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This paper presents the investigative study of power reduction technique using different coding schemes while keeping the low probability of bit error. Hamming, extended Golay and BCH (Bos-chdhuri-Hocquenghem) are selected to illustrate the purpose of power reduction. For the simulation purpose different rates along with different coding techniques are selected. The results show that an efficient and rightful selection of code can improve the performance of any communication system with lower (Ratio of the signal energy per bit to noise power density) and bit error values.
Digital communication has many advantages compare to Analog communication: like immune to channel noise and distortion, use of regenerative repeaters to maintain the strength of transmitted signal over a distance, use of microprocessor, signal coding to detect and correct errors etcâ€¦  Recently there is a tremendous growth in digital communication sector especially with the introduction of wireless and
Computer based networks. These systems usually use binary numbers to represent information. Finally the information is transformed into analog signals by using different available modulation schemes. The communication channel introduces noise and interference that corrupts the transmitted signal. This noise and interference introduces bit errors and right sequence of bits is not received at the receiving end. The bit error rate varies in different transmitting environments usually is a mechanism that is often used in known as communication channel. Channel coding digital communication systems to protect the digital information from noise and interference. Channel coding reduces the number of bit errors and also provides methods to recover some bit errors.
Figure 1: Channel Coding
As shown in the figure 1, data has to be coded into digital form in order to be further processed by digital communication. The purpose of channel encoder is to add redundancy for low error rate. Next block is of pulse code modulation, where the voice is converted into digital format. In the modulation block the frequency of the base band signal is shifted to carrier frequency. The last block is concerned with the multiple-Access technique, where the each user is assigned a Channel (unique) in the form of Walsh code. Here the data of the user is spreaded many times depends on the length of the Walsh Code. At the receiver end reverse process is performed i.e.. demodulation, channel decoding and source decoding.
Use of channel coding to design low bit error rate communication system is an active research area [1-3]. The ability of different codes to detect and correct data at receiving side improves the quality of communication and also minimizes the chances of re-transmissions. The importance of error rate is realized in [1,2, 9, 10].
Apart from the ability of using codes to minimize the error rate the possibility of reducing peak power by using specific codes is now under consideration in MC-CDMA (Multi-Code Code Division Multiple Access) and OFDM (Orthogonal Frequency Division Multiplexing)[1-8]. Use of codes to reduce power will help in building robust and stable systems with better quality of voice and data.
With the preference of wireless devices for the communication purpose the focus of research has now mainly shifted to wireless communication system design and also takes the channel coding aspect with it. The battery power is a big constraint for the long duration communication and adjustment of power during calls cause a lot of power usage. This problem gives a clear motivation for investigating such codes that can reduce the power transmission while keeping the same or low bit error rate [1, 4-8].
This paper presents an investigative study of using popular codes to minimize the transmission power. Effect of using codes on transmitted power is investigated in detail and observations are noted about the effect on bit error rate, which remains the main quality standard.
Rest of the paper is divided into 5 sections. Section 2 provides details about the well know codes like Hamming, Golay and BCH that are used in simulations. Section 3 presents details about simulation setup. Section 4 provides results and discussion on them. Finally section 5 gives conclusion and future directives.
2. Types of Codes
Digital communication systems mostly implements channel coding to protect information bits from noise and interference. Channel coding provides better bit error control and thus provides better quality communication. The basic idea of channel coding is to introduce some additional bits in transmitted information bit sequence, so these bits can be used to detect and sometimes correct errors at the receiving end. Thus these additional bits improve the reliability of information transmission. There are two main types of channel codes Block codes and Convolution codes.
Block codes are very famous codes used for both error detection and correction. They have their roots in abstract algebra and finite field arithmetic and abstract algebra. Block codes takes as input k information bits and produces a block of n coded bits by using predefined rules. Thus an addition of n-k redundant bits occurs and these redundant bits are responsible for error control. Generally, these codes are called (n,k) block codes. Among the block codes mostly used block codes are Hamming codes, Golay codes, Extended Golay, BCH codes, and Reed Solomon codes . This research work has utilized three of the well know block code namely Hamming, Extended Golay and BCH. Brief description is given as below.
Extension of hamming codes that can correct one and detect more than one error is widely used in different applications. The main principal behind working of Hamming codes is "parity". Parity is used to detect and correct errors. These parity bits are the resultant of applying parity check on different combination of data bits. Structural representation of Hamming codes can be given as 
Where .. For hamming codes Syndrome decoding is well suited. It is possible to use syndrome to act as a binary pointer to identify location of error.
If hard decision decoding is assumed then the probability of bit error can be given as
Where p is the channel symbol error probability . An identical equation can be written as .
2.2 Extended Golay
The extended Golay code uses 12 bits of data and coded it in 24-bit word. This (24,12) extended Golay is derived by adding parity bit to (23, 12) Golay code. This added parity bit increases the minimum distance from 7 to 8 and produces a rate ½ code, which is easier to implement than the rate that is original Golay code .
Though the advantages of using extended Golay is much more to that of ordinary Golay but at the same time the complexity of decoder increases and with the increase in code word size the bandwidth is also utilized more. Extended Golay is also considered more reliable and powerful as compared to Hamming code. If probability of bit error is given by and is 8 with the assumption of hard decision then error probability is given by 
2.3 BCH Codes
BCH belongs to powerful class of cyclic codes. BCH codes are powerful enough to detect multiple errors. The most commonly used BCH codes employs a binary alphabet and a codeword block length of , where .
2.4 Trade off using codes
As explained in the earlier sections that use of codes reduces the power and lowers the possibility of error rates. However, to do this we have to pay the price for it in terms of ore bandwidth. For example if we use the Extended Golay (24,12), we need twice the bandwidth of the message signal.
Mat Lab is used for simulation purpose.
Multiple Access technique: CDMA, because codes commonly used in CDMA and OFDM to provide reliability.
Frequency re-use factor: 100%
Error correcting codes: Block codes
Data rate: 9600bits per second
Model: Two Ray Ground
ERP (Effective Radiated Power of Transmitter): 46dB
Modulation Scheme: BPSK (Binary Phase Shift Keying)
Walsh code = 64, out of which W0 is used as a pilot channel, W1 to W7, only one for
paging, W32 for sync purpose, remaining 61 for traffic channel
In this simulation we used different code rates of hamming, golay and BCH. Eb/No is taken as a power comparison parameter for coded and uncoded signal. The parameter is calculated using formula 
Where R is the data rate in bits per second. Pr/No is ratio the received power to the noise.
Apart from comparison, the value of bit error rate is also compaired for coded and uncoded bit stream which is calculated by the formula given in eq 6 & eq 7 respectively 
Where Q(x) is called complementary error function or co-error function, it is commonly used symbol for probability under the tail of Gaussian pdf. Where Pu is probability of error in un-coded bit sequence and Pc is the probability of error in coded bit sequence. is ratio of energy per bit to noise spectrum density of coded bit sequence.
Finally the most important parameter that shows the edge of using codes with the data is calculated which is the probability of bit detected correctly for coded and uncoded bit sequence which is given by equations 
and are probability of un-coded message block received in error and probability of coded block received in error respectively.
4. Simulation results
This section presents graphs that are obtained through simulation. The parameter of investigation is of coded and uncoded sequences, Correlation Coefficient (coded power, code rate and error) and bit error propabiliy at receiving end.
Graph of figure 2 represents ratio of energy per bit to noise power densityon X-axis and error probability on the Y-axis. Graph shows that (error right curve) using code we have aquired reduction in power from 4 to 2 dB with same low probability of error i.e 3x10-2. . Thus with the help of codes it is shown that more reliable transmission with the reduced power is posible. Thus the power can be efficiently used and will help to improve the up time for the mobile devices with better quality of data transaction.
Graph of figure 3 shows correlation coefficient (Coded Power & Coded rate). This graph is based of three attributes of signal. One is Coded power, second is coded rate and third is Error. Interresting part to be noted from the graph is that from 12 dB(coded power) onwards we have almost '0' probability of error. This proves that coding may significantly reduces the error rate.
Finally graph of Figure 4 represents the most important comparision of different codes performances. This graph is obtained by keeping the same data rate and varying code rate and code types. For example as decsribed in ealier section three well know block code like Hamming, Extended Golay and BCH are taken for study. For hamming three different rate that is (7,4), (15,11) and (31,26) are taken. For Extended Golay (24,12) and for BCH (127,64) and (127,36) rates are used. The graph shows the performance of all the codes with Eb/No on X-axis and Error probability on the Y-axis. It can be eassily infered by the given graph that Golay and BCH shows better performance and these codes give the optimal power of 3.6 dB.
In this research we inferred that using codes we have low probaility of error with reduced power. Interesting part to be noted is that correlation coefficient between coded power & code rate vs. error showed that error is almost zero as the correlation coefficient increases from 12 (figure 3). The most important part is that at same data rate different codes have been used, but Golay and BCH gave optimized power at the expense of double bandwidth. For future work, new codes or algorithm may be designed to implement on multi-carrier systems such as MC-CDMA and OFDM, because these systems have very high peak, which is un-desirable.