Decoding Collided Acknowledgement Transmission in IEEE 802.11 ...

**Decod ing**

**in** **IEEE** **802.11** Networks

Abstract—The **IEEE** **802.11** medium access control (MAC) protocol

enforces explicit acknowledgement transmissions to achieve

reliable communications. However, this data-acknowledgement

protocol handshake fails to accommodate one-to-many transmissions

such as multicast**in**g. The current **IEEE** **802.11** standard

specifies no acknowledgement for one-to-many transmissions

mak**in**g the protocol unreliable at the MAC layer. This paper

proposes a mechanism that firstly enforces acknowledgement

reply for wireless multicast**in**g from all receivers and then employs

the physical-layer network cod**in**g technique for the sender

to decode collided acknowledgement transmission. We devise

a cod**in**g scheme that achieves the identification of **in**dividual

acknowledgement transmission from the collided transmission by

allow**in**g the multicast sender to decode the collided transmission.

We give a mathematical proof for the existence of such a cod**in**g

scheme and demonstrate its usage for wireless multicast**in**g.

I. INTRODUCTION

The recent advancements **in** the **IEEE** **802.11** wireless local

area networks (WLANs) have moved one step closer to realiz**in**g

ubiquitous access of multimedia contents over the Internet.

Efficient access to multimedia contents, especially real-time

multimedia content, relies on multicast**in**g technology. The

**IEEE** **802.11** WLANs that implement a contention based

medium access control (MAC) protocol **in**evitably **in**troduce

transmission collisions when simultaneous transmissions occur

[1]. The **IEEE** **802.11** MAC protocol enforces an explicit

acknowledgement by the receiver to detect a successful transmission

by the sender. However, this rule fails when a transmission

is multicast to a group of receivers as this will cause

a collision of simultaneous acknowledgement transmissions. It

is hence disabled, and such one-to-many transmissions rema**in**

unreliable **in** the current **IEEE** **802.11** WLANs.

There are several efforts to improve the reliability of wireless

multicast**in**g, particularly focus**in**g on ensur**in**g reliable

one-hop wireless transmission [2]–[5]. The general approach

has been f**in**d**in**g a method to resolve the collision of acknowledgement

transmissions by all receivers for a multicast

transmission. This approach **in**evitably **in**troduces transmission

overhead due to collision resolution. In this paper, we improve

the reliability of wireless multicast**in**g by allow**in**g all receivers

to acknowledge a multicast transmission caus**in**g a collision,

and then we propose a cod**in**g scheme that enables the sender

to decode the collided acknowledgement.

Unavoidably, simultaneous acknowledgement transmissions

by all receivers at the same time will cause a transmission

Chuan Heng Foh, Jianfei Cai, and Jalaludd**in** Qureshi

School of Computer Eng**in**eer**in**g

Nanyang technological University, S**in**gapore 639798

Email: {aschfoh, asjfcai, jala0001}@ntu.edu.sg

collision. By traditional rules, this transmission is undecodable

and considered useless. However, **in** a pioneer**in**g work by

Zhang et al., a study on turn**in**g a collision of two simultaneous

wireless transmissions **in**to a useful transmission is presented,

which they called physical-layer network cod**in**g (PNC) [6]. In

brief, two simultaneous wireless transmissions that are added

together at the electromagnetic wave level can be decoded

and mapped to produce an outcome such that the relationship

between the transmitted and the decoded b**in**ary **in**formation

follows the exclusive-or (XOR) pr**in**ciple.

While the considered modulation and mapp**in**g allow for

decod**in**g two simultaneous wireless transmissions, extend**in**g

the same technique to support decod**in**g of two or more

simultaneous wireless transmissions requires precise detection

of signal energy for the mapp**in**g to achieve the XOR pr**in**ciple.

This **in**troduces challenges **in** the practical design.

In this paper, we consider an arbitrary number of simultaneous

wireless transmissions. We first study the pr**in**ciple

of the relationship between the **in**put and the output b**in**ary

**in**formation for the collided transmission of multiple senders,

and then use the pr**in**ciple to devise a cod**in**g scheme that

enables the detection of the presence of each **in**dividual transmission.

We can then make use of this detection to identify

from a collided acknowledgement transmission which stations

transmitted their acknowledgement and which did not.

The rest of the paper is organized as follows. Section II

revisits the PNC technique, **in**troduces our proposed technique

to decode collided transmissions, and applies the technique to

improve wireless multicast**in**g. In Section III, we study our

cod**in**g scheme and discuss its applicability. F**in**ally, we draw

important conclusion is Section V.

II. DECODING A COLLISION

A. Physical-Layer Network Cod**in**g

The concept of PNC is first **in**troduced by Zhang et al.

**in** [6]. The authors proposed a frame-based Decode-and-

Forward strategy **in** packet forward**in**g. In their scenario,

two neighbor**in**g nodes transmit simultaneously to a common

receiver. Assum**in**g prefect transmission synchronization **in**

physical layer, based on the additive nature of simultaneously

arriv**in**g electromagnetic (EM) waves, the receiver detects the

added signal of the two transmitted modulated signals. Us**in**g

a suitable mapp**in**g scheme, they show that for some certa**in**

modulations, there exists a mapp**in**g scheme such that the

TABLE I

THE PNC MAPPING FOR TWO TRANSMITTING NODES USING BPSK.

Modulation mapp**in**g Demodulation mapp**in**g

at N1 and N3

at N2

Input Output Input Output

s1 s3 a1 a3 a1 + a3 s2

1 1 1 1 2 0

0 1 -1 1 0 1

1 0 1 -1 1 1

0 0 -1 -1 -2 0

relationship between the two transmitted b**in**ary bits and the

decoded b**in**ary bit follows the XOR pr**in**ciple.

We here revisit the PNC operation [6] and its mapp**in**g

scheme to achieve the XOR pr**in**ciple. Consider two senders,

N1 and N3, and a common receiver N2. Let s1 and s3 be

the b**in**ary bit transmitted by N1 and N3 at a particular time,

respectively, and s2 be the decoded b**in**ary bit. Based on BPKS

modulation, we have

r2(t) = a1 cos(ωt) + a3 cos(ωt) = (a1 + a3) cos(ωt) (1)

where r(t) is the received signal, a1 and a3 are the transmitted

amplitudes. For BPSK, aj = 2sj − 1 [6]. At N2, a scheme

(see Table I) that maps a strong energy signal to b**in**ary 0 (i.e.

|a1 + a3| = 2) and a weak energy signal (i.e. a1 + a3 = 0) to

b**in**ary 1 can be applied which gives

s2 = s1 ⊕ s3. (2)

Further PNC studies on the penalty of carrier-phase synchronization

errors, carrier frequency synchronization errors,

and time synchronization errors are given **in** [6], with results

show**in**g the practical potential of PNC.

B. **Acknowledgement** Collision **in** **IEEE** **802.11**

The **IEEE** **802.11** standard specifies explicit acknowledgement

transmission to **in**dicate a successful reception of a

data transmission. All acknowledgement transmissions are

performed us**in**g the def**in**ed basic data rate which uses DBPSK

for 1 Mb/s or DQPSK for 2 Mb/s for the modulation technique.

While an explicit acknowledgement transmission achieves

robust one-to-one data transmission, this mechanism is disabled

for one-to-many multicast transmissions to prevent unnecessary

collisions of all acknowledgement transmissions.

This causes the unreliability of the one-to-many multicast

transmissions as the sender cannot tell whether the transmission

to all its receivers is successfully.

Motivated by the concept of PNC, we improve the reliability

of such wireless multicast**in**g by allow**in**g all receivers of a

one-to-many transmission to acknowledge with a transmission.

In other words, after receiv**in**g a multicast transmission, us**in**g

the exist**in**g **IEEE** **802.11** MAC protocol operation, a receiver

replies an acknowledgement. Due to the common event of

the multicast transmission, acknowledgement replies from

all receivers occur almost simultaneously. This allows the

application of the PNC concept to achieve collision decod**in**g.

However, accord**in**g to Table I, reta**in****in**g the XOR pr**in**ciple

for an arbitrary number of simultaneous transmissions requires

precise detection of signal energy for the PNC mapp**in**g, which

TABLE II

AN EXAMPLE OF BPSK DEMODULATION FOR THREE TRANSMITTERS.

N1 0 0 0 0 1 1 1 1

Input N2 0 0 1 1 0 0 1 1

N3 0 1 0 1 0 1 0 1

Output N0 0 0 0 1 0 1 1 1

reduces its robustness. Based on the additive nature of EM

waves, consider**in**g the BPSK modulation scheme, it is not

difficult to see that the BPSK demodulation process follows

the majority pr**in**ciple.

To illustrate this, let us consider a simple case of three

transmitters, Ni (i = 1, 2, 3), and one common receiver, N0.

Let ai (i = 1, 2, 3) be the amplitude of the BPSK signals

correspond**in**g to the transmitted b**in**ary **in**formation, and a0

be the detected amplitude of the BPSK signals. Based on the

additive nature of EM waves, we have a0 = a1 + a2 + a3.

Consider**in**g a common design of a BPSK demodulator with

a matched filter and a detection device, the demodulator

produces 1 if a0 > 0 and 0 if a0 < 0. Table II exhausts

all possible **in**puts and shows the relationship between the

**in**put and the output b**in**ary **in**formation. As can be seen, the

relationship follows the majority pr**in**ciple.

A closer exam**in**ation to BPSK shows that any pair of **in**puts

that holds different b**in**ary **in**formation is offset when added

at the EM level. As a result, the rema**in****in**g **in**put decides

the b**in**ary outcome. In the case of a tie, s**in**ce the detected

energy fails to reach a threshold after the matched filter, a

consistent conclusion will be made. Without loss of generality,

we assume it to be b**in**ary 0.

C. Proposed Cod**in**g Scheme

Us**in**g the majority pr**in**ciple, we design a cod**in**g scheme

that enables the common receiver of a collided transmission

to tell the presence of **in**dividual transmission **in**volved **in** the

collision. Consider that a multicast transmission is address**in**g

to N stations. Such a multicast transmission may reach a

subgroup of stations due to, for example noise or the hidden

term**in**al problem. In our design, we assume that the multicast

sender embeds **in**formation **in** its data transmission to tell each

**in**dividual receiver of its unique identifier. The identifier will

be used for the acknowledgement transmission.

After receiv**in**g the multicast data, each receiver prepares

to reply with an acknowledgement. Instead of follow**in**g the

**IEEE** **802.11** standard, each receiver refers to its unique

identifier and uses the correspond**in**g predef**in**e bitstream for

its acknowledgement transmission. Then, each receiver replies

an acknowledgement with its correspond**in**g bitstream. These

simultaneous acknowledgement replies cause a transmission

collision. Note that, to improve robustness, each receiver may

use received signal strength **in**dicator available **in** the **IEEE**

**802.11** device to adjust its transmission power such that all

acknowledgement transmissions arrive at the multicast sender

with a similar transmission power.

Assum**in**g prefect synchronization **in** all replies 1 , the multicast

sender will detect and produce a bitstream that follows

1 The readers may refer to [6] for the prelim**in**ary study on the penalty of

time synchronization errors **in** PNC.

TABLE III

THE DECODED BITSTREAMS (BASED ON THE MAJORITY PRINCIPLE) OF

DIFFERENT RECEIVER COMBINATIONS FOR N = 3.

2 While N must be odd, we can produce N + 1 codes for even N.

3 Here we use +1 and −1 to replace 1 and 0 for better illustration.

We further use the notation |G0| to denote the card**in**ality

of the set G0, G ′ 0 = G \ G0 to denote the complementary set

of G0, and −→ G0 to denote a vector whose elements are

Receiver Comb**in**ation Decoded Bitstream

N1

110

N2

101

N3

011

(N1,N2) 100

(N1,N3) 010

(N2,N3) 001

(N1,N2,N3) 111

the majority pr**in**ciple. We shall show that there exists a cod**in**g

scheme such that the sender produces a unique bitsream for a

particular comb**in**ation of the receivers’ bitstreams.

Consider the number of receiver, N, to be an odd number,

and a bitstream has V bits. Let R = N+1

2 . We construct a

b**in**ary matrix of size N × V such that each column conta**in**s

exactly R of b**in**ary 1 and R − 1 of b**in**ary 0, with a unique

permutation. Exhaust**in**g all permutations given R number of

b**in**ary 1 and R − 1 number of b**in**ary 0 produces N

R unique

patterns, and hence V = N

R . With this construction, the

b**in**ary matrix holds N number of unique V -bit bitstreams,

each of which will be assigned to a receiver. Table III

illustrates our code design consider**in**g N = 3.

At the multicast sender, once the collided transmission is

decoded, the sender can identify whether a particular receiver

has returned an acknowledgement s**in**ce our cod**in**g scheme

guarantees a one-to-one relationship between the decoded

bitstreams and the comb**in**ations of the receivers. A retransmission

may apply as **in** the **IEEE** **802.11** MAC protocol operation

until either all receivers have received the multicast data

successfully, or the maximum retry limit has been reached.

Although we demonstrate our cod**in**g scheme with BPSK,

we can **in**clude a suitable mapp**in**g mechanism **in** the

transceivers to make our scheme suitable for DBPSK.

III. STUDY OF THE PROPOSED CODING SCHEME

Consider N stations2 , based on our design, we can construct

a coefficient matrix MN, where each of its elements is either

+1 or −13 . Let G = {1, ..., N} be the set conta**in****in**g all

stations and R = N+1

2 . Accord**in**g to our design, each of

the column **in** MN conta**in**s exactly R number of +1 and

R − 1 number of −1. In other words, for a given column

c,

r∈G MN(r, c) = 1. Based on this design, exhaustive

permutation of +1 and −1 for a column construction gives

N

R unique patterns. The coefficient matrix MN that holds

non-repetitive patterns of columns thus has a size of N × N

R .

We def**in**e F (G0, c) =

r∈G0 MN(r,

−→ 1, F (G0, c) ≥ 1

G0(c) =

(4)

0, F (G0, c) < 1

where c = 1, 2, ...,

c) where G0 ⊆ G.

In other words, the function F (G0, c) gives the sum of the

values correspond**in**g to a given column c and a particular

collection of stations G0. Let Ω+(G0, c) (resp. Ω−(G0, c))

denote the function that counts the number of +1 (resp. −1)

correspond**in**g to the the column c and the collection of stations

given **in** G0. By def**in**ition, we have

F (G0, c) = Ω+(G0, c) − Ω−(G0, c). (3)

N

N+1

R and R = 2 .

Based on the above def**in**ition, we first have the follow**in**g

properties about F (·).

Claim 1: Let G1, G2 ⊆ G and G1 ∩ G2 = ∅. If H =

G1 ∪ G2, then for all c, F (H, c) = F (G1, c) + F (G2, c).

Claim 2: Let G1 ⊂ G2 ⊆ G. If H = G2 \ G1, then for all

c, F (H, c) = F (G2, c) − F (G1, c).

The above claims can be easily established by set operations.

By def**in**ition, F (H, c) =

r∈H MN(r, c). Given that

H = G1 ∪ G2, we obta**in**

F (H, c) =

MN(r, c)

r∈(G1∪G2)

=

MN(r, c) +

r∈G1

MN(r, c)

r∈G2

s**in**ce G1 ∩G2 = ∅. With the above result, we have established

claim 1. Claim 2 can be established with the same approach.

S**in**ce **in** our design, each column **in** MN conta**in**s exactly

N+1

2 number of +1 and N−1

2 number of −1, then by def**in**ition

Ω+(G, c) = N+1

2

Ω−(G, c) = N−1

2

F (G, c) = 1.

(5)

The above gives the follow**in**g lemmas.

Lemma 1: Let G1 ⊂ G where |G1| = g and g is an odd

**in**teger ≤ N − 1. There exists a column c **in** MN such that

F (G1, c) = 1.

Proof: By def**in**ition, MN holds exhaustive patterns of

columns with exactly R number of +1 and R − 1 number of

−1. In other words, any column with exactly R number of +1

and R − 1 number of −1 is a column of MN.

Let G1 ⊂ G where |G1| = g and g is an odd **in**teger

≤ N − 1. We create a column c such that Ω+(G1, c) = g+1

2 ,

Ω−(G1, c) = g−1

2 and Ω+(G ′ 1, c) = Ω−(G ′ 1, c) = N−g

2 . S**in**ce

G = G1 ∪ G ′ 1 and G1 ∩ G ′ 1 = ∅, we yield

Ω+(G, c) = Ω+(G1, c) + Ω+(G ′ 1, c) = N+1

2 = R

Ω−(G, c) = Ω−(G1, c) + Ω−(G ′ 1, c) = N−1

2 = R − 1

which shows that c is a column of MN. S**in**ce Ω+(G1, c) =

Ω−(G1, c) + 1, by (3) we thus have F (G1, c) = 1.

Lemma 2: Let G1 ⊂ G where |G1| = g and g is a nonzero

even **in**teger ≤ N − 1. There exists a column c **in** MN such

that F (G1, c) = 0.

Proof: Let G1 ⊂ G where |G1| = g and g is a nonzero

even **in**teger. We create a column c such that Ω+(G1, c) =

Ω−(G1, c) = g

2 , Ω+(G ′ 1, c) = N−g+1

2 , and Ω−(G ′ 1, c) =

. S**in**ce G = G1 ∪ G ′ 1 and G1 ∩ G ′ 1 = ∅, we yield

N−g−1

2

Ω+(G, c) = Ω+(G1, c) + Ω+(G ′ 1, c) = N+1

2

Ω−(G, c) = Ω−(G1, c) + Ω−(G ′ 1, c) = N−1

2

= R

= R − 1

which shows that c is a column of MN. S**in**ce Ω+(G1, c) =

Ω−(G1, c), by (3) we thus have F (G1, c) = 0.

Proposition 1: Consider a certa**in** system with N stations

where N ≥ 1. For any G1, G2 ⊂ G and G1, G2 = ∅, −→ G1 = −→ G2

iif G1 = G2.

Proof: By def**in**ition given **in** (4), we can easily see that

if G1 = G2, then −→ G1 = −→ G2. In the follow**in**g, we shall prove

that if G1 = G2, then −→ G1 = −→ G2.

We will exam**in**e two cases: (i) |G1| is an odd **in**teger; (ii)

|G1| is an even **in**teger. Without loss of generality, we assume

that |G1| ≥ |G2|.

Case (i): |G1| is an odd **in**teger. Let g = |G1|. Based on

lemma 1, there exists a column c **in** MN such that

and hence accord**in**g to (4), we also have

−→

G1(c) = 1.

F (G1, c) = 1, (6)

This column will have the follow**in**g property

Ω+(G1, c) = g+1

2

Ω−(G1, c) = Ω+(G1, c) − 1 = g−1

2

Ω+(G ′ 1, c) = Ω−(G ′ 1, c) = N−g

2

with any permutation.

If G1 = G2, there exists K1 = G1 \ G2 = ∅ and K2 =

G2 \ G1 where |K1| = k1 ≥ 1 and |K2| = k2 ≥ 0. It is clear

that K1 ⊆ G1, K2 ⊆ G ′ 1 imply

1 ≤ k1 ≤ g, k2 ≤ N − g.

where g is an odd **in**teger and N − g is an even **in**teger.

With the above condition, there exists a permutation with**in**

c such that

Ω+(K1, c) = ⌊ k1

g+1

2 ⌋ + 1 ≤ 2

Ω−(K1, c) = ⌊ k1−1 g−1

2 ⌋ ≤ 2

Ω+(K2, c) = ⌊ k2 N−g

2 ⌋ ≤ 2

Ω−(K2, c) = ⌊ k2+1 N−g

2 ⌋ ≤ 2

that confirms K1 ⊆ G1, K2 ⊆ G ′ 1 given (7). The immediate

result gives

and

which yield

F (K1, c) =

F (K2, c) =

1, k1 = 1, 3, ...

2, k1 = 2, 4, ...

−1, k2 = 1, 3, ...

0, k2 = 0, 2, 4, ...

(7)

(8)

(9)

F (K1, c) − F (K2, c) ≥ 1. (10)

S**in**ce G2 = (G1 \ K1) ∪ K2, with (6) and (10), we obta**in**

F (G2, c) = F (G1, c) − F (K1, c) + F (K2, c) ≤ 0

and hence −→ G2(c) = 0. S**in**ce −→ G1(c) = 1, there exists a column

**in** MN such that −→ G2(c) = −→ G2(c), which is sufficient to show

that −→ G1 = −→ G2.

Case (ii): |G1| is an even **in**teger. Let g = |G1|. Based on

lemma 2, there exists a column c **in** MN such that

and hence accord**in**g to (4), we also have

−→

G1(c) = 0.

F (G1, c) = 0 (11)

This column will have the follow**in**g property

Ω+(G1, c) = Ω−(G1, c) = g

2

Ω+(G ′ 1, c) = N−g+1

2

Ω−(G ′ 1, c) = N−g−1

2

(12)

with any permutation.

If G1 = G2, there exist K1 = G1 \ G2 = ∅ and K2 =

G2 \ G1 where |K1| = k1 ≥ 1 and |K2| = k2 ≥ 0. It is clear

that K1 ⊆ G1, K2 ⊆ G ′ 1 imply

1 ≤ k1 ≤ g, k2 ≤ N − g.

where g is an nonzero even **in**teger and N −g is an odd **in**teger.

We first exclude the condition where k2 = 0. With the above

condition, there exists a permutation with**in** c such that

Ω+(K1, c) = ⌊ k1 g

2 ⌋ ≤ 2

Ω−(K1, c) = ⌊ k1+1 g

2 ⌋ ≤ 2

Ω+(K2, c) = ⌊ k2

N−g+1

2 ⌋ + 1 ≤ 2

Ω−(K2, c) = ⌊ k2−1 N−g−1

2 ⌋ ≤ 2

that confirms K1 ⊆ G1, K2 ⊆ G ′ 1 given (12). The immediate

result gives

and

which yield

F (K1, c) =

F (K2, c) =

−1, k1 = 1, 3, ...

0, k1 = 2, 4, ...

1, k2 = 1, 3, ...

2, k2 = 2, 4, ...

(13)

(14)

F (K2, c) − F (K1, c) ≥ 1. (15)

For k2 = 0 which implies G2 ⊂ G1, s**in**ce G2 cannot be

empty, k1 = g − |G2| must be ≤ g, there exists another permutation

**in** c such that Ω+(K1, c) < Ω−(K1, c) ≤ Ω−(G1, c)

giv**in**g

F (K1, c) =

−1, k1 = 1, 3, ...

−2, k1 = 2, 4, ...

(16)

and F (K2, c) − F (K1, c) ≥ 1 as **in** (15) s**in**ce F (K2, c) = 0.

Given that G2 = (G1 \ K1) ∪ K2, with (11) and (15), we

obta**in**

F (G2, c) = F (G1, c) − F (K1, c) + F (K2, c) ≥ 1

and hence −→ G2(c) = 1. S**in**ce −→ G1(c) = 0, there exists a column

**in** MN such that −→ G2(c) = −→ G2(c) which is sufficient to show

that −→ G1 = −→ G2.

With the above two cases, we have proven that if G1 = G2,

then −→ G1 = −→ G2. Together with the earlier establishment that if

G1 = G2, then −→ G1 = −→ G2, we conclude that for any G1, G2 ⊂

G and G1, G2 = ∅, −→ G1 = −→ G2 iif G1 = G2.

SIFS SIFS SIFS DIFS

Data Poll ACK Poll ACK

…

Td

SIFS DIFS

Data ACKs

Td

Ta

Tp

(a)

(b)

Fig. 1. Illustration of protocol handshake procedure for (a) the **IEEE** **802.11**b

PCF, (b) our proposed mechanism.

With Proposition 1, we have shown that based on our cod**in**g

scheme, there is a one-to-one relationship between the decoded

bitstreams and the comb**in**ations of the receivers. This one-toone

relationship allows a decoder to identify the presence of

each **in**dividual station **in** a collided transmission. In the case

that no station replies acknowledgement, an idle period will

occur on the channel. This idle channel will trigger the MAC

layer retransmission of the failed multicast transmission.

IV. PROTOCOL PERFORMANCE

In this section, we show the performance advantage of our

proposed approach. We consider the popular **IEEE** **802.11**b

standard [1] and summarize values of protocol parameters

needed for our performance evaluation **in** Table IV. The

full data rate of 11 Mbps transmission for data is assumed.

While the **IEEE** **802.11** standard does not enforce explicit

acknowledgement for a one-to-many transmission, for the performance

comparison, we consider the use of the standardized

but optional po**in**t coord**in**ation function (PCF) to achieve acknowledgement.

PCF uses power-save poll (PS-Poll) frame to

perform **in**dividual poll**in**g. Its protocol handshake procedure

is shown **in** Fig. 1(a), and the protocol handshake procedure

for our proposed method is also depicted **in** Fig. 1(b).

Based on Fig. 1 and Table IV, consider a d-byte payload to

multicast, we first have

Td = TP HY + 272+8·d

11

Tp = SIF S + δ + TP OLL + SIF S + δ + TACK

Ta = SIF S + δ + TCCF

(17)

where Td, Tp, and Ta is the duration of a data frame transmission

at 11 Mbps, the duration to poll a station, and the duration

for all stations to simultaneously return an acknowledgement,

respectively. With these tim**in**gs, consider a multicast**in**g to

n stations, we can determ**in**e the duration of the protocol

handshake procedure by

TST D = Td + nTp + DIF S + δ

TCC = Td + ⌈ n

9 ⌉Ta + DIF S + δ

(18)

where TST D and TCC are the durations us**in**g the standard

PCF mechanism and our proposed collision code mechanism

respectively. For our proposed mechanism, when the number

of stations exceed 9, we partition them **in**to several groups

for acknowledgement collisions. Fig. 2 plots and compares

the two protocol handshake durations. As can be seen, our

Protocol handshake

duration (second)

0.05

0.04

0.03

0.02

0.01

**IEEE** **802.11**b PCF

Our proposed scheme

0

0 10 20 30 40 50

Number of stations

Fig. 2. Protocol handshake duration comparison between the **IEEE** **802.11**b

PCF and our proposed mechanism with payload size of 8184 bits.

TABLE IV

TIMING FOR PROTOCOL PARAMETERS.

Protocol parameter Duration (µs)

Signal propagation delay, δ 1

SIFS 20

DIFS 50

PHY overhead, TP HY

192

PS-Poll frame, TP OLL

ACK frame, TACK

MAC data frame (d-byte payload), TDAT A

TP HY + 160

TP HY + 112

TP HY + 272+8·d

11

Collision code frame ∗ , TCCF

TP HY + 272 + 128

∗ Note: This collision code design supports up to 9 stations which

requires 126 bits or 16 bytes (with byte alignment).

mechanism us**in**g collision codes requires very short period to

complete the acknowledgement whereas the duration us**in**g the

**IEEE** **802.11**b PCF grows as the number of stations **in**creases.

V. CONCLUSION

Motivated by the concept of PNC, we proposed a collision

decod**in**g scheme that improves the reliability of wireless

multicast**in**g for the **IEEE** **802.11** MAC protocol. We first

established the majority pr**in**ciple between the **in**put and the

output bitstreams based on BPSK modulation. Us**in**g the

majority pr**in**ciple, we developed a cod**in**g scheme achiev**in**g

the identification of **in**dividual acknowledgement transmission

from a collided transmission. We applied our design to **in**crease

the reliability and reduce the overhead of wireless

multicast**in**g.

We believe that this paper pioneers **in** the MAC protocol

enhancement us**in**g PNC. There are other related issues that

require further research to address. In our scheme, although

acknowledgement transmissions appear simultaneously, they

are not necessarily synchronous **in** the physical layer. As

a future work, we will **in**vestigate the penalty of the time

synchronization and the impact on our cod**in**g scheme.

REFERENCES

[1] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY),

**IEEE** **802.11** Std., 1999.

[2] E. Pagani and G. P. Rossi, “Reliable broadcast **in** mobile multihop packet

networks,” **in** Proceed**in**gs of MobiCom, 1997.

[3] K. Tang and M. Gerla, “MAC reliable broadcast **in** ad hoc networks.”

[4] K. H. Lee and D. H. Cho, “A multiple access collision avoidance protocol

for multicast service **in** mobile ad hoc networks.”

[5] P. Rogers and N. Abu-Ghazaleh, “Directed broadcast: a MAC level

primitive for robust network broadcast.”

[6] S. Zhang, S. C. Liew, and P. P. Lam, “Hot topic: physical-layer network

cod**in**g,” **in** Proc. of MobiCom’06, 2006, pp. 358–365.