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Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Influe nce Of Soci al Medi a For

Ana lyzing Histo rical E vents With B engal Partitio n As C ase Study.

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Ethics and Information Technology (ETIT)

DOI: http://doi.org/10.26480/etit.02.2020.138.141

MODELING OF OPINION FORMATION UNDER INFLUENCE OF SOCIAL MEDIA FOR

ANALYZING HISTORICAL EVENTS WITH BENGAL PARTITION AS CASE STUDY

Priyadarsini Sinhaa*, Milan Mukherjeeb, Souvik Royc, Abhik Mukherjeea

a CST Dept, IIEST Shibpur

b Hyland Software

c IT Dept, IIEST Shibpur

*Corresponding Author Email: georgenelson5006@gmail.com

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, an d

reproduction in any medium, provided the original work is properly cited.

ARTICLE DETAILS

ABSTRACT

Article History:

Received 25 October 2020

Accepted 26 November 2020

Available online 03 December 2020

Error correcting codes are important for communication sys- tems to retrieve messages transmitted over

noisy channels. Recent ad- vancement of low density parity check (LDPC) codes has enabled reliable

communication in highly noisy environment of deep space or underwater. The LDPC decoder algorithm

employs localized neighbourhood based parity check equations to improve upon the error correcting

capability. It is shown in this work that such principle can be implemented on bi- partite graph to simulate

the connectivity among people of the society who form opinion through influence from their connected

neighbour- hood. With the advent of social media, this concept of neighbourhood has broken the localized

boundaries so that influencing opinions can be far spread. Historical event like Partition of Bengal in 1947,

when revis- ited in light of this model, provides alternate course of history.

KEYWORDS

online social media, graph algorithm, error correcting codes.

1. INTRODUCTION

Error correcting codes is a well studied subject in communication theory

(Lin and Costello, 1999). Low Density Parity Check (LDPC) codes are one

of the best error correcting codes (apart from Turbo codes) till now for

practical applications like wireless communications and deep space

missions. The decoders of LDPC codes are, by nature, some generic

iterative decoders which can be used to decode any block code for a given

channel. Iterative decoders are different from the standard algebraic

decoders that settle in one pass for the codeword situated at global

minimum distance from the received word. Rather, they care for the

connectivity established by the individual bits of the parity check

equations and initiate corrections so that all parity check equations are

satisfied. The process does not often terminate in one pass and may

require a good number of iterations before convergence of the parity

check equations. The process may terminate without being decisively able

to resolve the ambiguity even after running large number of iterations.

In the present work, individuals of the society are considered to be

represented by the bits who participate in parity check equations where

they try to settle to some convergent opinion by changing their own

opinion based on majority of opinions they receive.

The binary content of the bit is suitable to implement the two possible

states of being agitated (1) or at peace (0) with the issue in question. The

codeword has two parts, the message bits and check bits. Here the check

bits are considered to be the influencing members of society who matter

to the individuals while forming their opinion through the satisfying of

parity check equations. Analogy may be drawn with how individual

opinions can converge to some opinion about some societal issue.

The main contention of this paper is to show how more influencing fro m

remotely located individuals could dominate over local influences or

global trends resulting in convergence to different state. This arguably is

one of the main feature today with the exodus of social media in the life of

an individual. For this, we have chosen the historical event of Bengal

partition (Chatterjee, 1994) that was decided largely through localized

political interest groups. We have argued that an alternate course of

history could have been arrived at if social media was present in that era.

This is hypothetical reasoning but nevertheless useful for understanding

how opinions form in the present and what the future holds.

2. ERROR CORRECTING LDPC CODES

Early variant of LDPC code was discovered by Robert in early 1960s

(Gallager, 1962). Largely suppressed from further research due to

technical limitations. Tanner’s graph theoretic view (Tanner, 1981) on

block codes presented in 1981 was also ignored. Late 1990s came up with

the same idea of LDPC code when a researchers and other eminent

researchers fo und out these codes independently while investigating on

graph based iteratively decodable codes (Davey et al., 1998; MacKay,

1999).

An LDPC code is defined with respect to its parity check matrix. They are

a subclass of block codes in general. The term low density signifies a sparse

parity check matrix in terms of the number of 1s present in the matrix. Due

to this sparseness, LDPC codes possess great advantages in terms of

efficient decoder implementation and storage and can approach the

Shannon Limit very effectively. It has been implemented in various

practical standards such as IEEE 802.16, IEEE 802.20, IEEE 802.3, DVB-

Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141

Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or

Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.

Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141

.

RS2 and many others. Such is the advantage that now researchers are even

investigating non-binary LDPC codes and their applicabilities.

An

(

N, w

c

, w

r)

LDPC code with a parity check matrix

H

of size (

M

×

N

),

where the Hamming weight of each column and each row are two fixed

integers

,

w

c

and

w

r

respectively with

w

r

> w

c

>

2. Since the matrix is

sparse in nature, so

w

c ≪

M

and

w

r ≪

N.

The total number of

1

s

=

w

c

×

N

=

w

r

×

M

.

Thus,

M

=

(

N

×

w

c

)

must be an integer. This also

implies that every code bit participates in

w

c

parity check sums and each

parity check sum involve

s

w

r

code bits. The density of this parity check

matrix is defined as

Ψ

= wr

= wc .

This helps to understand, both

intuitively and mathematically, how much sparse

H

really is.

R. M. Tanner in 1981 showed the existence of a bijection between the

parity check matrix of any block code and a bipartite graph (Tanner,

1981). This graph is now referred to as

a Tanner graph. Each row of a

(

n

−

k

) ×

n

parity check matrix

H

of a block code denotes a parity check

sum

f

i

for all

i

= 0

,

1

, . . . ,

(

n

−

k

).

Each column denotes a particular position

,

c

j

for all

j

=

0

,

1

, . . . , n

of the code word with block length

n

.

Whenever

H

[

i,

j

]

=

1,

it indicates that the

i

th

parity check sum affects the

j

th

code bit

position or the

j

th

code bit. From this Tanner constructed a bipartite

graph where the two sets of vertices/nodes consists of the parity check

sums and code bits as nodes respectively.

(

f

i

, c

j

)

is an edge in the graph

whenever

H

[

i, j

]

=

1.

Construction of the generator matrix can be initiated by forming a sub-

matrix

H

0

of size M ×

N

as follows : each row of

H

0

has

w

r 1

s

in

such a way that the

i

th row of

H

0

contains all its

w

r 1

s

in the

columns [(

i

− 1)

.w

r + 1] to

i.w

r.

After this, the entire parity check

matrix can be constructed by stacking any

(

w

c − 1) column

permutations

of

H

0

. Here

Π

k

(

H

0

),

k ≠

1,

denotes a sub-matrix obtained

by permuting the columns of

H

0

randomly while

Π

1(

H

0

) =

H

0

.

If each

permutation is chosen randomly, it can sometimes produce good code. The

average minimum distance of the code increases with

N

for

w

c ≥ 3.

Since

the so designed LDPC code is not necessarily linear code,

Rank

(

H

) ≤

M

.

Therefore dimension of the code is

Dim

(

C

) ≥ (

N

−

M

) or

K

≥

(

N

−

M

).

Hence rate of the code

R

=

K

N- M

= 1 − wc .

Hence the actual rate of

the code is higher than the

H

matrix suggests as the designed rate. F or

practical LDPC codes

N

is taken to be quite large, like

N >

5000,

while

the column weight is held around 3 or 4, so the density of 1s in the matrix

is quite low.

3. ITERATIVE DECODER ALGORITHM

Iterative decoding principle is employed for decoding of LDPC codes.

Unlike one shot method used in algebraic decoding of linear block codes,

this uses multiple iterations capable of eliminating high noise. A study

introduced a simple Bit-Flipping algorithm that corrected a single bit in

every iteration (Gallager, 1962). If multiple bits are allowed to flip in one

iteration, then the algorithm is called a Multi-Bit-Flipping (MBF)

Algorithm.

In every iteration of this algorithm the code word bit(s) with the highest

number of a metric are flipped. Metric is characterized by the type of

algorithm: Hard-Decision and Soft-Decision. Hard decision metric is the

number of unsatisfied parity check equations. Soft decision metric consists

both the number of unsatisfied and satisfied parity check sums, since

reliability information is present. An algebraic decoding algorithm in this

context can only correct up to its random error correcting capability. But

due to the sparse nature of H, the MBF algorithm may correct error

patterns whose number of errors exceeds the error correcting capability

of the code. Since the present work relies on hard decision message

passing only, the details of soft decision algorithm that exploits reliability

information is not introduced.

Message Passing Algorithm (MPA) in context of LDPC codes can be

visualized more easily if we refer to the Tanner graph of t he associated

code. Messages are passed between message nodes and check nodes along

the edges of the Tanner graph. The information that is sent from a node vi

to vj in MPA should not get influenced by the node

v

j

i.e., in other words,

the data that is being sent to a node must depend only on the other nodes.

This type of message is called an “extrinsic message” or “extrinsic

information”.

The generic message passing structure is as follows :

1) Initialize the decoder by sending the received values of the message

nodes to check nodes.

2) In each check node, an extrinsic message for each neighbor variable

node is calculated and sent.

3) Each message node calculates a new value for itself depending on the

previous received values and the information from the check nodes. The

output is then checked by all the parity check equations and if all of them

agree, decoding stops. Otherwise, an extrinsic message for each neighbor

check node is calculated and sent.

4) Repeat steps 2 and 3 until a maximum number of iterations is reached.

4. ANALOGY WITH SOCIETAL OPINION FORMATION

4.1 Dynamics of opinion formation

One large binary string with a number of zeros and ones can be considered

as a received word. Each bit can be considered as an individual having a

binary state of mind w here one represents agitated state and zero

represents peaceful state. Some of these individuals may be considered to

be influential and thus considered as check bits. The bipartite graph can

then be constructed with edges drawn between individual nodes on one

side and the influencing nodes on the other side.

Analogy can be drawn between this construction and the MPA decoder of

LDPC code discussed in the previous section. Each individual node is

connected to a number of influencing nodes.

Thus they receive message of being in agitated or peaceful state from each

such check node. Then they arrive at the majority and accordingly retain

or flip the bit, implying that they may go from agitated to peaceful state or

vice versa based on collected majority opinion.

This process may continue over a number of iterations with the

terminating condition described as reaching all zero codeword or

exceeding a certain number of iterations. Check bits also appear as

individuals thereby allowing flexibility of opinion for all.

The main argument is that with localized influence it is not possible to get

back from a number of ones and zeros in the received word back to the all

zero codeword. Along similar lines, unless the individual nodes get

connected to some remote influencing nodes, it is not at all possible for the

MPA of the iterative decoding algorithm to get to the all zero state. One

important flavour about the success of MPA is that the parity check matrix

is sparse yet it provides a spread of the check nodes.

4.2 Simulation results for message passing

The 20, 3, 4 code has been tested by creating bit strings where the all zero

code word resembling peaceful state is contaminated with number of 1s

(Gallager, 1962). The message passing based iterative decoder algorithm

is run on these simulated received words.

Success and failure along with the number of 1s corrected to 0s is reported

in Table 1 along with number of iteration needed to achieve the success. It

can be seen that for some cases, even after 5000 iterations, the error does

not get corrected. It depends on the distribution of the error with respect

to the generator matrix used for the code. The corresponding bipartite

graph is shown in Figure 1.

Figure 1: Bipartite graph showing the interaction among the nodes

The generator matrix is such that for the first five rows the influence is

localized,

so that

f

i

influences

c

4i+1 to

c

4i+4. However, apart

from

f

1,

c

1 is also influenced by

f

8

and

f

14.

Likewise,

c

2 is influenced by

f

1,

f

9

and

f

12.

In this manner, the

localized

influence is perturbed and the maximum likelihood or

minimum distance decoding philosophy gets altered.

Results are tabulated in Table 1, clearly showing large number of

additional errors or agitated opinions getting corrected. Some of these

results are

Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141

Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or

Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.

Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141

.

Table 1: Iterative decoding success for 20,3,4 LDPC code

Iteration count

Bits corrected

Remarks

102

12

Success

18

9

Success

9

8

Success

73

12

Success

5000

3

Failure

5000

4

Failure

5000

5

Failure

5000

9

Failure

indeed encouraging from our present perspective. Large number of

individuals in riotous state (1) can be brought to pacified state (0) through

the message passing algorithm that relies upon flipping of node bit based

on majority of its influencing bits.

It can be seen that often large number of iterations are needed, sometimes

the process fails in the long term as well. But this brings out the

importance of geographical spread of influencing bits beyond localised

boundaries. We found that the system inevitably terminates with failure if

influence is localized, c heck bits are less in number and the 1’s are

concentrated in some locality, it is never possible to get to the all zero

codeword at all.

5. CASE STUDY OF BENGAL PARTITION

5.1 Historical perspective

The first attempt towards partition of Bengal by the British in 1905 was

thwarted through peoples’ struggle and forced to be nullified in 1911. But

the second one by the same British rulers was rather invited - by the same

people in a gap of only 40 years. A spate of communal riots spread across

the entire territory of undivided Bengal; with Kolkata, Dhaka,

Mymensingh, Chittagong all throwing in their bit; gradually became

uncontrollable.

During the initial years, the communal riots of undivided Bengal largely

originated due to economic oppression. The feudal economic structure of

Bengal was such that the oppressing Zamindars or landlords of Eastern

Bengal were mostly Hindus and their Ryots r epresenting the peasantry

were mainly Muslims. The signature of this class character dominated till

1926 as claimed by the historians (Das, 2010). Such crowd leader

dichotomy however shifted during the 1930’s when the British

government were clearly instigating the riots, for example the Chittagong

riots of 1930. Finally, in the 1940’s the political parties came to the

forefront of the riotous population.

With two nation theory and its inevitable logic of Bengal partition

suddenly becoming the agenda of all the political outfits, this obviously

dominated the discussion forums. Under such circumstances, opinion poll

of the legislature representatives were held regarding the partition in a

state where the democratic institution was also cut across communal lines

as part of British policy of representation (Chatterjee, 1994). As expected,

the opinion was biased, driven by narrow interests of the representatives

and ignorant of public opinion altogether. Even, the decision of Eastern

Bengal legislature was not binding on the West. Hence the voting pattern

was highly communal and localized.

The localization can be understood from the distribution of minority

population on either side of the border as shown in Figure 2(L)

(Chatterjee, 1947). However, organized working class existed in the

Railways and to an extent in the trade unions of Jute industry and in these

spheres, there was a small spread cutting across the local barriers as

depicted in Figure 2(R).

But this was too weak compared to the geographical spread enjoyed by the

online social media of today. Recent Brexit debate has seen huge number

of such cross votings mainly from Conservative party bac kbenchers and

few Labour Party MPs as well in the British parliament, mainly because of

various extraneous influences (Aidt et al., 2019).

Figure 2: Map showing minority population on either side of the border,

indicator of local influence (Left) Map showing manufacturing industry

on either side of the border, indicator of remote influence (Right)

5.2 Presence of social media

To revisit the Bengal partition, the influence and spread of social media in

Bangla speaking regions is considered. Whatsapp or Facebook

connectivity depends more on acquaintance like school or office, such

friendship is sparse across the border. Friendship groups do exist but their

presence is formal. For example, the information shared by Bangladesh

India Friendship Association, a community in Facebook, are either visa

related or about health care services.

We therefore looked for some social media that binds on language and

discusses on convergent issues. Quora is one such platform and analysis of

Quora discussion forums can be fo und in literature as well (Wang et al.,

2013; Maity et al., 2018). So for the present work, Quora Bangla dataset

has been taken and the spread of interactions on Quora Bangla posts

amongst the Bangla speaking community across the border is explored.

Quora Bangla data was collected for 10 questions raised in the platform

with 3006 responding users along with the users profile location. Figure 3

shows the binding of both sides of the partition. The nodes depict the user

profile (blue for users from Bangladesh and red for users from West

Bengal) and two nodes are connected via edges depending on upvote and

comments response. The group attribute layout of the graph is shown

depending on country attribute which shows how engrossed both sides of

the partition are in this respect.

Typical location specific results are shown in Figure 3(R) which depicts

response from Bangladesh users (A: Dhaka & Southwards; B: Mymensingh

& Northwards; C: Chittagong & Eastwards; and D: Bangladesh other area)

for the posts from West Bengal users and response from West Bengal (A:

Kolkata & Southwards; B: Siliguri & Northwards; C: North East India) for

the posts from Bangladesh users.

Figure 3: Left: Quora response graph with Attribute view; Right: Response

statistics

5.3 Simulation perspective

We look back at the excitors and inhibitors of communal tension in terms

of the propaganda on either side of the divide (Chatterjee, 1994). The

bipartite graph based model can be useful with edge being drawn between

groups of the population based on their roles as excitors and inhibitors.

The graph would be sparse but with strong possibility of cycles. We

consider binary opinion for the legislative representatives. As political

groups, they employ local connectivity. Their initial state is highly biased

as most Congress and Hindu Mahasabha legislators with majority located

in West Bengal were in favour of partition (state 1) and tho Muslim League

Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141

Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or

Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.

Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141

.

and Praja Krishak Party legislators with majority in East Bengal wanting

to avoid partition (state=0). Purely local connectivity can never result in

convergence to the all zero state.

Now, the LDPC code example discussed in previous section allows remote

influence of check bits on code bits. In some form, social media was

present, like the newspaper or leaflet to circulate opinions. But that is not

adequate enough to guarantee the sort of remote connectivity needed to

make the mark. Updating of the state at each node is based on the majority

rule applied by considering all opinions that reach it. Now, some of the

representatives are allowed remote connectivity outside their party

opinion to an extent as per the permutation based construction of the

parity check matrix described in previous section (see Figure 1). Iterative

decoding can be employed and the system is able to reach sometimes the

stable all zero state which implies thwarting of partition. Hence with the

kind of influencing Quora Bangla provides, the chances of alternate

courses of history might have been realized.

6. CONCLUSION

There is no way to go back in time and change the course of historical

events. However, it is worthwhile to learn lessons from history and

deconstruct the events in light of modernity to explore new possibilities.

This work looks back at the Bengal partition in light of the advent of online

social media,

This leads us to the conclusion that there was lack of enough

communication amongst the people of undivided Bengal to the detriment

of different options reaching them and influencing their decision. The

probability of alternative discourse would have been higher in today’s

connected world. However, here only some random simulation

perspective is given. To present more realistic picture of history, we have

plans to incorporate the traits of legislators who actually participated in

the process.

ACKNOWLEDGEMENT

This work received support of MHRD/ICSSR IMPRESS project.

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