Checksum Checking

1.1.1 Checksum Technique

The checksum method is based on binary addition of all the sub partition of the data. The summation of data in the blocks is calculated. Then one’s complement of the summation is computed. The summation and it’s one’s complement are added to the end of the data units as a redundancy which is defined as checksum. The extended redundancy field with data are sent to the receiver as given in Equation 2.1. On the receiver side, the summation of all blocks and 1`s complement of this result is computed. Finally accept the pattern if the one’s complement of summation is zero otherwise sending for re-execution as given in Equation 1.2 [19].

Suppose, total binary bits = n and k is the number of segments of n data and block of messages come from original data of m. Summation of all blocks (S), One’s Complement of Checksum , Generated Codeword , and Summation of all blocks after appended Checksum .

Summation of all blocks S = (2.1)

One’s Complement of summation of blocks = . Generated codeword = number of n binary stream and appended with .

On the receiving side, the is a block from the codeword of checksum.

Summation on receiving side = (2.2)

Accept the result if it is = 0, otherwise it is neglected in Equation 2.2. The Time complexity = O(S + ) of checksum [22].

1.1.2 Cyclic Redundancy Checking

CRC error detection technique is mainly based on the binary division as shown in Figure 2.7. The polynomial divisor G(x) operates on the binary division with original data and appends a sequence of redundant extra zero and added the remainder is called the CRC. If the length of polynomial divisor G(x) is n, the extra (n-1) zeros are appended with original data. On the receiver side, the received codeword is divided by the same polynomial divisor G(x). Finally accept if the remainder is zero otherwise requesting for resending or re-execution as shown in Figure 2.8 [19].

Figure 2.7: Cyclic redundancy checking technique [19] [58].

Let G(x) is the CRC polynomial divisor and the maximum degree of polynomial code n-1 indicates the polynomial W= + + + ……+ where, W and x is coefficient and variable respectively [75].

W(x) = (2.3)

Figure 2.8: CRC error detection technique using binary division [19] [58].

On the receiving side, when the codeword is not divided by polynomial G(x), it may be changed to E(x) error bits. R(x) is the receiving data in Equation 2.5. So we can find an easy way [75].

R(x) = + (2.4)

If error E(x) is zero, then data are received error-free.

R(x) = + 0

Complexity = O (2× + ) (2.5)

So, the time complexity of CRC is more than other as given in Equation 2.5 [22] [58].

1.1.3 Hamming Code Mechanism

Hamming code is a mechanism for error detection and correction. When the huge data are transmitted from the sender to the receiver, it may be errors occurred. Redundant extra bits are generated and added with the information bits of data. It ensures error free data transmission from source to destination [19].

The formula of redundant bits is calculated ≥ m + r + 1, here r is the redundant bits, m is used for data bits. For an example number of data bits is 8, the amount of redundant bits is calculated by formula ≥ 8 + 4 + 1 and the amount of redundant bits are 4 [19].