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Chapter 25 - Coding and error control (Review/Recap). The following will be discussed in this chapter: CRC Algorithms, ECC, block ECC, convolutional code, turbo codes (block +convolutional), ns2 intro and installation. | Coding and Error Control Review/Recap Lecture 25 Overview CRC Algorithms ECC Block ECC Convolutional Code Turbo Codes (Block +Convolutional) ns2 Intro and installation CRC Algorithm Q:- List three different ways in which the CRC algorithm can be described. Cyclic Redundancy Check (CRC) Burst errors will most likely go undetected by a simple parity check scheme Instead, a more elaborate technique called Cyclic Redundancy Check (CRC) is typically implemented CRC appends redundant bits to the frame trailer called Frame Check Sequence (FCS) FCS is later utilized at RX for error detection In a given frame containing n bits, we define: k = number of original data bits (n – k) = number of bits in the FCS field (i.e. additional bits) So, that the total frame length is k + (n – k) = n bits CRC Generation CRC generation is all about finding the FCS given the data (D) and a divisor (P) There are three equivalent ways to generate the CRC code: Modulo-2 Arithmetic Method Polynomial Method Digital Logic Method Modulo 2 Arithmetic Binary arithmetic without carry Equivalent to XOR operation i.e: 0 0 = 0; 1 0 = 1; 0 1 = 1; 1 1 = 0 1 0 = 0; 0 1 = 0; 1 1 = 1 Examples: 1010 +1010 __ 0000 CRC Error Detection Process Given k-bit data (D), the TX generates an (n – k)-bit FCS field (F) such that the total n-bit frame (T) is exactly divisible by some (n-k+1)-bit predetermined devisor (P) (i.e. gives a zero remainder) In general, the received frame may or may not be equal, in value, to the sent frame Let the received frame be (T’) In error-free transmission T’ = T The RX then divides (T’) by the same known divisor (P) and checks if there is any remainder If division yields a remainder then the frame is erroneous If the division yields zero remainder then the frame is error-free unless many erroneous bits in T’ resulted in a new exact division by P (This is very unlikely but possible, causing an undetected error!) CRC Generation Data D: T = | Coding and Error Control Review/Recap Lecture 25 Overview CRC Algorithms ECC Block ECC Convolutional Code Turbo Codes (Block +Convolutional) ns2 Intro and installation CRC Algorithm Q:- List three different ways in which the CRC algorithm can be described. Cyclic Redundancy Check (CRC) Burst errors will most likely go undetected by a simple parity check scheme Instead, a more elaborate technique called Cyclic Redundancy Check (CRC) is typically implemented CRC appends redundant bits to the frame trailer called Frame Check Sequence (FCS) FCS is later utilized at RX for error detection In a given frame containing n bits, we define: k = number of original data bits (n – k) = number of bits in the FCS field (i.e. additional bits) So, that the total frame length is k + (n – k) = n bits CRC Generation CRC generation is all about finding the FCS given the data (D) and a divisor (P) There are three equivalent ways to generate the CRC code: Modulo-2 Arithmetic Method Polynomial
