binary data gathering with a helper in internet matsumoto, tad

Japan Advanced Institute of Science and Technology

JAIST Repositoryhttps://dspace.jaist.ac.jp/

Title

Binary Data Gathering with a Helper in Internet

of Things: Distortion Analysis and Performance

Evaluation

Author(s)Lin, Wensheng; He, Xin; Juntti, Markku;

Matsumoto, Tad

Citation IEEE Access, 7: 12855-12867

Issue Date 2019-01-15

Type Journal Article

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URL http://hdl.handle.net/10119/15724

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Binary Data Gathering with a Helper inInternet of Things: Distortion Analysisand Performance EvaluationWENSHENG LIN1, (Student Member, IEEE), XIN HE2, MARKKU JUNTTI3, (SeniorMember, IEEE), AND TAD MATSUMOTO1,3, (Fellow, IEEE)1School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan (e-mail: {linwest, matumoto}@jaist.ac.jp)2School of Computer and Information, Anhui Normal University, Anhui, China (e-mail: [email protected])3Centre for Wireless Communications, University of Oulu, Oulu, 90014, Finland (e-mail: {markku.juntti, tadashi.matsumoto}@oulu.fi)

Corresponding author: Wensheng Lin (e-mail: [email protected]).

This work is funded in part by China Scholarship Council (CSC) and in part by JAIST Core-to-Core Program. This work is also in partfunded by National Natural Science Foundation of China (NSFC), No. 61702011 and Anhui Provincial Natural Science Foundation, No.1808085QF191.

ABSTRACT This paper focuses on one-helper assisted binary data gathering networks, for example, suchas in Internet of Things (IoT), where a destination makes estimates of binary data relying on a numberof agents and one helper. Due to the noise, corrupting errors already exist in the agent observations. Toanalyze performance of this system, we formulate this system as a binary chief executive officer (CEO)problem with a helper. Initially, we use a successive decoding scheme to decompose the binary CEOproblem with a helper into the multiterminal source coding and final decision problems. Then, we presentan outer bound on the rate-distortion region for multiterminal source coding with binary sources and ahelper. After solving a convex optimization problem formulated from the derived outer bound, we obtainthe final distortion by substituting the minimized distortions of observation into the distortion propagatingfunction (DPF), which is derived to bridge the relationship between the joint decoding results and finaldecision. Finally, we analyze the trade-off of rate-distortion through theoretical calculation and simulations.Both the theoretical and simulation results demonstrate that a helper can obviously reduce the signal-to-noise ratio (SNR) threshold. We also have an in-depth discussion on the differences of system performanceimprovement between locating a helper and including an additional agent.

INDEX TERMS Binary CEO problem, binary data gathering, Internet of Things, rate-distortion, sideinformation

I. INTRODUCTION

Internet of Things (IoT) attracts increasing attentions ofacademia and industry, owing to the significant role of IoTin the smart society. Due to the frequent use of binary sig-nalling, in general, binary data gathering plays fundamentalroles of IoT in the big data era. Generally, binary datagathering is based on direct detection and/or with the aid ofagents. However, direct transmissions are almost impossiblein some strict communications environment, e.g., path lossdue to the long distance between the original binary data andthe destination, and/or time varying nature of the channelsdue to fading. Therefore, the destination has to only relyon the data received from the agents and make estimationsof the original binary data. Essentially, this scenario can

be formulated as the chief executive officer (CEO) problem[1] with binary sources. In the ordinary case, the agentobservations of the original data may contain errors whenthe agents suffer from noise. Consequently, the estimate ofthe target information could be a lossy recovery, if the ratessupported by the channels are not large enough due to theharsh communications environment.

Nowadays, to make connections more robust and enhancethe system performance, several wireless communicationssystems introduce the concept of helper [2]–[5]. These ap-plications of the helper inspire us to refine the performanceof binary data gathering in IoT system by the assistanceof a helper. As illustrated in Fig. 1, there are many agentsobserving the same binary data while errors corrupt the data

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W. Lin et al.: Binary Data Gathering with a Helper in Internet of Things: Distortion Analysis and Performance Evaluation

Agent

Helper

Destination

Agent

Errors

Binary

data

FIGURE 1. A scenario of binary data gathering with a helper in IoT.

sequences. Subsequently, the agents independently encodeand transmit the error-corrupted sequences to the destina-tion; meanwhile, a helper generates the helper sequence bymonitoring the agents and then send it to the destination.After decoding the received sequences from all agents andthe helper, the destination makes the final estimation of theoriginal binary data.

Since the system model shown in Fig. 1 can be formulatedas a binary CEO problem with a helper, we can analyze thesystem performance inspired by the previous achievementsrelated to the binary CEO problem. He et al. [6] presented alower bound of Hamming distortion for the binary CEO prob-lem with two sources, and the result was further extendedto solve the binary CEO problem with many sources in [7].Razi and Abedi [8] developed a method to analyze the con-vergence of iterative decoding for the binary CEO problem.An iterative joint decoding algorithm was implemented intothe wireless sensor networks (WSNs) with binary sourcesaccording to the model of binary CEO problem by Haghighatet al. in [9]. It is noticed that the binary CEO problem issolved in [6], [7] by decomposing the problem into multi-terminal source coding and final decision, i.e., a successivedecoding process. Likewise, for the performance analysis ofthe binary CEO problem with a helper, we can start from theproblem of multiterminal source coding with a helper andthen investigate the distortion of final decision.

Regarding the theoretical work related to multiterminalsource coding with a helper or side information, Ahlswedeand Korner [10] derived the rate region for source codingwith a helper providing side information. In [11], Wynerand Ziv characterized the rate-distortion function for lossycompression with side information, where only one sourceneeds to be recovered and another one provides assistancewithout rate limit. Slepian and Wolf [12] presented the fun-damental theorem of lossless multiterminal source coding,where each source can be viewed as the side information foranother one. The Slepian-Wolf theorem asserts a surprisingresult that distributed compression has the same achievablerate region as joint source coding. For the system withoutnecessary requirements of the full source recoveries, Berger[13] and Tung [14] derived the inner and outer bounds onthe rate-distortion region of the lossy multiterminal source

coding problem. In [15], Wagner and Anantharam extendedthe Berger-Tung bounds to the case with multiple sources andone link of uncompressed side information.

In the final decision step, the bit error probability of binarydata gathering was analyzed in [16], where many correlatedsources in a WSN have diverse bit-flipping probabilities,and soft combining is implemented as the final decisionrule. Based on these previous achievements, we establish theframework of the binary CEO problem with a helper as a suc-cessive encoding/decoding process, i.e., encoding/decodingthe multiple sources with the assistance of a helper and thencombining the joint decoding results. By this means, we havefinished the performance analysis for binary data gatheringwith a helper in IoT.

The contributions of this paper are summarized as follows:• To theoretically analyze the system performance, we

formulate binary data gathering by a one-helper assistedIoT as a binary CEO problem with a helper. Basedon the Berger-Tung outer bound, we derive an outerbound on the rate-distortion region of multiterminalsource coding problem with many agents and a helperfor binary sources. Then, the outer bound is utilizedto formulate a convex optimization problem, for thepurpose of minimizing distortions when reconstructingobservations.

• Moreover, we analyze the distortion propagating fromthe estimate of agent sequences to the final decision.By substituting the solution of the convex optimizationproblem, we investigate the trade-off of rate-distortionfor binary data gathering with a helper in IoT.

• Finally, we propose a practical coding scheme and eval-uate the system performance through simulations forbinary data gathering with a helper in IoT. Besides,we make a comparison of performance improvementbetween the system with a helper and that with anadditional agent.

The rest of this paper is organized as follows. Section IIformulates binary data gathering with a helper in IoT as thebinary CEO problem with a helper. In Section III, we ana-lyze the rate-distortion performance of the formulated binaryCEO problem with a helper. Then, Section IV evaluates thesystem performance through computer simulations for binarydata gathering with a helper in IoT. Finally, we conclude thiswork in Section V.

II. SYSTEM MODELNotation. The random variables and their realizations aredenoted by uppercase and lowercase letters, respectively.Calligraphic letters X , Y , · · · denote the finite alphabets ofa random variable. The superscript of a random vector andits realization represent the length of the vector. We use tto denote the time index and i to denote the index of anagent. The random variable with a finite alphabet as subscriptdenotes a set of all random variables with index in the finitealphabet, such as XL = {Xi|i ∈ L}. For a subset S ⊆ L, Screpresents the corresponding complementary set.

2 VOLUME x, 2019




Final

decision...

X1n

X2n

XLn

RL

Yn

Joint

decoder

^X1n

^X2n

^XLn

Xn

RH

R2

R1

M1

M2

ML

MH

g(·)

Multiterminal source coding with a helper Final decisionB1n

B2n

BLn

^Xn

Encoder 1

Encoder 2

Encoder L

Encoder H

FIGURE 2. A binary CEO problem with a helper.

As mentioned above, the IoT system depicted in Fig. 1can be formulated as the binary CEO problem with a helperin Fig. 2, where a binary source X acts as a commonsource. The discrete memoryless source (DMS) X gener-ates independent and identically distributed (i.i.d.) sequencexn = {x(t)}nt=1 by taking values from the binary alphabetX = {0, 1} for each time slot. The source X is observed byL agents at the same time. Due to the influence of noise, theobservation xni = {xi(t)}nt=1, where i ∈ L = {1, 2, · · · , L},may contains errors bni = {bi(t)}nt=1 [1]. Hence, the errorprobability Pr{xi(t) 6= x(t)} = pi for Bi ∼ Bern(pi). Theerroneous sequences are still forwarded to the destination,which is referred to as lossy-forward [17], [18]. Simultane-ously, a helper generates the helper sequence yn = {y(t)}nt=1

from the agent sequences bit by bit, and then transmitsthe helper sequence to the destination after compressing it.Therefore, all the Xi and Y can be also regarded as DMS.The sequences xni and yn are encoded at rates Ri and RH

by encoder i and encoder H, respectively. Encoder i andencoder H assign an index to each sequence according to thefollowing mapping rules:

ϕi : Xni 7→ Mi = {1, 2, · · · , 2nRi}, (1)

ϕH : Yn 7→ MH = {1, 2, · · · , 2nRH}. (2)

Then, the encoder outputs ML and MH are transmitted to ajoint decoder. The joint decoder constructs the estimates x̂nLfrom indices ML and MH by utilizing the mapping rule, as:

ψ :M1 ×M2 × · · · ×ML ×MH

7→ Xn1 ×Xn2 × · · · × XnL . (3)

Since the estimate x̂ni may occasionally deviate from theobservation xni , the Hamming distortion measure is definedto describe the distortion level between xi(t) and x̂i(t), as

di(xi(t), x̂i(t)) =

{1, if xi(t) 6= x̂i(t),

0, if xi(t) = x̂i(t).(4)

Hence, the expected distortion between the sequences xni andx̂ni is

di(xni , x̂

ni ) =

1

n

n∑t=1

di(xi(t), x̂i(t)). (5)

For given distortion values DL, the rate-distortion regionR(DL), consisting of all achievable rate tuple (RL, RH), isdefined as

R(DL) = {(RL, RH) : (RL, RH) is admissible such thatlimn→∞

E(di(xni , x̂

ni )) ≤ Di + ε,

for i ∈ L, and any ε > 0}. (6)

Finally, the destination reconstructs the estimate of xn

from x̂nL. Obviously, the distortion between xni and x̂ni willdetermine the final estimate x̂n. Hence, the final distortion

E

[1

n

n∑t=1

d(x(t), x̂(t))

]≤ D + ε, (7)

can be formulated as a function FDP(·) ofDL, where FDP(·)is referred to as distortion propagating function (DPF). TheDPF is defined as D = FDP(DL), which highly depends onthe decision rule. It should be emphasized here that the DPFlimits the decoding scheme to successive decoding, i.e., firstreconstructing x̂nL and then making the final decision.

III. RATE-DISTORTION ANALYSISThe first step of performance analysis for binary data gath-ering with a helper in IoT is to derive an outer bound onthe achievable rate-distortion region of multiterminal sourcecoding with a helper. By utilizing the derived outer bound, wecan formulate a convex optimization problem to minimize thedistortions in the step of multiterminal source coding. Then,by investigating the DPF with respect to specified decisionrule, we can obtain the distortion of final decision and finishthe performance analysis.

A. MULTITERMINAL SOURCE CODING WITH A HELPER1) Outer Bound of Rate-Distortion RegionFrom the extended Berger-Tung outer bound [15] with mul-tiple sources and one link of side information, we can obtain

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the outer bound for multiterminal source coding with a helperas presented in the following proposition.

Proposition 1: Let (XL, Y ) be a (L + 1)-DMS anddi(xi, x̂i) for i ∈ L be distortion measures. If a rate tuple(RL, RH) is achievable with distortion tuple DL for dis-tributed lossy source coding with a helper observing Y , thenit must satisfy the inequalities∑

i∈SRi ≥ I(XL;US |USc , V ), (8)

RH ≥ I(Y ;V ), (9)

for some conditional probability mass function p(uL, v|xL, y), and functions x̂i(uL, v) such that Ui → Xi →Xj and Xi → Xj → Uj form Markov chains andE(di(Xi, X̂i)) ≤ Di, where i, j ∈ L and i 6= j.

It is easy to understand that the constraint of (9) resultsfrom the rate limit on the helper instead of uncompressed sideinformation. Then, we introduce the definitions to be used inthe derivation of the outer bound for binary sources.

Definition 1: We define the following variables:

αi = pi ∗ h−1(1− [Ri]−), (10)

βi = pi ∗Di, (11)

where the operation ∗ denotes the binary convolution pro-cess; [Ri]

− = min{1, Ri}; h(·) and h−1(·) denote the binaryentropy function and its inverse, respectively.

Definition 2: According to [7], given a set of crossoverprobabilities {P}with a common sourceX , the joint entropyf(·) of the outputs from independent binary symmetric chan-nels (BSCs) is calculated as

f({P}) = −2|P|∑j=1

qj log2(qj), (12)

where | · | denotes the cardinality of the set, and

qj = 0.5

∏k∈Ai

pk∏k′∈Ac

i

p̄k′ +∏k∈Ai

p̄k∏k′∈Ac

i

pk′

, (13)

with p̄ = 1− p and Ai ⊆ {1, 2, · · · , |P|}.Now, we calculate the outer bound for binary sources.

Consider∑i∈S

Ri ≥ I(XL;US |USc , V )

= H(XL|USc , V )−H(XL|US , USc , V )

= H(XL|USc)− I(XL;V |USc)

−H(XL|US , USc) + I(XL;V |US , USc)

= I(XL;US |USc)− I(XL;V |USc)

+ I(XL;V |US , USc)

= I(XL;US |USc) + I(XS ;V |UL)

− I(XS ;V |UL)− I(XL;V |USc)

+ I(XL;V |US , USc). (14)

Then, we calculate I(XL;US |USc) + I(XS ;V |UL) and−I(XS ;V |UL) − I(XL;V |USc) + I(XL;V |US , USc) sep-arately. Consider

I(XL;US |USc) + I(XS ;V |UL)

= I(XS ;US |USc) + I(XSc ;US |USc , XS)

+ I(XS ;V |UL)

= I(XS ;US |USc) +H(XSc |USc , XS)

−H(XSc |US , USc , XS) + I(XS ;V |UL)

= I(XS ;US |USc) +H(XSc |USc , XS)

−H(XSc |USc , XS) + I(XS ;V |UL) (15)= I(XS ;US |USc) + I(XS ;V |UL)

= I(XS ;US , USc)− I(XS ;USc)

+ I(XS ;V |US , USc)

= I(XS ;UL, V )− I(XS ;USc)

≥ I(XS ; X̂S)− I(XS ;USc), (16)

where (15) follows the fact that Ui → Xi → Xj form aMarkov chain for i ∈ S and j ∈ Sc; (16) follows dataprocessing inequality when estimating X̂S from (UL, V ). Byapplying the result in [7] into (16), we have

I(XL;US |USc) + I(XS ;V |UL)

≥ f({pS , αSc})− f({αSc})−∑i∈S

h(Di), (17)

Next, consider

− I(XS ;V |UL)− I(XL;V |USc) + I(XL;V |US , USc)

= −I(XS ;V |UL)−H(V |USc)

+H(V |XL, USc) +H(V |US , USc)

−H(V |XL, US , USc)

= −I(XS ;V |UL)−H(V |USc) +H(V |XL)

+H(V |US , USc)−H(V |XL) (18)= H(V |UL, XS)−H(V |UL)−H(V |USc)

+H(V |US , USc)

= −I(V ;US , XS |USc)

= −I(V ;XS |USc), (19)

where (18) and (19) follow since Ui → Xi → V form aMarkov chain for i ∈ L. To further calculate (19), consider

I(V ;XS |USc) ≤ I(V ;XS) (20)≤ I(V ;Y ) (21)≤ RH, (22)

where (20) follows since condition reduces entropy, and (21)follows since XS → Y → V form a Markov chain. Noticethat the equality of (20) holds when no mutual informationexists between V and USc , i.e., the helper allocates full rateto help recovering XS . The equality of (21) holds when thehelper only utilize XS to generate the helper information Y .Moreover, the equality of (22) holds when the helper rate iscompletely exploited for compression. Consequently, there is

4 VOLUME x, 2019




no waste of the helper rate if the conditions for the equalityof (20-22) are satisfied. In this case, it is obvious that thestructure of the helper is optimal. By assuming that we havean optimal helper and substituting (17), (19) and (22) into(14), we can finally obtain∑i∈S

Ri

≥ f({pS , αSc})− f({αSc})−∑i∈S

h(Di)−RH. (23)

Remark 1: Since we assume that the structure of the helperis optimal, the constraint on the helper link, i.e., the inequality(9), is satisfied by the helper encoder, which finds a propercodeword MH to make I(Y ;V ) as large as possible.

Remark 2: If we set RH = 0, i.e., the helper link isequivalently cut off, (23) reduces to the outer bound withouta helper in [7].

2) Distortion MinimizationSince the final distortion D is a function of DL by thesuccessive decoding for given RL and RH, we can firstminimize the l2-norm of the vector [D1, D2, · · · , DL] bysolving a convex optimization problem [6], [7], which isformulated from the outer bound. Then, we calculate theminimum distortion D∗ by substituting the solution of theconvex optimization problem into DPF. Notice that for apractical communications system with channels, the channelcapacity should also be taken into consideration. Accordingto Shannon’s lossy source-channel separation theorem [19],[20], the distortion tuple DL is achievable if the followinginequalities hold:{

Ri(Di) · ri ≤ C(γi), for i ∈ L,RH · rH ≤ C(γH),

(24)

where C(γi) and C(γH) are the Shannon capacity usingGaussian codebook with γ as the signal-to-noise ratio (SNR)of the channel; ri and rH represent the end-to-end codingrates [21] of each agent link and the helper link, respectively.By applying the outer bound derived above, we can formulatethe convex optimization problem for the system with anoptimal helper as

minD1,D2,··· ,DL

‖[D1, D2, · · · , DL]‖2

s.t.∑i∈S

h(Di) ≥ f({pS , αSc})− f({αSc})−∑i∈S

C(γi)

ri

− C(γH)

rH,

0 ≤ Di ≤ 0.5, i ∈ L. (25)

After solving the convex optimization problem, we canobtain the minimum value of distortion D∗i for i ∈ L. Then,we use the estimates X̂n

L with minimum distortions D∗L tomake final decision.

B. FINAL DECISIONNotice that the compressed side information V n is not usedin the final decision to minimize the distortion between Xn

and X̂n. Hence, it is necessary to discuss the influence of thecompressed side information on final decision. We considerthe theoretically optimal case and a practical case, i.e., major-ity voting decision, respectively. For the final decision withcompressed side information, i.e., the system model shownin Fig. 3, when the final decision is optimal, consider

H(X)− h(d̃)

≤ I(X; X̂)

≤ I(X; X̂L, V ) (26)

= I(X; X̂L) + I(X;V |X̂L)

= I(X; X̂L) +H(V |X̂L)−H(V |X̂L, X) (27)

= I(X; X̂L), (28)

where d̃ is a dummy variable, and the steps are justified as:(26) according to data processing inequality, information lossmay happen in the final decision,(27) notice that V is a function of Y and Y is a function ofXL, and hence V is a function of XL, i.e., V = g′(XL).If H(V |X̂L) = H(g′(XL)|X̂L) > 0, it means that there isstill some information of XL not utilized in joint decoding.Hence, some distortions Di for i ∈ L can be further reducedin the convex optimization problem. Consequently, we haveH(V |X̂L) = 0 andH(V |X̂L, X) = 0 for the best utilizationof helper information in multiterminal source coding.

It is obvious that (26) is equal to (28), i.e., the com-pressed side information does not change the minimum finaldistortion. Similarly, for the majority voting decision, sincewe use the successive decoding scheme, the distortions DLmust be minimized after joint decoding. This means thatthe helper information has been completely utilized in jointdecoding step. Hence, the final distortion will not furtherreduce, whether the compressed side information is takeninto consideration or not in the majority voting decision. It issufficient to derive the DPF FDP(DL) for both optimal andmajority voting decision without side information.

For the optimal decision rule, consider

H(X)− h(d̃)

≤ I(X; X̂)

≤ I(X; X̂L) (29)

= H(X) +H(X̂L)−H(X, X̂L)

= H(X) + f({βL})− f({0, βL}), (30)

where the steps are justified as:(29) the probable information loss in the final decision,(30) X can be regarded as the output of a BSC with itself asthe input and the crossover probability equal to 0.

Consequently, we have

d̃ ≥ h−1[f({0, βL})− f({βL})]. (31)

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Final

decision...

X1n

X2n

XLn

RL

Yn

Joint

decoder

^X1n

^X2n

^XLn

Xn

RH

R2

R1

M1

M2

ML

MH

g(·)

B1n

B2n

BLn

^Xn

Encoder 1

Encoder 2

Encoder L

Encoder H

FIGURE 3. The system model for final decision with compressed side information.

Obviously, the minimum final distortionD, i.e., the distortionby optimal decision, is given by

D = h−1[f({0, βL})− f({βL})]. (32)

Since the optimal decision specifies a universal lowerbound, here, we consider another practical decision scheme,i.e., majority voting. The distortion between Xn and X̂n bymajority voting is the sum probability of several events ina Poisson binomial process [16]. We introduce a functionto evaluate the distortion in a Poisson binomial process asfollows:

Definition 3: Poisson binomial distortion function [16].The distortion between Xn and X̂n, which is estimated fromX̂nL by majority voting, is calculated by D = PB(βL) as

PB(βL) =

L∑j=L+1

2

Pr(J = j), if L is odd,

1

2Pr(J =

L

2)

+L∑

j=L2 +1

Pr(J = j), if L is even,

(33)

where

Pr(J = j)

=

L∏i=1

(1− βi), j = 0,

1

j

j∑i=1

(−1)(i−1)Pr(J = j − i)λ(i), j > 0,

(34)

with λ(i) =∑Lk=1( βk

1−βk)i for 0 ≤ j ≤ L.

By utilizing the Poisson binomial distortion function, wecan calculate the distortion D by majority voting among X̂Las

D = PB(βL). (35)

Remark: If pi are various among all links, weighted major-ity voting should be implemented to generate more accurateestimate of Xn. The error probability by weighted majority

voting is presented in Appendix A. In this paper, we focus onthe system with homogeneous agents for simplicity, and theresults can be easily extended to the case with heterogeneousagents according to Appendix A.

In summary, the DPFs for optimal decision and majorityvoting are (32) and (35), respectively. Therefore, we canobtain the minimum final distortion between Xn and X̂n

by substituting the solution D∗L of the convex optimizationproblem into DPF as D∗ = FDP(β∗L), where β∗L = {pi ∗D∗i |i ∈ L}.

C. NUMERICAL RESULTSNow, we start investigations on the trade-off of rate-distortionfor binary data gathering with a helper in IoT through numer-ical results. A memoryless source X ∼ Bern(0.5) is used inthe following. Initially, we compare the bit error rate (BER)performance between majority voting and optimal decision.By utilizing the DPF after solving a corresponding convexoptimization problem, we can depict the curve of SNR foreach link versus BER as shown in Fig. 4. All the crossoverprobabilities between X and Xi are set at the same value of0.01. Moreover, the end-to-end coding rate is set at 1

2 , andthe SNR is set at the same level for all of the agent and helperlinks. Notice from the results that whether there is a helper ornot, a gap obviously appears between the Poisson binomial(PB) process, i.e., majority voting, and the theoretical lowerbound (LB), i.e., optimal decision. The reason for the perfor-mance gap is that it is extremely difficult to completely utilizethe mutual information between Xn and Xn

L. For instance,assuming that there are 2K agents with Xt = X1,t = · · · =XK,t = 0 and XK+1,t = · · · = X2K,t = 1 at some timeindex t, it is obvious that there is some mutual informationbetween Xt and {X1,t, · · · , XK,t}. However, decision errorwill still occur in the Poisson binomial process, resulting inthe loss of mutual information between Xt and X̂t. It shouldbe also noticed that the gap is sensitive to the number ofagents, i.e., the gap is smaller when there are odd number ofagents. Because there could be equal number of “0" and “1"at the same bit of the agent sequences, if the number of agentsis even. In this draw case, the bit of final decision by majority

6 VOLUME x, 2019




-12 -10 -8 -6 -4 -2 0

10-4

10-3

10-2

10-1

100

(a) The number of agents is even.

-12 -10 -8 -6 -4 -2 010

-6

10-5

10-4

10-3

10-2

10-1

100

(b) The number of agents is odd.

FIGURE 4. Comparison of system performance between majority voting andoptimal decision, where pi = 0.01.

voting is randomly selected, resulting in more performanceloss. Hence, the majority voting decision can achieve betterperformance if odd number of agents are deployed. For theeffect of a helper, we find that the helper can reduce BERat small SNR value range, but keep the same BER floor asthe case without a helper. Because for sufficiently large SNR,there is already no distortion between Xn

i and X̂ni , and the

side information Y n generated fromXnL becomes redundant.

We further investigate the effect on rate-distortion by in-troducing a helper with majority voting decision in Fig. 5.Since the rate allocation scheme is out of the scope in thispaper, the rate is evenly allocated to all nodes includingagents and helper. Surprisingly, the helper can reduce thefinal distortion D before achieving the distortion floor, eventhough the agent rate decreases by sharing the sum rate witha helper. This phenomenon indicates that it is possible toimprove the system performance for multiple access channelswith the same sum rate by introducing a helper. However, the

0 0.5 1 1.5 2

0

0.1

0.2

0.3

0.4

0.5

1.8 1.9 210

-6

10-4

10-2

FIGURE 5. The trade-off of rate-distortion with a majority voting helper, wherepi = 0.01 for all agents.

curve with a helper will finally converge with the no-helpercase at the same distortion floor. Notice the fact that the curvewith a helper is still valuable, although the improvement isvery small.

Finally, we make a comparison of rate-distortion betweenmajority voting and optimal decision with diverse pi. Fig. 6shows an inclination that the more correlated observationsare, i.e., pi is smaller, the faster the distortion floor isachieved. Because it is easier to minimize the distortion be-tweenXn

i and X̂ni for more correlated observations, owing to

more mutual information among the observations. Moreover,as the correlation among the agent observations increases,the distortion floor decreases for both majority voting andoptimal decision. We can also find the same phenomenonas Fig. 4 that the gap between majority voting and optimaldecision is smaller for odd number of agents, even if thenumber of agents in Fig. 6(a) is less than that in Fig. 6(b). Inaddition, since in the situation where the mutual informationis lost less frequently with smaller pi, the gap betweenmajority voting and optimal decision is smaller with morecorrelated observations.

IV. PRACTICAL PERFORMANCE EVALUATIONA. SIMULATION DESIGNIn this section, we evaluate the practical performance ofbinary data gathering with a helper in IoT through simu-lations. As depicted in Fig. 7, there are L encoders sepa-rately encode the observations Xn

i , which is detected from acommon source sequence Xn and mixed with the error Bni .Simultaneously, the encoder H encodes the side informationY n generated from the agent observations. Next, the encodedsequences are sent to a fusion center through additive whiteGaussian noise (AWGN) channels after modulation. Thefusion center first demodulates the received signals and thenjointly decodes them. Finally, the estimate of all sequences inthe last round of iteration is used to make final decision.

Regarding the helper sequence Y n, since its optimal

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0 0.5 1 1.5 2 2.5

0

0.1

0.2

0.3

0.4

0.5

2.4 2.6 2.8

10-4

10-2

(a) L = 3.

0 0.5 1 1.5 2 2.5

0

0.1

0.2

0.3

0.4

0.5

2.4 2.6 2.8

10-4

10-2

(b) L = 4.

FIGURE 6. The trade-off of rate-distortion with diverse number of agents.

structure is still an open problem, we select two frequentlyimplemented structures in practice as g(·), i.e., the helperinformation generated by modulo-2 sum or majority voting.The g(·) by modulo-2 sum is illustrated in Fig. 8, where Xn

i

is interleaved by Πi,1 for the first step; subsequently, Y n isproduced by the modulo-2 sum of interleaved Xn

L bit by bit.By the interleaver Πi,1, the distribution of Y is approximateto Bern(0.5), i.e., Y n can contain side information as muchas possible.

Fig. 9 shows the structure of encoders. In order to betterexploit the correlation amongXn

L, the interleaver Πi,1 is usedto disperse noises into different bits ofXn

i . Subsequently, theinterleaved Xn

i is outer-encoded with a convolutional code(CC). For the purpose of utilize the principle of turbo code[22] in decoding, an accumulator (ACC) [23] inner-encodesthe interleaved outer code processed by another interleaverΠi,2. For the helper, only one interleaver ΠH is neededbetween CC and ACC.

The general structure of joint decoder is depicted inFig. 10. A decoder of ACC (ACC−1) and a decoder of CC

(CC−1) decode inner code and outer code, respectively. In lo-cal iteration, the extrinsic information is exchanged betweenACC−1 and CC−1 via an interleaver Π and its correspondingdeinterleaver Π−1. After several rounds of local iteration,the CC−1 outputs a posteriori log-likelihood ratio (LLRp) ofinformation bits. In global iteration, an extrinsic informationexchanger updates a priori LLR (LLRa) with the extrinsicLLR (LLRe), which is calculated by (LLRp − LLRa). Thejoint decoder alternately executes local iteration and globaliteration, until the mutual information calculated from LLRpiis large enough or the maximum iteration time is exceeded.Finally, the estimate of Xn

i is produced by the hard decisionof LLRpi in the last round of local iteration.

The extrinsic information exchanger updates the LLRa

according to the rules shown in Fig. 11. For the case withhelper information generated by modulo-2 sum, the LLRe

of all agents and the helper is first exchanged based on thesame principle for the check node of low-density parity-check (LDPC) codes [24], as

LLRtmpi = LLRei − 2arctanh

( ∏j∈W

tanh−LLRej

2

· tanh−LLReH

2

), (36)

LLRaH = LLReH − 2arctanh

(∏i∈L

tanh−LLRei

2

), (37)

where W = L \ i, and LLRtmpi is the temporary result for

agents. Then, according to the correlation model [25], theLLRtmp

i is deinterleaved by Π−1i,1 and further calculated bythe LLR updating function µ(·) for correlated source [26].Finally, Πi,1 interleaves the output of µ(·) again to provideLLRai . The structure of extrinsic information exchanger ismuch simpler for g(·) being majority voting. As illustratedin Fig. 11(b), µ(·) directly updates all of the LLRei afterdeinterleaving with the LLReH, and then the outputs from µ(·)for agents are interleaved into LLRai .

B. SIMULATION RESULTS

TABLE 1. Basic Settings of Simulation Parameters

Parameter ValueNumber of Blocks 1000

Block length 10000 bits

Distribution of X Bern(0.5)

Generator polynomial of CC G = ([3, 2]3)8

Rate of CC 1/2

Type of interleaver random interleaver

Modulation method BPSK

Maximum iteration time 30

Fig. 12 compares the simulation results between g(·) beingmodulo-2 sum (M2S) and majority voting (MV), where the

8 VOLUME x, 2019




Encoder 1

Final

decision...

X1n

Encoder 2X2

n

Ecnoder LXL

n

^Xn

Encoder HY

n

Joint

decoder

^X1n

Xn

Modulator Demodulator




^X2n

^XLn

g(·)

B1n

B2n

BLn

Fusion center

FIGURE 7. Simulation system.

Yn

∏2,1X2n

∏1,1X1n

...

∏L,1XLn

FIGURE 8. Generation of helper information by modulo-2 sum.

CC ∏i,2 ACC∏i,1Xin

(a) Agent encoder i.

CC ∏H ACCYn

(b) Helper encoder H.

FIGURE 9. The structure of encoders.

CC-1

LLR

LLR-

LLR

ACC-1

CC-1

LLR

LLR- LLR

∏H

ACC-1

∏i,2

: local itera"on : global itera"on

∏-1

i,2

∏-1

H

Extrinsic informa"on

exchanger

Helper link

Agent links

^X in

FIGURE 10. The structure of joint decoder.

basic parameter settings are listed in Table 1. Since the ma-jority voting decision rule is implemented in simulations, weuse the limit derived from Poisson binomial as the theoretical

LLR

∏i,1

LLR

Check

node

LLR LLR

∏-1

i,1

μ (·)

LLR

∏-1

j,1

∏j,1

LLR

LLR LLR

(a) The helper information is generated by modulo-2 sum, wherei, j ∈ L and i 6= j.

LLR

∏i,1

∏-1

i,1

LLRμ (·)

LLR

LLR

(b) The helper information is generated by majority voting.

FIGURE 11. The structure of extrinsic information exchanger.

bound. Clearly, the trade-off of rate-distortion in simulationsperfectly matches that in theoretical analysis, i.e., a helpercan shift the turbo cliff to left but cannot reduce the BERfloor. It should be highlighted that shifting SNR to left alsomeans eliminating distortions for low SNR level. Moreover,the helper with g(·) being majority voting can obviouslyreduce the SNR threshold more than the helper which gen-erates its information by modulo-2 sum. The reason for thedifference of performance is that the distortion is included inthe helper sequence with modulo-2 sum operation if there isonly one check node. If one of the LLRi is with the oppositesign, all of the other (L − 1) LLRs will get negative helperinformation. However, such negative helper information can-not be reversed again as in the LDPC codes, because no othercheck nodes exist in the system with only one helper. Hence,if the SNR is in an extremely low level, the helper withg(·) being modulo-2 sum will lose its effect due to the largedistortion of Xi. This problem also results in the reductionof helper efficiency for large L, i.e., it is difficult to shift theturbo cliff by further increasingL. Therefore, the system withonly one helper for g(·) being modulo-2 sum cannot obtainenough gains as the LDPC codes with a lot of check nodes.Nevertheless, the helper with its information generated by

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-12 -10 -8 -6 -4 -2

10-4

10-3

10-2

10-1

100

(a) L is even.

-12 -10 -8 -6 -4 -2

10-4

10-3

10-2

10-1

100

(b) L is odd.

FIGURE 12. Comparison of simulation results between different structures ofhelper, where pi = 0.03.

majority voting still can obviously reduce the SNR thresholdwith larger L. Because not only can the helper informationgenerated by majority voting preserve large enough mutualinformation among XL for lower error-corrupted probabilitypi, but the distortions occurring at the small part of nodes arealso not dominant when exchanging extrinsic information.Besides, the simulation results for both structures of helpercan achieve the bound derived from Poisson binomial pro-cess. Hence, we can draw a conclusion that it is convincibleand effective to predict the trade-off of rate-distortion for apractical system by applying the theoretical results.

Finally, we make a comparison between (L + 1) agentsand a helper for diverse pi as illustrated in Fig. 13 andFig. 14. Since majority voting shows a better performancethan modulo-2 sum as the helper structure, we only plot thecurves of majority voting for comparison. It is remarkablein Fig. 13(a) and Fig. 14(a) that the system with (L + 1)

-12 -10 -8 -6 -4 -2

10-4

10-3

10-2

10-1

100

(a) L is even.

-12 -10 -8 -6 -4 -2

10-4

10-3

10-2

10-1

100

(b) L is odd.

FIGURE 13. Comparison between one additional agent and a helper, wherepi = 0.03.

agents can achieve the BER floor of the case with (L + 2)agents, when L is an even number. Because one additionalagent provides extra information of X , and this avoids thedraw case that equal number of “0" and “1" appear in thesame bit of agent sequences when L is even. However, thesystem with a helper has a lower SNR threshold for arbitraryL, due to the larger mutual information between Y n and Xn

Lby majority voting. Especially when pi becomes larger or Lis odd, the gap of turbo cliff between (L + 1) agents and ahelper is very conspicuous. We can also find that the systemwith (L+ 1) agents keeps the same BER floor as one-helpersystem when L is odd, even though one more agent providesextra mutual information about X . Consequently, except theadditional implementation cost needed, it is better to add ahelper than one more agent for a system with odd number ofagents. If the wireless channels are good enough, one moreagent can make the estimate of source more accurate for the

10 VOLUME x, 2019




-12 -10 -8 -6 -4 -210

-4

10-3

10-2

10-1

100

(a) L is even.

-12 -10 -8 -6 -4 -210

-4

10-3

10-2

10-1

100

(b) L is odd.

FIGURE 14. Comparison between one additional agent and a helper for moreindependent sources, where pi = 0.05.

system already having even number of agents. However, inan extremely noisy environment, i.e., before achieving BERfloor and/or pi is relatively large, the system performance canbenefit more from a helper than adding an additional agent.In addition, there is another noticeable phenomenon that theBER floor is not immediately achieved for relatively largerpi and L after turbo cliff appears. Because for the bits atthe same time index, they need to obtain enough extrinsicinformation from each other, so as to decode correctly whenSNR is extremely low. Hence, only the bits almost withoutcorrupting errors can accumulate their extrinsic informationand be correctly decoded. The SNR threshold decreases asthe number of agents increases, while larger SNR is requiredfor large pi to correctly decode all bits at the same time index.Once the SNR threshold decreases to the level in which thebits with some corrupting errors decode fail, the BER isnot able to achieve the BER floor as soon as the turbo cliff

appears.

V. CONCLUSIONWe have analyzed and evaluated the performance of binarydata gathering with a helper in IoT. To begin with, weformulate binary data gathering with a helper in IoT as abinary CEO problem with a helper. Then, we decompose thebinary CEO problem with a helper into two sub problemsas multiterminal source coding with a helper and final de-cision. Subsequently, we derive an outer bound on the rate-distortion function for the multiterminal source coding stepand the DPF for the final decision step. Based on the derivedouter bound, a convex optimization problem is formulatedto minimize the distortion of observations with given agentand helper link rates. By substituting the minimized distor-tions into DPF, we investigate the relationship between linkrates and final distortion. Although there is an obvious gapbetween majority voting and optimal decision, they show thesame tendency on the trade-off of rate-distortion. Finally, wehave risen an encoding/decoding scheme and design a simu-lation for practical performance evaluation, so as to comparewith the theoretical results and analyze the trade-off of rate-distortion for binary data gathering with a helper in IoT. Boththe theoretical and simulation results indicate that a helpercan reduce the SNR threshold, while the BER floor doesnot change. Moreover, a helper with its structure as majorityvoting has a better performance than an additional agent forthe system with odd number of agents or in extremely noisycommunication environment. These significant observationsare extremely useful for the design of practical systems.

APPENDIX A ERROR PROBABILITY BY WEIGHTEDMAJORITY VOTINGRegarding the error probability by weighted majority voting,the final decision x̂ follows [27]:

x̂ =

{1, if wzT > 0,

0, otherwise,(38)

where w = [log 1−p1p1

, · · · , log 1−pLpL

] and z = 2 ·[x̂1, · · · , x̂L]− 1. Similarly to the Poisson binomial process,the error probability for the estimate of x is given by

pe = Pr

∑k∈Z+

wk >∑j∈Z−

wj

+

1

2Pr

∑k∈Z+

wk =∑j∈Z−

wj

, (39)

where Z+ = {i|zi = +1} and Z− = {i|zi = −1}. Note thatin order to calculate (39), it needs to carry out the search overall the possible combinations of wi.

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[2] P. Ostovari, J. Wu, and A. Khreishah, “Cooperative internet access usinghelper nodes and opportunistic scheduling,” IEEE Transactions on Vehic-ular Technology, vol. 66, no. 7, pp. 6439–6448, Jul. 2017.

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[5] K. Cao, Y. Wu, Y. Cai, and W. Yang, “Secure transmission with aid of ahelper for MIMOME network having finite alphabet inputs,” IEEE Access,vol. 5, pp. 3698–3708, Feb. 2017.

[6] X. He, X. Zhou, P. Komulainen, M. Juntti, and T. Matsumoto, “A lowerbound analysis of hamming distortion for a binary CEO problem with jointsource-channel coding,” IEEE Transactions on Communications, vol. 64,no. 1, pp. 343–353, Jan. 2016.

[7] X. He, X. Zhou, M. Juntti, and T. Matsumoto, “A rate-distortion regionanalysis for a binary CEO problem,” in IEEE 83rd Vehicular TechnologyConference (VTC Spring), Nanjing, China, May 2016, pp. 1–5.

[8] A. Razi and A. Abedi, “Convergence analysis of iterative decoding forbinary CEO problem,” IEEE Transactions on Wireless Communications,vol. 13, no. 5, pp. 2944–2954, May 2014.

[9] J. Haghighat, H. Behroozi, and D. V. Plant, “Iterative joint decodingfor sensor networks with binary CEO model,” in IEEE 9th Workshopon Signal Processing Advances in Wireless Communications (SPAWC),Recife, Brazil, Jul. 2008, pp. 41–45.

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[11] A. Wyner and J. Ziv, “The rate-distortion function for source codingwith side information at the decoder,” IEEE Transactions on informationTheory, vol. 22, no. 1, pp. 1–10, Jan. 1976.

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[14] S. Y. Tung, “Multiterminal source coding,” Ph.D. dissertation, School ofElectrical Engineering, Cornell University, Ithaca, New York, 1978.

[15] A. B. Wagner and V. Anantharam, “An improved outer bound for multiter-minal source coding,” IEEE Transactions on Information Theory, vol. 54,no. 5, pp. 1919–1937, May 2008.

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[17] X. Zhou, M. Cheng, X. He, and T. Matsumoto, “Exact and approximatedoutage probability analyses for decode-and-forward relaying system al-lowing intra-link errors,” IEEE Transactions on Wireless Communications,vol. 13, no. 12, pp. 7062–7071, Dec. 2014.

[18] P.-S. Lu, X. Zhou, K. Anwar, and T. Matsumoto, “Joint adaptive network–channel coding for energy-efficient multiple-access relaying,” IEEE Trans-actions on Vehicular Technology, vol. 63, no. 5, pp. 2298–2305, Jun. 2014.

[19] C. E. Shannon, “A mathematical theory of communication,” Bell SystemTechnical Journal, vol. 27, no. 3, pp. 379–423, Jul. 1948.

[20] ——, “Coding theorems for a discrete source with a fidelity criterion,” IRENat. Conv. Rec, vol. 4, no. 142-163, p. 1, Mar. 1959.

[21] A. El Gamal and Y.-H. Kim, Network information theory. UK: Cambridgeuniversity press, 2011.

[22] C. Berrou and A. Glavieux, “Near optimum error correcting coding anddecoding: Turbo-codes,” IEEE Transactions on Communications, vol. 44,no. 10, pp. 1261–1271, Oct. 1996.

[23] K. Anwar and T. Matsumoto, “Accumulator-assisted distributed turbocodes for relay systems exploiting source-relay correlation,” IEEE Com-munications Letters, vol. 16, no. 7, pp. 1114–1117, Jul. 2012.

[24] R. Gallager, “Low-density parity-check codes,” IRE Transactions on In-formation Theory, vol. 8, no. 1, pp. 21–28, Jan. 1962.

[25] J. Garcia-Frias and Y. Zhao, “Near-Shannon/Slepian-Wolf performance forunknown correlated sources over AWGN channels,” IEEE Transactions onCommunications, vol. 53, no. 4, pp. 555–559, Apr. 2005.

[26] X. Zhou, X. He, K. Anwar, and T. Matsumoto, “GREAT-CEO: larGe scaledistRibuted dEcision mAking Technique for wireless Chief Executive Of-

ficer problems,” IEICE Transactions on Communications, vol. 95, no. 12,pp. 3654–3662, Dec. 2012.

[27] X. He, Binary information sensing and multiterminal source coding: Rate-distortion analysis and transmission design. Japan: JAIST Press, Jun.2016.

WENSHENG LIN (S’17) received the B.Eng.degree in communication engineering, and theM.Eng. degree in electronic and communica-tion engineering from Northwestern Polytechni-cal University, Xi’an, China, in 2013 and 2016,respectively. He is currently pursuing the Ph.D.degree at the School of Information Science, JapanAdvanced Institute of Science and Technology(JAIST), Ishikawa, Japan. His research interestsinclude network information theory, distributed

source coding, helper structure design, and optimal encoding/decodingdesign.

XIN HE received the M.Sc. in Information Sci-ence from School of Information Science, JapanAdvanced Institute of Science and Technology(JAIST), Ishikawa, Japan, in 2013, and the Ph.D.degree from JAIST and the University of Oulu,Oulu, Finland in 2016. He is currently an asso-ciate professor with the School of Computer andInformation, Anhui Normal University. Also, he isa postdoc researcher with the School of ComputerScience and Technology, University of Science

and Technology of China (USTC), Hefei, China. His research interestsinclude joint source-channel coding, cooperative wireless communications,network information theory, energy harvesting and backscatter communica-tions.

12 VOLUME x, 2019




MARKKU JUNTTI (S’93-M’98-SM’04) receivedhis M.Sc. (EE) and Dr.Sc. (EE) degrees from Uni-versity of Oulu, Oulu, Finland in 1993 and 1997,respectively.

Dr. Juntti was with University of Oulu in 1992-98. In academic year 1994-95, he was a VisitingScholar at Rice University, Houston, Texas. In1999-2000, he was a Senior Specialist with NokiaNetworks. Dr. Juntti has been a professor of com-munications engineering since 2000 at University

of Oulu, Centre for Wireless Communications (CWC), where he leadsthe Communications Signal Processing (CSP) Research Group. He alsoserves as Head of CWC - Radio Technologies (RT) Research Unit. Hisresearch interests include signal processing for wireless networks as well ascommunication and information theory. He is an author or co-author in some350 papers published in international journals and conference records aswell as in books WCDMA for UMTS and Signal Processing Handbook. Dr.Juntti is also an Adjunct Professor at Department of Electrical and ComputerEngineering, Rice University, Houston, Texas, USA.

Dr. Juntti is an Editor of IEEE Transactions on Communications andwas an Associate Editor for IEEE Transactions on Vehicular Technologyin 2002-2008. He was Secretary of IEEE Communication Society FinlandChapter in 1996-97 and the Chairman for years 2000-01. He has beenSecretary of the Technical Program Committee (TPC) of the 2001 IEEEInternational Conference on Communications (ICC 2001), and the Co-Chairof the Technical Program Committee of 2004 Nordic Radio Symposiumand 2006 IEEE International Symposium on Personal, Indoor and MobileRadio Communications (PIMRC 2006), and the General Chair of 2011IEEE Communication Theory Workshop (CTW 2011). He has served asCo-Chair of the Signal Processing for Communications Symposium ofGlobecom 2014 Signal Processing for Communications Symposium andIEEE GlobalSIP 2016 Symposium on Transceivers and Signal Processingfor 5G Wireless and mm-Wave Systems, and ACM NanoCom 2018.

TAD MATSUMOTO (S’84-SM’95-F’10) receivedhis B.S., M.S., degrees, both under the mentorshipby Prof. Shin-Ichi Takahashi, and Ph.D. degreeunder the supervision by Prof. Masao Nakagawa,from Keio University, Yokohama, Japan, in 1978,1980, and 1991, respectively, all in electrical engi-neering.

He joined Nippon Telegraph and TelephoneCorporation (NTT) in April 1980. Since he en-gaged in NTT, he was involved in a lot of research

and development projects, all for mobile wireless communications systems.In July 1992, he transferred to NTT DoCoMo, where he researched Code-Division Multiple-Access techniques for Mobile Communication Systems.In April 1994, he transferred to NTT America, where he served as aSenior Technical Advisor of a joint project between NTT and NEXTELCommunications. In March 1996, he returned to NTT DoCoMo, wherehe served as a Head of the Radio Signal Processing Laboratory untilAugust of 2001; He worked on adaptive signal processing, multiple-inputmultiple-output turbo signal detection, interference cancellation, and space-time coding techniques for broadband mobile communications. In March2002, he moved to University of Oulu, Finland, where he served as aProfessor at Centre for Wireless Communications. In 2006, he served as aVisiting Professor at Ilmenau University of Technology, Ilmenau, Germany,funded by the German MERCATOR Visiting Professorship Program. SinceApril 2007, he has been serving as a Professor at Japan Advanced Instituteof Science and Technology (JAIST), Japan, while also keeping a cross-appointment position at University of Oulu.

He has led a lot of projects funded by Academy-of-Finland, EuropeanFP7, and Japan Society for the Promotion of Science as well as by Japaneseprivate companies.

Prof. Matsumoto has been appointed as a Finland Distinguished Professorfor a period from January 2008 to December 2012, funded by the FinnishNational Technology Agency (Tekes) and Finnish Academy, under whichhe preserves the rights to participate in and apply to European and Finnishnational projects. Prof. Matsumoto is a recipient of IEEE VTS OutstandingService Award (2001), Nokia Foundation Visiting Fellow Scholarship Award(2002), IEEE Japan Council Award for Distinguished Service to the Society(2006), IEEE Vehicular Technology Society James R. Evans Avant GardeAward (2006), and Thuringen State Research Award for Advanced AppliedScience (2006), 2007 Best Paper Award of Institute of Electrical, Communi-cation, and Information Engineers of Japan (2008), Telecom System Tech-nology Award by the Telecommunications Advancement Foundation (2009),IEEE Communication Letters Exemplary Reviewer (2011), Nikkei WirelessJapan Award (2013), IEEE VTS Recognition for Outstanding DistinguishedLecturer (2016), and IEEE Transactions on Communications ExemplaryReviewer (2018). He is a Fellow of IEEE and a Member of IEICE. He isserving as an IEEE Vehicular Technology Distinguished Speaker since July2016.

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binary data gathering with a helper in internet matsumoto, tad

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