Exact Bit Error Probability of Multi-hop Decode-and-Forward Relaying with Selection Combining Bao Quoc Vo-Nguyen and Hyung Yun Kong Department of Electrical Engineering, University of Ulsan, San 29 of MuGeo Dong, Nam-Gu, Ulsan, 680-749 Korea {baovnq,hkong}@mail.ulsan.ac.kr http://wcomm.ulsan.ac.kr

Abstract. In this paper, an exact closed-form bit error rate expression for M -PSK is presented for multi-hop Decode-and-Forward Relaying (MDFR) scheme, in which selection combining technique is employed at each node. We have shown that the proposed protocol offers remarkable diversity advantage over direct transmission as well as the conventional decode-and-forward relaying (CDFR) scheme. Simulations are performed to confirm our theoretical analysis. Keywords: Bit Error Rate (BER), Decode-and-Forward Relaying, Rayleigh fading, Selection Combining, M -PSK, cooperative communication.

1

Introduction

Recently, relaying dual-hop transmission has gained more attention under forms of cooperative communications and it is treated as one of the candidates to overcome the channel impairment like fading, shadowing and path loss [1]. The main idea is that in a multi-user network, two or more users share their information and transmit jointly as a virtual antenna array. This enables them to obtain higher diversity than they could have individually [1-9]. In the past, relatively few contributions concerning evaluating performance of the DF relaying protocol with multi relays and maximal ratio combining (MRC) or selection combining (SC) have been published [2-9]. In particular, in [2], Jeremiah Hu and Norman C. Beaulieu derived a closed-form expression for outage probability of the CDFR networks with SC when the statistics of the channels between the source, relays, and destination are assumed to be independent and identically distributed (i.i.d.) and independent but not identically distributed (i.n.d.). In [4, 5], the performance of CDFR with maximal ratio combining at the destination in terms of outage probability and bit error probability over independent but not identically distributed channels was also examined. In [3, 6-9], a class of multi-hop cooperative scheme employing decode-and-forward relaying with MRC, called multi-hop Decode-and-Forward Relaying (MDFR) scheme, was proposed, and various performance metrics were also provided. D.-S. Huang et al. (Eds.): ICIC 2009, LNAI 5755, pp. 718–727, 2009. c Springer-Verlag Berlin Heidelberg 2009 

Exact Bit Error Probability of MDFR with Selection Combining

719

However, to the best of the authors’ knowledge, there is no publication concerning the exact expression for bit error rate of the MDFR with selection combining in both i.i.d. and i.n.d. Rayleigh fading channels. In this paper, we focus on selective decode-and-forward relaying where the relay must make an independent decision on whether or not to decode and forward source information [1]. In addition, a concept of cooperative diversity protocols for multi-hop wireless networks, which allows relay nodes to exploit all information they overhear from their previous nodes along the route to the destination to increase the change of cooperation, is applied. To that effect, the receiver at each node can employ a variety of diversity combining techniques to obtain diversity from the multiple signal replicas available from its preceding relaying nodes and the source. Although optimum performance is highly desirable, practical systems often sacrifice some performance in order to reduce their complexity. Instead of using maximal ratio combining which requires exact knowledge of the channel state information, a system may use selection combining which is the simplest combining method. It only selects the best signal out of all replicas for further processing and neglects all the remaining ones. The benefit of using SC as opposed to MRC is reduced hardware complexity at each node in the network. In addition, it also reduces the computational costs and may even lead to a better performance than MRC, because in practice channels with very low SNR can not accurately estimated and contribute much noise. The contributions of this paper are as follows. We derive an exact closedform expression bit error rate for M -PSK of the MDFR scheme. In addition, the comparison between the performance of MDFR and that of CDFR [2] is performed and it confirms that the proposed protocol outperforms CDFR in all range of operating SNRs. The rest of this paper is organized as follows. In Sect. 2, we introduce the model under study and describe the proposed protocol. Section 3 shows the formulas allowing for evaluation of average BER of the system. In Sect. 4, we contrast the simulations and the results yielded by theory. Finally, the paper is closed in Sect. 5.

2

System Model

We consider a wireless relay network consisting of one source, K relays and one destination operating over slow, flat, Rayleigh fading channels as illustrated in Fig. 1. The source terminal (T0 ) communicates with the destination (TK+1 ) via K relay nodes denoted as T1 , · · · , Tk , · · · , TK . Due to Rayleigh fading, the channel powers, denoted by αTi ,Tj = |hTi ,Tj |2 are independent and exponential random variables where hTi ,Tj is the fading coefficient from node Ti to node Tj with i = 0, · · · , K, j = 1, · · · , K + 1 and i < j. We define λTi ,Tj as the expected value of αTi ,Tj . The average transmit powers for the source and the relays are denoted by ρTi with i = 0, · · · , K, respectively. We further define γTi ,Tj = ρTi αTi ,Tj as the instantaneous SNR per bit for the link Ti → Tj .

720

B.Q. Vo-Nguyen and H.Y. Kong

T2 T1

T0

T3

T4

Fig. 1. A MDFR system with 3 relays (K = 3)

For medium access, a time-division channel allocation scheme with K +1 time slots is occupied in order to realize orthogonal channelization, thus no inter-relay interference is considered in the signal model. According to the selective DF relaying protocol [1], the relay decides to cooperate or not with the source in its own time slot, based on the quality of its received signals. Since selection combining technique is used, the relay adaptively chooses the strongest signal (on the basic of instantaneous SNR) among available ones to demodulate and then check whether its received data are right or wrong. If they are right, that relay will cooperate with the source in its transmission time slot, otherwise, it will keep silent. We define a decoding set D(Tk ) for node Tk , k = 1, 2, · · · , K + 1, whose members are its preceding relays which decode successfully. So it is obvious that D(Tk ) is a subset of C = {T1 , T2 , · · · , TK }. In real scenario, the decoding set is determined after receiving one frame by employing cyclic-redundancy-check (CRC). However, in this paper, we assumed that the decoding set can be decided by symbol-by-symbol for mathematical tractability of BER calculation [4]. We further assume that the receivers at the destination and relays have perfect channel state information (CSI) but no transmitter CSI is available at the source and relays.

3

BER Analysis

Similarly as in [2-7], namely applying the theorem of total probability, the bit error rate of the multi-hop decode-and-forward relaying can be derived as a weighted sum of the bit error rate for SC at the destination, BD [D(TK+1 )], corresponding to each set of decoding relay D(TK+1 ). Thus the end-to-end bit error rate for M -PSK of the system Pb can be written as  Pb = Pr [D(TK+1 )] BD [D(TK+1 )] (1) D(TK+1 )∈2C

where 2C denotes the power set of C that is the set of all subsets of C.

Exact Bit Error Probability of MDFR with Selection Combining

721

Since selection combining is exploited at each relay and the destination, the signal with largest SNR is always selected from the signals received from its k decoding set as well as from the source. Let us define {γi }ni=1 as the instantaneous SNR per bit of each path received by the node Tk from the set D∗ (Tk ) with their k expected values {¯ γi }ni=1 , respectively, where D∗ (Tk ) = D(Tk ) ∪ {T0 } and nk is the cardinality of the set D∗ (Tk ), i.e., nk = |D∗ (Tk )|. Under the assumption that all links are subject to independent fading, the cumulative distribution function (CDF) of βk = max ρTi αTi ,Tk = max γi ∗ i=1,...,nk

Ti ∈D (Tk )

can be determined by [10] Fβk (γ) = Pr[γ1 < γ, . . . , γi < γ, . . . , γnk < γ] =

nk  

1 − e−γ/¯γi

 (2)

i=1

Hence, the joint pdf of βk is given by differentiating (2) with respect to γ [11]. ⎡ ⎤ nk nk   ∂ ⎢ ⎥ i−1 Fβ (γ) = fβk (γ) = (3) ωi e−ωi γ ⎦ ⎣(−1) ∂γ k m ,...,m =1 i=1 1

i

m1 <···
i −1 where ωi = l=1 γ¯m . It is noted that the joint pdf of βk is expressed under a l mathematic tractable form, which offers a convenient way to derive the average bit error probability of the system. Due to the fact that the decoding set is determined on symbol-by-symbol basics, the conditional probability that relay node Tk is involved in the cooperative transmission is obtained as follows: Pr[Tk ∈ D(TK+1 )|D∗ (Tk )] = 1 − STk

(4)

where STk denotes the average symbol error rate (SER) of M -PSK modulated symbols transmitted from D∗ (Tk ). For the case of coherently detected M -PSK, to evaluate STk , the MGF-based approach is used [12], namely  

1 (M−1)π/M log (M )gMP SK STk = M βk − 2 dθ (5) π 0 sin2 θ where gMP SK = sin2 (π/M ) and Mβk (s) is defined as follows [12, eq. (1.2)]: ⎡ ⎤

∞ nk nk   1 ⎢ ⎥ i−1 Mβk (s) = fβk (γ)esγ dγ = (6) ⎣(−1) −1 ⎦ 1 − sω i m ,...,m =1 i=1 1

0

i

m1 <···
Finally, substituting (6) into (5) and after some manipulations [12, eq. (5.79)] give us the desired result as eq. (7) as follows: ⎡ ⎤ (M−1)π/M n n k k  sin2 θ 1 ⎣(−1)i−1 STk = dθ ⎦ π sin2 θ+gM P SK ωi −1 log M i=1

m1 ,...,mi =1

2

0

m⎡ 1 <···
2

1+gM P SK ωi

log2 M

⎤⎤⎫ (7) ⎬  ⎦⎦ π ⎭

M

722

B.Q. Vo-Nguyen and H.Y. Kong

By using the relation of joint probability of mass function (pmf) and sequence of conditional pmf [13], the decoding set probability can be written as follows: Pr[D(TK+1 )] =   ∗ Pr [Tk ∈ D(TK+1 )|D (Tk )] ×  Tk ∈D(TK+1 )   (1 − Pr [Tl ∈ / D(TK+1 )|D∗ (Tl )])

(8)

Tl ∈C\D(TK+1 )

The closed-form expression for conditional bit error rate at the destination can be obtained by proceeding analogous to [14]. M  1 em Pr {θ ∈ Θm } BD [D(TK+1 )] = log2 M m=1

(9)

m m where Θm = [θL , θU ] = [(2m − 3)π/M, (2m − 1)π/M ] for m = 1, · · · , M and em is the number of bit errors in the decision region Θm . Without loss of generality, it is assumed that φ = 0, the probability Pr{θ ∈ Θm } is ⎤ ⎡ m

θU ∞ nK+1 nK+1 ⎢   ⎥ m m Pr{θ ∈ Θm }= fθ (θ |φ , γ)fβK+1(γ)dγdθ= ⎣(−1)i−1 I θU , θL ; ωi−1 ⎦(10) m0 θL

i=1

m1 ,...,mi =1 m1 <···
where fθ (θ|φ, γ) is defined by [14, eq. (9b)]. Furthermore, using the analysis in m m , θL ; ωi−1 ) can be derived as follows: [14], I(θU      m m  m m −1  θU 1 m 1 tan−1 (αm tan−1 (αm −θL m 1 U) L) + ψU + + , θL ; ω i = I θU −ψL (11) 2π 2 2 π 2 π with

  −1 m m m = log2 (M )ωi sin(θU ), μL = log2 (M )ωi−1 sin(θL )   m m log2 (M )ωi−1 cos(θU ) log2 (M )ωi−1 cos(θL ) m ! ! αm , α = = U L 2 2 (μm (μm U) +1 L) +1 m m μ μ m m ψU = ! mU = ! mL , ψL 2 (μU ) + 1 (μL )2 + 1 μm U

(12a) (12b) (12c)

Substituting (8)-(9) into (1), we can obtain the exact closed-form expression for bit error rate of the system.

4

Numerical Results

In this section, we provide some simulation results of the proposed protocol and verify these results with our derived formula. We consider a linear network

Exact Bit Error Probability of MDFR with Selection Combining

723

consisting of multiple nodes. The average channel power due to transmission between node Ti and node Tj is modeled as λTi ,Tj = κ0 d−η where dTi ,Tj is the Ti ,Tj distance from node Ti to node Tj , η is the path loss exponent and κ0 captures the effects due to antenna gain, shadowing, etc [15]. However, for a fair of comparison to direct transmission, the overall distance of all hops is normalized to be one, i.e., K k=0 dTk ,Tk+1 = 1, and the uniform power allocation is employed in order to keep the total power constraint. Without loss of generality, we assume κ0 = 1, η = 3 and each node is equidistant from each other, i.e., dTi ,Tj = (j − i)/(K + 1) for all results except those in Fig. 4.

0

10

−5

Bit Error Rate

10

DT − Analysis DT − Simulation K=1 Analysis K=1 Simulation K=2 Analysis K=2 Simulation Increasing K K=3 Analysis K=3 Simulation K=4 Analysis K=4 Simulation

−10

10

−15

10

0

5

10 15 20 Average SNR per Bit [dB]

25

30

Fig. 2. Effect of increasing the number of relays on the average bit error rate of the multi-hop decode-and-forward cooperative networks with BPSK modulation (M = 2)

Fig. 2 shows the bit error rate of MDFR for BPSK with different numbers of cooperative nodes. As can clearly be seen in high SNR regime, the improvement of bit error rate is proportional to the number of relays. In Fig. 3, we study the average BER performance for different levels of M PSK. Note that with Gray code used for bit-symbol mapping, average BER for QPSK is same with that of BPSK. Furthermore, as expected, the results from theory and from simulation are in excellent agreement. In Fig. 4, the performance of MDFR in both independent and identically distributed (i.i.d.) and independent but not identically distributed (i.n.d.) channels is examined. The results are based on the assumption that λTi ,Tj is set to be one and to be uniformly distributed between 0 and 1 for the i.i.d and i.n.d. case, respectively. It can be seen that the performance of MDFR under i.i.d. channels is better than that under i.n.d. channels. In Fig. 5, the performance of CDFR and MDFR are compared and illustrated. As clearly shown, MDFR always outperforms direct transmission as well as CDFR with transmit power gain of about 2 dB and 4 dB for K = 2 and K = 4, respectively, for any value of operating SNRs.

724

B.Q. Vo-Nguyen and H.Y. Kong

0

10

Increasing M

−2

Bit Error Rate

10

−4

10

BPSK Analysis BPSK Simulation QPSK Analysis QPSK Simulator 8−PSK Analysis 8−PSK Simulation 16−PSK Analysis 16−PSK Simulation 32−PSK Analysis 32−PSK Simulation 64−PSK Analysis 64−PSK Simulation 128−PSK Analysis 128−PSK Simulation

−6

10

−8

10

−10

10

0

5

BPSK & QPSK

10 15 20 Average SNR per Bit [dB]

25

30

Fig. 3. Effect of modulation levels on the average bit error rate of the multi-hop decodeand-forward cooperative networks with K = 2

0

10

i.n.d.

−2

10

−4

Bit Error Rate

10

K=1 Analysis −i.i.d. K=1 Simulation − i.i.d. K=1 Analysis −i.n.d. K=1 Simulation − i.n.d. K=3 Analysis −i.i.d. K=3 Simulation − i.i.d. K=3 Analysis −i.n.d. K=3 Simulation − i.n.d. K=5 Analysis −i.i.d. K=5 Simulation − i.i.d. K=5 Analysis −i.n.d. K=5 Simulation − i.n.d.

−6

10

−8

10

−10

10

i.i.d.

−12

10

0

5

10 15 20 Average SNR per Bit [dB]

25

30

Fig. 4. BEP for 4-PSK (M = 4) of the multi-hop decode-and-forward cooperative networks under i.i.d. channels (λTi Tj = 1) and i.n.d. channels (λTi Tj are uniformly distributed between 0 and 1) with i = 0, · · · , K, j = 1, · · · , K + 1 and i < j

In Fig. 6, we investigate the bit error rate of the multi-hop decode-and-forward cooperative networks in different communication environments, η. More specifically, η typically varies between 2 (free-space path loss) and 5 to 6 (shadowed areas and obstructed in-building scenarios) [16]. It can be seen that under same conditions, the MDFR offers more benefit in poor communication environments.

Exact Bit Error Probability of MDFR with Selection Combining

725

0

10

Direct Transmission

−5

Bit Error Rate

10

DT − Analysis DT − Simulation K=2 CDFR Analysis K=2 CDFR Simulation K=2 MDFR Analysis K=2 MDFR Simulation K=4 CDFR Analysis K=4 CDFR Simulation K=4 MDFR Analysis K=4 MDFR Simulation

−10

10

−15

10

0

5

10 15 20 Average SNR per Bit [dB]

25

30

Fig. 5. Performance comparison between MDFR and CDFR with QPSK modulation (M = 4) 0

10

−1

10

−2

Bit Error Rate

10

−3

10

−4

10

E /N =0 dB b

0

E /N =5 dB b

−5

0

E /N =10 dB

10

b

0

Eb/N0=15 dB −6

10

2

3

4 η

5

6

Fig. 6. Effect of pass loss exponents on the average bit error rate of the multi-hop decode-and-forward cooperative networks with 16-PSK modulation (M = 16)

Finally, in Fig. 7, we study the effect of diversity technique on the average BER of the multi-hop decode-and-forward cooperative networks. The BER curses confirm that, under same channel conditions, the performance of the system employing MRC receiver is always better as compared to an equivalent system using SC. Furthermore, the performance-loss gap between two systems tends to increase to be proportional to the number of relays. For example, the performance loss for the cases K = 1, 2 and 3 are 1,2 and 3 dB, respectively. However, it is reasonable because the advantage of MRC over SC comes at the price of complexity of the receiver at each node in the networks.

726

B.Q. Vo-Nguyen and H.Y. Kong

0

10

−2

10

−4

Bit Error Rate

10

−6

10

K=1 − SC K=1 − MRC K=2 − SC K=2 − MRC K=3 − SC K=3 − MRC

−8

10

−10

10

−12

10

0

10 20 30 Average SNR per Bit [dB]

40

Fig. 7. Effect of combining technique on the average bit error rate of the multi-hop decode-and-forward cooperative networks with 8-PSK modulation (M = 8)

5

Conclusion

We have presented the exact closed-form expression for bit error rate of multihop DF relaying over Rayleigh fading channels. Its validity was demonstrated by a variety of Monte-Carlo simulations. The expression is general and offers a convenient way to evaluate MDFR system which exploits SC technique. In addition, the results were shown that employing the MDFR significantly enhances the system performance compared to that of CDFR.

Acknowledgment This research was financially supported by the Ministry of Commerce, Industry and Energy (MOCIE) and Korea Industrial Technology Foundation (KOTEF) through the Human Resource Training Project for Regional Innovation.

References 1. Laneman, J.N., Tse, D.N.C., Wornell, G.W.: Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior. IEEE Transactions on Information Theory 50(12), 3062–3080 (2004) 2. Hu, J., Beaulieu, N.C.: Performance Analysis of Decode-and-Forward Relaying with Selection Combining. IEEE Communications Letters 11(6), 489–491 (2007) 3. Jung, Y.S., Lee, J.H.: A New Participation Strategy for Cooperative Diversity with Multiple Partners. IEICE Trans. Commun. E89-B(11), 3152–3155 (2006) 4. Lee, I.H., Kim, D.: BER Analysis for Decode-and-Forward Relaying in Dissimilar Rayleigh Fading Channels. IEEE Communications Letters 11(1), 52–54 (2007)

Exact Bit Error Probability of MDFR with Selection Combining

727

5. Beaulieu, N.C., Hu, J.: A Closed-Form Expression for the Outage Probability of Decode-and-Forward Relaying in Dissimilar Rayleigh Fading Channels. IEEE Communications Letters 10(12), 813–815 (2006) 6. Sadek, A.K., Su, W., Liu, K.J.R.: A Class of Cooperative Communication Protocols for Multi-Node Wireless Networks. In: IEEE 6th Workshop on Signal Processing Advances in Wireless Communications (2005) 7. Sadek, A.K., Su, W., Liu, K.J.R.: Multinode Cooperative Communications in Wireless Networks. IEEE Transactions on Signal Processing 55(1), 341–355 (2007) 8. Boyer, J., Falconer, D.D., Yanikomeroglu, H.: Multihop Diversity in Wireless Relaying Channels. IEEE Transactions on Communications 52(10), 1820–1830 (2004) 9. Boyer, J., Falconer, D.D., Yanikomeroglu, H.: Cooperative Connectivity Models for Wireless Relay Networks. IEEE Transactions on Wireless Communications 6(5), 1–9 (2007) 10. Papoulis, A., Pillai, S.U.: Probability, Random Variables, and Stochastic Processes, 4th edn. McGraw-Hill, Boston (2002) 11. Bao, V.N.Q., Kong, H.Y., Hong, S.W.: Performance Analysis of M-PAM and M-QAM with Selection Combining in Independent but Non-Identically Distributed Rayleigh Fading Paths. In: IEEE 68th Vehicular Technology Conference, 2008. VTC 2008-Fall, Calgary, Canada, pp. 1–5 (2008) 12. Simon, M.K., Alouini, M.-S.: Digital Communication over Fading Channels, 2nd edn. John Wiley & Sons, Hoboken (2005) 13. Leon-Garcia, A.: Probability and Random Processes for Electrical Engineering, 2nd edn. Addison-Wesley, Reading (1994) 14. Chennakeshu, S., Anderson, J.B.: Error Rates for Rayleigh Fading Multichannel Reception of MPSK Signals. IEEE Transactions on Communications 43(234), 338–346 (1995) 15. Proakis, J.G.: Digital communications, 4th edn. McGraw-Hill, Boston (2001) 16. Karl, H., Willig, A.: Protocols and Architectures for Wireless Sensor Networks. Wiley, Hoboken (2005)

Exact Bit Error Probability of Multi-hop Decode-and ...

sion for M-PSK is presented for multi-hop Decode-and-Forward Relaying. (MDFR) scheme, in ... and transmit jointly as a virtual antenna array. This enables them ... (MRC) or selection combining (SC) have been published [2-9]. In particular, in.

235KB Sizes 1 Downloads 212 Views

Recommend Documents

An Exact Closed-Form Expression for Bit Error Rate of ...
prove the performance of wireless communications over fading channels without the need ... error rate of DF relaying systems that employ MRC at the des- tination are ...... PCS mobile phone systems and LG chairman's office planning future ...

Exact outage probability of cognitive AF relaying with ...
harmful interference on PUs, the transmit power at SU-Tx Ps is set at. Ps = Ip/|hs,p|2, where Ip is the maximum tolerable interference power at PU and hs,p is the ...

Bit Error Rate Performance of Multiple-Channel OTDM ...
APIDLY GROWING Internet traffic volume is the major driving force for the deployment of low cost ultrahigh capacity optically-transparent photonic ... MUX) an optical fiber link, a CSMZ demultiplexer, an optical. R. 1930-529X/07/$25.00 © 2007 ...

Exact outage probability of cognitive AF relaying with ...
Foundation for Science and Technology Development (NAFOSTED). (No. ... V.N.Q. Bao (Posts and Telecommunications Institute of Technology,. Vietnam).

Bit Error Rate Performance Comparison of Equal ...
Channel Spacing and Repeated Unequal Spacing in. Reducing the ... Email:[email protected]. †. Department of ... (DSFs) in optical WDM systems enable a very high bit rate by keeping ..... dispersion schemes,” Opt. Eng., vol. 42, pp.

Bit Error Rate Performance Comparison of Equal ...
Abstract—The bit error rate (BER) performance comparison of a wavelength ... decreases due to a number of fiber nonlinearity effects, like. FWM, self and cross ...

Error Amplification in Failure Probability Estimates of ... - CiteSeerX
University of Florida. Copyright .... used to fit the response surface approximation. Results ... Table 2 which also shows that the fit is reasonably good. However ...

Error Amplification in Failure Probability Estimates of ... - CiteSeerX
Analytical and engineering application examples are investigated to ... used to alleviate the computational expense in reliability ...... probability calculation.

Performance Evaluation of Parallel Opportunistic Multihop ... - CiteSeerX
of the IEEE International Conference on Communications, Seattle,. WA, pp. 331-335 ... From August 2008 to April 2009, he was with Lumicomm Inc.,. Daejeon ...

Error Probability Performance for Multi-hop Decode ...
and to mitigate wireless channel impairment as well as to solve the high ... performance where there is no need a brute-force summation over all possible correct ...

On the bit error probabilities of GMSK in the Rayleigh ... - IEEE Xplore
detector, also known as MSK-type receiver, can be employed instead of a rather complicated ... literature, a number of studies have been reported focusing.

Global Effects of Local Transmission Strategies in Multihop Wireless ...
for home, campus, and business environments. In some ... A crucial design aspect of a wireless network is in the medium access control (MAC) protocol.1 A ...

Evaluation of Watermarking Low Bit-rate MPEG-4 Bit ... - CiteSeerX
other digital networks are means for freely and widely distributing high fidelity duplicates of digital media, which is a boon for authorized content distribution but ...

Symbol error probability of hop-by-hop beamforming in Nakagami-m ...
Nov 18, 2009 - is derived which reveals the array and diversity gain. Numerical results .... where v ј w А i ю 1, m ј v ю i ю 1=2, s ј a1l ю a2u=g0 ю b, j ј.

Evaluation of Watermarking Low Bit-rate MPEG-4 Bit ... - CiteSeerX
using a spatial-domain or transform-domain watermarking technique, and then ..... Average subjective test scores of each watermarked bit-stream and bit-rate.

Error-Locality-Aware Linear Coding to Correct Multi-bit ...
coverage. Bit Position. Endoded Data Bits. ➢ Necessary condition for single error correction: Enough parity bits to .... 2. 2G5L(23, 12) vs. Golay(23,12):3G.

Error-Locality-Aware Linear Coding to Correct Multi-bit ...
INTERNATIONAL TEST CONFERENCE. 1. 978-1-4244-7207-9/10/$26.00 .... proposed in 1959 for double adjacent errors in telephone lines and magnetic tapes ...

Hierarchically-organized, multihop mobile wireless ...
three key components of this system: the clustering procedures for defining a virtual, hierarchical control struc- ... 95-C-D156, as part of the Global Mobile Information Systems (GloMo) program. 1 ...... an accounting operation which keeps track of

List of Holidays - BIT Institute of Technology
Jul 29, 2014 - GENERAL ADMINISTRATION (POLL. ... (BY ORDER AND IN THE NAME OF THE GOVERNOR OF ANDHRA PRADESH). DR. P.K. MOHANTY.