way of further example, the following Table 8
lists, in a similar manner, multiplication coefficients for
various values v of memory order for recursive 8-PSK STTCM
codes for four output symbols, i.e. for four transmit antennas:
Memory Order
v
3 4 5
Sxmin 2 2 3
pdn,in 73.72 96.0 118.63
(ao,ao,ao,ao) (2,1,2,4) (0,4,4,4) (3,4,4,3)
( ai ~ ai ~ ai (2, 4, 2, (4, 2, 2, (0, 4, 2,
~ ai ) 1) 0) 6)
(bo,bo,bo,bo) (0,4,4,2) (1,0,1,1) (1,0,6,0)
(bl~bl~bi~b1) (4,0,4,0) (2,1,0,5) (0.,1,2,2)
(bz,bZ,b2,b~) - (0,1.,1,5) (6,0,1,4)
(do,do,do,do) (4,6,3,0) (3,1,2,2) (1,1,5,2)
(dl,di~di~d1) (2,1,6,4) (6,4,4,3) (3,1,0,1)
(dz.dz.dz.dz) _ - (1,1.3.0)
Table 8
For 8-PSK symbols for four transmit antennas for fast
fading channels, the recursive STTCM coders are represented by
Equation (2) given above but with n Ef1,2,3,4} corresponding to
the four output paths. The form of STTCM coders for other
combinations of M-PSK symbols and numbers of transmit antennas
can be seen from these examples.
Fig. 5 illustrates a decoding arrangement for use in
a receiver for receiving signals from a transmitter using a
coding arrangement as described above with reference to Fig. 3.
The receiver (not shown) may have a single receive antenna and
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related circuits, such as down converters and signal amplifiers
and samplers, to provide received symbols which are supplied to
the input of the decoding arrangement as described below, or it
may have two or more receive antennas the signals from which
are supplied to a correspondingly modified decoding
arrangement.
The decoding arrangement comprises a de-puncturing
selector 60, two soft output trellis code decoders 61 and 62,
symbol-based interleavers 63 and 64, and symbol-based de-
interleavers 65 and 66. The de-interleavers 65 and.66 operate
with the same symbol-based de-interleaving as the de-
interleaves 36 of the turbo coding, arrangement of Fig. 3,
conversely to the interleaving operation of the interleavers 63
and 64 and, equivalently, the bit group interleaves 34 of the
turbo coding arrangement.
The decoding arrangement of Fig. 5 is a symbol-by-
symbol log-MAP (maximum a posteriors) decoder, with respect to
which reference is directed to the Robertson et al. publication
referred to above, which contains a detailed discussion of such
decoders. As is known, the decoders 61 and 62, which are
complementary to the component coders 30 and 32 respectively of
the turbo coding arrangement of Fig. 3, operate iteratively to
take advantage of the turbo coding gain. Thus the decoder 61
operates on non-interleaved or de-interleaved information, and
the decoder 62 operates on interleaved information, the
interleavers 63. and 64 and the de-interleaves 65 providing the
symbol-based interleaving and de-interleaving of information
coupled to and between these decoders. After a desired number
of iterations, an output decision is derived from the decoder
62 via the de-interleaves 66.
Accordingly, in alternating symbol intervals
determined by a control signal of alternating ones and zeros
CA 02429658 2003-05-21
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(1010...) supplied to the selector 60, received symbols r are
supplied to the decoder 61 and are interleaved by the
interleaver 63 to produce interleaved received symbols r which
are supplied to the decoder 62. In a first iteration of the
decoding arrangement, the decoder 61 determines. extrinsic and
systematic information (as described in the Robertson et al.
publication, these are inseparable in a symbol-by-symbol
decoding arrangement) Ales, constituting log-likelihood ratios
for respective received symbols, which are interleaved by the
interleaver 64 to produce interleaved extrinsic and systematic
information Ales. This interleaved extrinsic and systematic
information is supplied to the decoder 62, which uses it as a
priori information to decode the interleaved received symbols
r. The decoder 62 consequently produces interleaved extrinsic
and systematic information AZ,es and interleaved information AZ
representing the received symbols. The interleaved extrinsic
and systematic information A2,es is de-interleaved by the de-
interleaver 65 to produce extrinsic and systematic information
na,es which is supplied to the decoder 61 for use as a priori
information in a second iteration of the decoding arrangement.
This process is repeated for the desired number of iterations,
after which the information A2 produced by the decoder 62 is
de-interleaved by the de-interleaver 66 to provide an output
decision for the respective symbols.
It is observed that, as described in the Robertson et
al. publication, the decoders 6l and 62 are arranged to avoid
using the same systematic information more than once in each
iteration.
Although particular embodiments of the invention are
described in detail above, it can be appreciated that numerous
modifications, variations, and adaptations may be made within
the scope of the invention as defined in the claims. In
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particular, it is observed that other recursive STTCM component
codes, bit group sizes, M-PSK symbols, and numbers of output
paths or transmit antennas can be used.
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