List the properties of generator polynomial of cyclic codes

 Generator polynomial is a factor x(p) and (pn+1)

 Code polynomial, message polynomial and generator polynomial are related by, X(p) = M(p)G(p)

 Generator polynomial is of degree “q”

PART-B

 Explain Shannon-Fano algorithm.

Shannon – Fano Encoding Algorithm:

Shannon-Fano source encoding follows the steps

Step1: Order symbols mi in descending order of probability

Step2: Divide symbols into subgroups such that the subgroup’s probabilities

(i.e. information contests) are as close as possible can be two symbols as a subgroup if there are two close probabilities (i.e. information contests), can also be only one symbol as a subgroup if none of the probabilities are close

Step3: Allocating codewords: assign bit 0 to top subgroup and bit 1 to bottom subgroup Step4: Iterate steps 2 and 3 as long as there is more than one symbol in any subgroup Step5: Extract variable-length codewords from the resulting tree (top-down)

Note: Codewords must meet condition: no codeword forms a prefix for any other codeword, so they can be decoded unambiguously

Example

Consider the message ensemble S = {s1, s2, s3, s4, s5, s6, s7, s8} with P ={1/4,1/4,1/8,1/8,1/16,1/16}

k=8

Entropy (H) =

∑

P k log 2 (1/pk)

k=1 k=8

Average codeword length (L) =

∑

^{P k Nk}

k=1

ή = H L

H = 2×1/4 log 4+ 2×1/8log 8+ 4×1/16 log 16= 2.75 bits/symbol.

L = 2×1/4+ 2×1/4+ 3×1/8+ 3×1/8+ 4×1/16+ 4×1/16+ 4×1/16+ 4×1/16= 2.75 binits / symbol.

Ƞ %= H/N = 100%

 A discrete memory less source X has five symbols m1,m2,m3,m4,m5,m6,m7 and m8 with probabilities p(m1) = 0.27, p(m2) = 0.2, p(m3) = 0.17, p(m4) = 0.16, p(m5) = 0.06, p(m6) = 0.06, p(m7) = 0.04 and p(m8) = 0.04 .Construct a Shannon – Fano code for X and calculate the efficiency of the code.

Solution:

Less probable symbols are coded by longer code words, while higher probable symbols are assigned short codes.

Assign number of bits to a symbol as close as possible to its information content and no codeword forms a prefix for any other codeword.

k=8

Entropy (H) =

∑

^{P k log 2 (1/pk)}

k=1

H = 2.6906 (bits/symbol)

k=8

Average codeword length (L) =

∑

^{P k Nk}

k=1

L= 0.47 ×2 + 0.33× 3 + 0.2 × 4 = 2.73 (bits/symbol) Code efficiency (ή) = H

L

ή

=2.6906/2.73= 98.56%

 A discrete memory less source X has five symbols A, B, C, D, E, F, G and H with probabilities A = 1/2, B = 1/4, C = 1/8, D= 1/16,E =1/32, F = 1/64, G = 1/128 and H

=1/128.

Construct a Shannon – Fano code for X and calculate the efficiency of the code.

Solution:

k=8

Entropy (H) =

∑

^{P k log 2 (1/pk)}

k=1

H = 1/2×1 +1/4× 2 +1/8× 3 +1/16× 4 +1/32× 5 +1/64× 6 + 2×1/128× 7

=127/64

(bits/symbol)

k=8

Average codeword length (L) =

∑

P k Nk

k=1

L= 1/2× 1 +1/4× 2 +1/8× 3 +1/16×4 +1/32× 5 +1/64× 6 + 2×1/128× 7

=127/64

(bits/symbol)

ή = H L

Coding efficiency =100%

Note: (Coding efficiency is 66% if codewords of equal length of 3-bits are used)

 Explain Huffman encoding algorithm with example.

Huffman source encoding follows the steps

Step1: Arrange symbols in descending order of probabilities

Step2: Merge the two least probable symbols (or subgroups) into one subgroup

Step3: Assign ’0’ and ’1’ to the higher and less probable branches, respectively, in the subgroup Step4: If there is more than one symbol (or subgroup) left, return to step 2

Step5: Extract the Huffman code words from the different branches (bottom-up) EXAMPLE: Consider 8 symbols with respective probabilities.

 Intermediate probabilities: m7,8 = 0.08; m5,6 = 0.12; m5,6,7,8 = 0.2; m3,4 = 0.33;

m2,5,6,7,8 = 0.4; S1,3,4 = 0.6.

 When extracting codewords, remember ”reverse bit order” - This is important as it ensures no codeword forms a prefix for any other codeword

.

k=6

Entropy (H) =

∑

P k log 2 (1/pk)

k=1 k=6

Average codeword length (L) =

∑

P k Nk

k=1

ή = H L

Average code word length with Huffman coding for the given example is also 2.73 (bits/symbol), and coding efficiency is also

98.56%.

      Explain in detail about convolution encoder with neat diagram.(16)

Nov/dec 2012

May/Jun 2013 Convolutional encoder

The performance of a convolutional code depends on the coding rate and the constraint length Longer constraint length K

      • More powerful code       • More coding gain

       Coding gain: the measure in  the difference between the signal to noise ratio (SNR) levels between the uncoded system and coded system required to reach the same bit error rate (BER) level        • More complex decoder

       • More decoding delay Smaller coding rate Rc =k/n

       • More powerful code due to extra redundancy        • Less bandwidth efficiency

An Example of Convolutional Codes: �

 Convolutional encoder (rate ½, K=3) with message sequence (101)

       3 shift­registers, where the first one takes the incoming data bit and the rest form the memory of the encoder.

Input message (M) = (101); Encoded output (U) = (11 10 00 10 11) Effective code rate (Reff)

 Initialize the memory before encoding the first bit (all­zero)

 Clear out the memory after encoding the last bit (all­zero)

 Hence, a tail of zero­bits is appended to data bits. 

L is the number of data bits, L should be divisible by k Reff =L/n[L/k+(K­1)]

     Example: m=[101];

      n=2, K=3, k=1, L=3

       Reff=3/[2(3+3­1)]=0.3

Vector representation:

       Define n vectors, each with Kk elements (one vector for each modulo­2 adder). The i­th element in each vector, is “1” if the  i­th stage in the shift register is connected to the corresponding modulo­2 adder, and “0” otherwise.

Polynomial representation(1) :

Define n generator polynomials, one for each modulo­2 adder. Each polynomial is of degree Kk­1 or less and describes the connection of the shift registers to the corresponding modulo­

2 adder.

Examples: k=1

Polynomial representation (2):

Example: m= (1 0 1)

Tree diagram to describe a convolutional code:

A convolutional encoder is a finite­state machine:

       The state is represented by the content of the memory, i.e., the  (K­1)k previous bits, namely, the (K­1)k bits contained in the first (K­1)k stages of the shift register. Hence, there are 2 (K­1)k states.

Example: 4­state encoder

 A state diagram is simply a graph of the possible states of the encoder and the possible transitions from one state to another. It can be used to show  the relationship between the encoder state, input, and output.

 The stage diagram has 2 (K­1)k nodes, each node standing for one encoder state.

 Nodes are connected by branches

 Every node has 2k branches entering it and 2k branches leaving it.

 The branches are labelled with c, where c is the output.

When k=1

 The solid branch indicates that the input bit is 0.

 The dotted branch indicates that the input bit is 1.

Trellis Diagram:

      Explain in detail the Viterbi algorithm for decoding of convolution codes with a suitable example.

       The trellis diagram of a convolutional code is obtained from its state diagram. All state transitions at each time step are explicitly shown in the diagram to retain the time dimension, as is present in the corresponding tree diagram. Usually, supporting descriptions on state transitions, corresponding input and output bits etc. are labelled in the trellis diagram. It is interesting to note that the trellis diagram, which describes the operation of the encoder, is very convenient for describing the behaviour of the corresponding decoder, especially when the famous ‘Viterbi Algorithm (VA)’ is followed.  Figure 2 shows the trellis diagram for the encoder in Figure1. 

       Fig. 1 A convolutional encoder with k=1, n=2 and r=1/2

Hard­Decision and Soft­Decision Decoding 

      Hard­decision and soft­decision decoding are based on the type of quantization used on the received bits. Hard­decision decoding uses 1­bit quantization on the received samples. Soft­

decision decoding uses multi­bit quantization (e.g. 3 bits/sample) on the received sample values.

Hard­Decision Viterbi Algorithm 

       The Viterbi Algorithm (VA) finds a maximum likelihood (ML) estimate of a transmitted code sequence c from the corresponding received sequence r by maximizing the probability p(r|c) that sequence r is received conditioned on the estimated code sequence c. Sequence c must be a valid coded sequence. 

       The Viterbi algorithm utilizes the trellis diagram to compute the path metrics. The channel is assumed to be memory less, i.e. the noise sample affecting a received bit is independent from

the noise sample affecting the other bits. The decoding operation starts from state ‘00’, i.e. with the

in our example) and chose the state with minimum overall ‘accumulated path metric’ as the

‘winning node’ for the first codeword. Then we trace back the history of the path associated with this winning node to identify the codeword tagged to the first branch of the path and declare this codeword as the most likely transmitted first codeword. 

      The above procedure is repeated for each received codeword hereafter. Thus, the decision for a codeword is delayed but once the decision process starts, we decide once for every received codeword.   For   most   practical   applications,   including   delay­sensitive   digital   speech   coding   and transmission, a decision delay of Lx k codewords is acceptable. 

Soft­Decision Viterbi Algorithm 

       In soft­decision decoding, the demodulator does not assign a ‘0’ or a ‘1’ to each received bit but uses multi­bit quantized values. The soft­decision Viterbi algorithm is very similar to its hard­

decision algorithm except that squared Euclidean distance is used in the branch metrics instead of simpler Hamming distance. However, the performance of a soft­decision VA is much more impressive compared to its HDD (Hard Decision Decoding)  Fig 3 (a) and (b)]. The computational requirement of a Viterbi decoder grows exponentially as a function of the constraint length and hence it is usually limited in practice to constraint lengths of K = 9.

Fig. 3 (a) Decoded BER vs input BER for the rate – half convolutional codes with Viterbi Algorithm ; 1) k = 3 (HDD),2) k = 5 (HDD),3) k = 3 (SDD), and 4) k= 5 (SDD). HDD: Hard

Decision Decoding; SDD: Soft Decision Decoding.

Algorithm ; 1) Uncoded system; 2) with k = 3 (HDD) and 3) k = 3 (SDD).

• Supplementary services 

When a user/call moves to a new cell, then a new base station and new channel should be 

Approach SDMA TDMA FDMA CDMA

Idea Segment space

into cells/sectors Segment sending time into disjoint

time slots,

demand driven or fixed patterns

Segment the band frequency into disjoint sub-bands

Spread the spectrum using orthogonal codes

Terminals Only one

terminal be active in one cell/one sector

All terminals are active for short periods of time on the frequency

Every terminal has its own frequency, uninterrupted

All terminals can be active at the same

Advantages Very simple, increases

capacity per km2

Established ,fully digital, very flexible

Simple, established, robust

Flexible, less planning needed, soft handover

Disadvantages Inflexible, antennas typically fixed

Guard space

needed Inflexible

frequencies are a scare resource

Complex receivers,

needs more

complicated power control for senders

Comments Only in

combination with TDMA, FDMA or CDMA

Standard in fixed networks, together with SDMA/FDMA used in many mobile

networks

Typically combined with TDMA and SDMA

Used in many 3G systems, higher complexity, lowered expectations;

integrate with TDMA/FDMA

 Explain the concept of frequency reuse and handoff in cellular network.

Frequency Re-use:

• The design is done in two steps – Area coverage planning

– Channel (Frequency) allocation

• An efficient way of managing the radio spectrum is by reusing the same frequency, within the service area, as often as possible

• The concept of simultaneous use of same frequency at different cells that are sufficiently placed at a distance from each other. Re-use distance and re-use factor are the two elements determine the frequency reuse.

• We form a cluster of cells

– Divide the total number of channels (frequencies) between the cells of the cluster.

– All the channels within the cluster are orthogonal

• We repeat the cluster over the service area

• No interference between cells of the same cluster

• The distance between the clusters is called the reuse distance D

• The design reduces to finding D!

• For hexagonal cells, the number of cells in the cluster is given by

N

Handoff

The mobile unit moves, they pass from cell to cell, which require transferring of call from one BS to another BS. This process is called handoff

Handoff is the procedure for changing the channel assignments of MS from one BS to another as the MS moves from one cell to another.

Handoff is classified as

Hard handoff (break-before-make): MS connects to single BS at a time. It is employed by disconnecting with the base station before switching to another base station in a communication network.

Applications: VoIP

Soft handoff (make-before-make): MS connects to multiple BS at a time. It is employed by establishing connection with another base station before disconnecting from the Existing BS in the network.

Handover decision:

Network controlled handoff: both the measurements of performance metrics such as BER, block error rate, received signal strength, signal to noise ratio, distance between the BS and MS are taken by network element and the decision is also made by network. Duration is about the 100ms-200ms.

Mobile-assisted handoff: measurements are taken by MS and decisions are taken by BS.Duration is about 1second and GSM is example for this.

Mobile controlled handoff: both the measurements and decisions are taken by mobile itself with handoff duration of 0.1 sec.

∆ = Phandoff-Pmin-usable.

Phandoff- Received signal threshold at which handoff initiated.

Pmin-usable.- minimum usable signal level.

Ways to improve handoff:

 Optimize ∆.

 Prioritize handoff.

 Minimize delay at MSC.

 Mobile assisted handoff

Handover Performance Metrics

 Cell blocking probability – probability of a new call being blocked

 Call dropping probability – probability that a call is terminated due to a handover

 Call completion probability – probability that an admitted call is not dropped before it terminates

 Probability of unsuccessful handover – probability that a handover is executed while the reception conditions are inadequate

 Handoff blocking probability – probability that a handoff cannot be successfully completed

 Handoff probability – probability that a handoff occurs before call termination

 Rate of handoff – number of handoffs per unit time

 Interruption duration – duration of time during a handoff in which a mobile is not connected to either base station

 Handoff delay – distance the mobile moves from the point at which the handoff should occur to the point at which it does occur

Power Control

• Why transmitter power control?

– Reduce terminal power consumption

– Reduce interference within the cellular system and improve quality – Efficient handling of mobility

– In SS systems using CDMA, it’s desirable to equalize the received power level from all mobile units at the BS

• Reduce near-far problem

• Open-loop power control

– Depends solely on mobile unit – No feedback from BS

– Not as accurate as closed-loop, but can react quicker to fluctuations in signal strength

• Closed-loop power control

– Adjusts signal strength in reverse channel based on metric of performance

– BS makes power adjustment decision and communicates to mobile on control channel

 Explain SDMA,FDMA, TDMA and CDMA?

Space Division Multiple Access (SDMA)

 Space Division Multiple Access (SDMA) is used for allocating a separated space to users in wireless networks. It involves assigning an optimal base station to a mobile phone user. The mobile phone may receive several base stations with different quality.

 A MAC algorithm decides which base station is best, taking into account which frequencies (FDM), time slots (TDM) or code (CDM) are still available (depending on the technology).

 Typically, SDMA is never used in isolation but always in combination with one or more other schemes. The basis for the SDMA algorithm is formed by cells and sectorized antennas which constitute the infrastructure (SDM) .

 The channels k1 to k3 can be mapped onto the three ‘spaces’ s1 to s3 which clearly separate the channels and prevent the interference ranges from overlapping. The space between the interference ranges is sometimes called guard space.

 Each subscriber is given a separate pair of copper wires to the local exchange

 Countermeasures- Interference is overlapping of cells,leaving the protective distance between MS and devices solves the problem

Frequency division Multiple Access (FDMA)

 Frequency division Multiple Access (FDMA) is a technology where the total amount of spectrum is divided in a number of channels. Each channel can be

assigned to a different user.

 FDMA is commonly used in analog mobile radio, including analogue cellular mobile telephone systems like AMPS, NMT and TACS.

 Between the different used frequency channels is a small amount of bandwidth not used.

This space is called a guard band. This bandwidth is necessary to cater for instability of the sender, frequency shifts due to movement (the Doppler effect) and no-ideal filtering.

 Guard spaces are needed to avoid frequency band overlapping ( adjacent channel interference). This scheme is used for radio stations within the same region, where each radio station has its own frequency

 FDMA is usually implemented either in narrowband systems or to produce few subchannels. It combined with other multiple access techniques (e.g., TDMA,CDMA).

 FDMA systems have to cope with intermodulation (IM) products interference.

 In cellular systems, the two directions, base to mobile station and vice versa, are usually separated in frequency. This scheme is called FDD.

 Both receiver and transmitter have to know the frequencies in advance since the receiver must be able to tune properly. few bits are needed for overhead purposes such as synchronization and framing as compared to TDMA.

TDMA

 A channel ki is given the whole bandwidth for a certain amount of time, i.e., all senders use the same frequency but at different points in time.

 Guard spaces, which now represent time gaps, have to separate the different periods when the senders use the medium.

 If two transmissions overlap in time, this is called co-channel interference.

 To avoid this type of interference, precise synchronization between different

Senders is necessary.

 Disadvantage- as all senders need precise clocks Code division multiple access (CDMA)

 Code division multiple access (CDMA) systems use exactly these codes to separate different users in code space and to enable access to a shared medium without interference.

 CDMA is a method in which users occupy the same time and frequency allocations, and are channelized by unique assigned codes. The signals are separated at the receiver by using a correlator that Access

 It accepts only signal energy from the desired channel. Undesired signals contribute only to the noise.

 A CDMA system uses effective power control process.

 The main problem is how to find “good” codes and how to separate the signal from noise generated by other signals and the environment.

 A code for a certain user should have a good autocorrelation and should be orthogonal to other codes.

 Orthogonal- Two vectors are called orthogonal if their inner product is 0, as is the case for the two vectors (2, 5, 0) and (0, 0, 17): (2, 5, 0)*(0, 0, 17) = 0 + 0 + 0 = 0.

 The Barker code (+1, –1, +1, +1, –1, +1, +1, +1, –1, –1, –1) has a good autocorrelation, i.e., the inner product with itself is large, the result is 11. This code is used for ISDN and IEEE 802.11.

Salient Features of CDMA

• It is an advanced comm. Technology.

• It has Anti-jam and security features.

• Large capacity as compared to other Technology like FDMA and TDMA.

• It uses spread spectrum technology.

• Better use of the multipath.

• In CDMA reuse patterns are not required.

The main advantages of this technology are:

• Fast Network deployment.

• Reduced service interruptions.

• Low Maintenance & operational cost.

• Better system coverage flexibility

• Higher capacity

• Easy transition to mobile services.

Disadvantages of CDMA

• DSSS is more complex than techniques used in TDMA/FDMA.

• Power control in CDMA is more complicated.

• The bandwidth obtained by each user is limited due to spread spectrum. (The signal will occupy a large bandwidth but the actual spectrum is only a fraction of it. It is fine for voice and low data speed applications but not for 4G

 Explain in detail about Bluetooth

 Simple, cheap, replacement of IrDA, low range, lower data rates, low-power

 Worldwide operation: 2.4 GHz

 Resistance to jamming and selective frequency fading:

 FHSS over 79 channels (of 1MHz each), 1600hops/s

 Coexistence of multiple piconets like CDMA

 Links: synchronous connections and asynchronous connectionless

 Interoperability: protocol stack supporting TCP/IP, OBEX, SDP

 Range: 10 meters, can be extended to 100 meters Bluetooth Application Areas:

 Data and voice access points

 Real-time voice and data transmissions

 Cable replacement

 Eliminates need for numerous cable attachments for connection

 Low cost < $5

 Ad hoc networking

 Device with Bluetooth radio can establish connection with another when in range

Protocol Architecture

 Bluetooth is a layered protocol architecture

 Core protocols

 Cable replacement and telephony control protocols

 Adopted protocols

 Core protocols

 Radio

 Baseband

 Link manager protocol (LMP)

 Logical link control and adaptation protocol (L2CAP)

 Service discovery protocol (SDP)

Piconets and Scatternets

 Piconet

 Basic unit of Bluetooth networking

 Master and one to seven slave devices

 Master determines channel and phase

 Scatternet

 Device in one piconet may exist as master or slave in another piconet

 Allows many devices to share same area

 Makes efficient use of bandwidth Network Topology

 Piconet = set of Bluetooth nodes synchronized to a master node

 The piconet hopping sequence is derived from the master MAC address (BD_ADDR IEEE802 48 bits compatible address)

 Scatternet = set of piconet

 Master-Slaves can switch roles

Radio Specification

 Classes of transmitters

o Class 1: Outputs 100 mW for maximum range

• Power control mandatory

• Provides greatest distance o Class 2: Outputs 2.4 mW at maximum

• Power control optional o Class 3: Nominal output is 1 mW

• Lowest power

Baseband layer:

 FH occurs by jumping from one channel to another in pseudorandom sequence

 Hopping sequence shared with all devices on piconet

 Hopping sequence shared with all devices on piconet

In document ADC-CS6304-Q&A (Page 74-101)