Space time block coding is a technique used in wireless communication to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data transfer. The fact that the transmitted signal must traverse a potentially difficult environment with scattering, reflection, refraction and so on and may then be further corrupted by thermal noise in the receiver means that some of the received copies of the data may be closer to the original signal than others. This redundancy results in a higher chance of being able to use one or more of the received copies to correctly decode the received signal. In fact, space–time coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible.

1. SUBMITTED BY
FAIZAN SHAFI [21304012]
M.Tech (ECE) - Ist year
SUBMITTED TO
Dr. P. Samundiswary
ASSOCIATE PROFESSOR
Dept. Of Electronics Engineering
PRESENTATION
ON
“SPACE TIME BLOCK CODES"
DEPARTMENT OF ELECTRONICS ENGINEERING
SCHOOL OF ENGINEERING AND TECHNOLOGY
PONDICHERRY UNIVERSITY,KALAPET,
PUDUCHERRY-605014

2. CONTENTS
 INTRODUCTION
 BLOCK CODES
 PROPERTIES OF BLOCK CODES
 SPACE TIME CODES
SPACE TIME BLOCK CODE
SPACE TIME TRELLIS CODE
 ORTHOGONALITY
 QUASI-ORTHOGONAL STBCs
 REFERENCES
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3. INTRODUCTION
 Equalization, Diversity, and Channel Coding are three techniques which can be used
independently or in tandem to improve received signal quality and link performance over
small-scale times and distances.
 Equalization compensates for intersymbol interference (ISI) created by multipath within time
dispersive channels. As we know, if the modulation bandwidth exceeds the coherence
bandwidth of the radio channel, ISI occurs and modulation pulses are spread in time into
adjacent symbols. An equalizer within a receiver compensates for the average range of
expected channel amplitude and delay characteristics. Equalizers must be adaptive since the
channel is generally unknown and time varying.
 Diversity is another technique used to compensate for fading channel impairments, and is
usually implemented by using two or more receiving antennas. The evolving 3G common air
interfaces also use transmit diversity, where base stations may transmit multiple replicas of the
signal on spatially separated antennas or frequencies. As with an equalizer, diversity improves
the quality of a wireless communications link without
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4. INTRODUCTION
altering the common air interface, and without increasing the transmitted power or bandwidth.
However, while equalization is used to counter the effects of time dispersion (ISI), diversity usually
employed to reduce the depth and duration of the fades experienced by a receiver in a local area
which are due to motion. Diversity techniques can be employed at both base station and mobile
receivers. The most common diversity technique is called spatial diversity, whereby multiple
antennas are strategically spaced and connected to a common receiving system. Other diversity
techniques include antenna polarization diversity, frequency diversity, and time diversity. CDMA
systems often use a RAKE receiver, which provides link improvement through time diversity.
 Channel coding improves the small scale link performance by adding redundant data bits in the
transmitted message, so that if an instantaneous fade occurs in the channel, the data may still
be recoverd at the receiver. At the baseband portion of the transmitter, a channel coder maps
the user’s digital message sequence into another specific code sequence containing a greater
number of bits than originally contained in the message. The coded message is then modulated
for transmission in the wireless channel.
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5. INTRODUCTION
 Channel coding is used by the receiver to detect or correct some (or all) of the errors
introduced by the channel in a particular sequence of message bits. Because decoding is
performed after the demodulation portion of the receiver, coding can be considered to be a
post detection technique. The added coding bits lowers the raw data transmission rate
through the channel (that is, coding expands the occupied bandwidth for a particular message
data rate). There are three general types of channel codes: block codes, Convolutional codes,
and turbo codes. Channel coding is generally treated independently from the type of
modulation used, although this has changed recently with the use of trellis coded modulation
schemes that combine coding and modulation to achieve large coding gains without any
bandwidth expansion.
 The three techniques of equalization, diversity, and channel coding are used to improve radio
link performance (i.e. to minimize the instantaneous bit error rate), but the approach, cost,
complexity, and effectiveness of each technique varies widely in practical wireless
communication systems.
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6. BLOCK CODES
 Block codes are forward error correction (FEC) codes that enable a limited number of errors to
be detected and corrected without retransmission. Block codes can be used to improve the
performance of a communication system when other means of improvement (such as
increasing transmitter power or using a more sophisticated demodulator) are impractical.
 In block codes, parity bits are added to blocks of message bits to make codewords or code
blocks. In a block encoder, k information bits are encoded into n code bits. A total of n-k
redundant bits are added to the k information bits for the purpose of detecting and correcting
errors [Lin83]. The block code is referred to as an (n,k) code, and the rate of the code is defined
as 𝑅𝑐= k/n and is equal to the rate of information divided by the raw channel rate.
 The ability of a block code to correct errors is a function of the code distance. Many families of
codes exist that provide varying degrees of error protection [Cou93], [Hay94], [Lin83], [Skl93],
and [Vit79].
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7. PROPERTIES OF BLOCK CODES
 Linearity:- Suppose Ci and Cj are two code words in an (n,k) block code. Let ɑ1 and ɑ2 be any
two elements selected from the alphabet. Then the code is said to be linear if and only if ɑ1C1
+ ɑ2C2 is also a code word. A linear code must contain the all-zero code word. Consequently, a
constant-weight code is nonlinear.
 Systematic:- A systematic code is one in which the parity bits are appended to the end of the
information bits. For an (n, k) code, the first k bits are identical to the information bits, and the
remaining n-k bits of each code word are linear combinations of the k information bits.
 Cyclic:- Cyclic codes are a subset of the class of linear codes which satisfy the following cyclic
shift property: If C =[c𝑛 − 1, 𝑐𝑛 − 2, … . . . , 𝑐0] is a code word of a cyclic code, then [c𝑛 −
2, 𝑐𝑛 − 3, … . . , 𝑐0, 𝑐𝑛 − 1] , obtained by a cyclic shift of the elements of C, is also a code word.
That is, all cyclic shifts of C are code words. As a consequence of the cyclic property, the codes
possess a considerable amount of structure which can be exploited in the encoding and
decoding operations.
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8. SPACE TIME CODES
 There are two types of Space Time Codes: STBC and STTC
 SPACE TIME BLOCK CODE(STBC):-Space time block coding is a technique used
in wireless communication to transmit multiple copies of a data stream across a number
of antennas and to exploit the various received versions of the data to improve the reliability of
data transfer. The fact that the transmitted signal must traverse a potentially difficult
environment with scattering, reflection, refraction and so on and may then be further corrupted
by thermal noise in the receiver means that some of the received copies of the data may be
closer to the original signal than others. This redundancy results in a higher chance of being able
to use one or more of the received copies to correctly decode the received signal. In fact, space–
time coding combines all the copies of the received signal in an optimal way to extract as much
information from each of them as possible.
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9. SPACE TIME CODES
 A class of linear coding for MIMO systems that aims to maximize the system diversity gain.
 Space-time block codes operate on a block of input symbols producing a matrix output over
antennas and time.
 STBC was developed by Alamouti.
 An STBC is usually represented by a matrix. Each row represents a time slot and each column
represents one antenna's transmissions over time.
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10. SPACE TIME CODES
 Here, Sij is the modulated symbol to be transmitted in time slot i from antenna j. There are to be
T time slots and nT transmit antennas as well as nR receive antennas. This block is usually
considered to be of 'length’ T.
 The code rate of an STBC measures how many symbols per time slot it transmits on average over
the course of one block. If a block encodes k symbols, the code-rate is
r=k/T
 Advantages
Constructed from known orthogonal designs.
Easily decoded by maximum likelihood decoding via linear processing at the receiver.
 Disadvantages
They suffer from lack of coding gain.
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11. SPACE TIME CODES
 SPACE TIME TRELLIS CODE (STTC):-
This scheme transmits multiple, redundant copies of a trellis (or convolutional) code
distributed over time and a number of antennas ('space').
Space-time trellis codes operate on one input symbol at a time producing a sequence of
spatial vector outputs.
 Advantage
Possesses both diversity and coding gain.
 Disadvantage
These are complex to decode .
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12. ORTHOGONALITY
 STBCs as originally introduced, and as usually studied, are orthogonal. This means
that the STBC is designed such that the vectors representing any pair of columns
taken from the coding matrix is orthogonal. The result of this is simple, linear,
optimal decoding at the receiver. Its most serious disadvantage is that all but one of
the codes that satisfy this criterion must sacrifice some proportion of their data
rate.
 Moreover, there exist quasi-orthogonal STBCs that achieve higher data rates at the
cost of inter-symbol interference (ISI). Thus, their error-rate performance is lower
bounded by the one of orthogonal rate 1 STBCs, that provide ISI free transmissions
due to orthogonality.
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13. QUASI-ORTHOGONAL STBCs
 These codes exhibit partial orthogonality and provide only part of the diversity gain mentioned
above. An example reported by Hamid Jafarkhani is:
The orthogonality criterion only holds for columns (1 and 2), (1 and 3), (2 and 4) and (3 and 4).
Crucially, however, the code is full-rate and still only requires linear processing at the receiver,
although decoding is slightly more complex than for orthogonal STBCs. Results show that this Q-
STBC outperforms (in a bit-error rate sense) the fully orthogonal 4-antenna STBC over a good
range of signal-to-noise ratios (SNRs). At high SNRs, though (above about 22 dB in this particular
case), the increased diversity offered by orthogonal STBCs yields a better BER. Beyond this point,
the relative merits of the schemes have to be considered in terms of useful data throughput.
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14. REFERENCES
 Rappaport T S, “Wireless Communications: Principles and Practice”, 2nd Edition,
Pearson India, 2010.
 https://en.wikipedia.org/wiki/Space%E2%80%93time_block_code#:~:text=Space
%E2%80%93time%20block%20coding%20is,the%20reliability%20of%20data%2
0transfer.
 https://www.electronics-notes.com/articles/antennas-propagation/mimo/space-
time-block-alamouti-codes-coding.php
 https://engineering.uci.edu/files/Jafarkhani-Space-Time-Block-Codes-July-
1999.pdf
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