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- Code Error Detection and correction

- Parity

- Cyclical Redundancy Coding (CRC)

- Hamming Code

- Digital Modulation Techniques

- Frequency Shift Keying (FSK)

- Binary Phase Shift Keying (BPSK)

- Quadrature Phase Shift Keying (QPSK)

- Channel Access

- Time Division Multiple Access (TDMA)

- Code Division Multiple Access (CDMA)

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- 1. * Clyde A. Lettsome, Ph.D., P.E.
- 2. * Digital Communication Overview * Digital Modulation Techniques * Frequency Shift Keying * Binary Phase Shift Keying * Code Error Detection and Correction Methods * Parity * Cyclical Redundancy Check * Block Error Detection and Correction * Hamming Code * Reed Solomon * Channel Access Methods * Time Division Multiple Access (TDMA) * Code Division Multiple Access (CDMA) *
- 3. *
- 4. Satellite, Television, Radio Broadcast Data Storage, Hard drives, USB drives Digital Communications is Everywhere Wireless Routers, Cellular networks, Bluetooth * CD, MP3, MPeg
- 5. * Reduced bandwidth if modulated on an analog carrier * Noise Immunity * Errors may be detected * Errors may be corrected * Easily manipulate to improve transmission * Time Division Multiple Access (TDMA) * Code Division Multiple Access (CDMA) *
- 6. Convert to Binary Data Encoding Modulation Transmission Medium Storage Device Transmission Medium Storage Device Demodulation Data Decoding System dependent * Convert to Original Form
- 7. *
- 8. * Frequency Shift Keying (FSK) - transmission method in which the modulating wave shifts between two predetermined frequencies. *Figure from Modern Communications by Beasley & Miller *
- 9. * Binary Phase Shift Keying (BPSK) - transmission method in which the modulating wave shifts between two phases 180o out of phase. *Figure from Modern Communications by Beasley & Miller *
- 10. * What if a bit(s) is(are) messed up during transmission or storage? * Examples: atmospheric noise, intrinsic noise, scratches on CDs, single-event upsets, etc. * Digital coding has many advantages over analog coding * Immunity to noise * Errors can be detected and corrected *
- 11. *
- 12. * Error detection –Retransmit the block * Parity * Cyclic Redundancy Check * Block Codes * Error correction – Fix errors at the receiver via FEC – Forward Error Correction (Adding more coding bits increases the correction capability but reduces throughput.) * * Block Codes * Hamming Code * Reed Solomon
- 13. * Arguably the most common method of error detection. * A single bit called parity bit is added to each transmitted code. * Parity bit makes the code either be even or odd * Even parity makes the total number of ones even * Odd parity makes the total number of ones odd * Example: Code [1001] * Even parity transmitted code: [1001|0] * Odd parity transmitted code: [1001|1] *
- 14. *Will detect error only if an unexpected parity is received * Odd parity transmitted code: [1001|1] * Received code indicates error [1101|1] * Received code does not indicate error [1111|1] *Good for random errors (single bit errors but not for burst errors (multiple consecutive errors) *Used with ASCII *
- 15. * Effectively detect 99.95 % errors. * Block of data (D) is combined with a frame check sequence (F) to compose a frame to be transmitted (T). * The Frame check sequence is developed by mathematically dividing the block of data by a predetermined divisor (P). * On the receiver side the transmitted frame (T) is divided by the divisor (P). If the remainder is zero then no error is detected. *
- 16. Example: Develop a (7,4) cyclic code from a transmitter where the data to be transmitted(D) = [1100] and divisor (P) =[1011]. 1100/1011 = 1110 <-[D]/[P] 1011 1110 1011 1010 1011 010 <-Remainder (Block Check Code) Transmitted(T) = [D R] = [1100010] *
- 17. Decoding in the receiver 1100010 /1011 = 1110 <-[T]/[P] 1011 1110 1011 1011 1011 00 <-Remainder *
- 18. * The Hamming distance is the number of bits that are different between allowed transmitted code words * d(code block, received block) * d(00000,00100) = 1 * d(00111,00100) = 2 * The greater the Hamming distance the more errors need to be corrected. *
- 19. * Example: Block code example * Let 0 be represented by 00. * Let 1 be represented by 11. * The code block is two bits long. * The number of bits that are different between each allowed code word is 2. Therefore the Hamming distance is 2. * If 01 or 10 is received at the receiver then a bit error occurred. * This code can detect one bit error per block but cannot correct a bit error *
- 20. * Example: Block code example * Let 0 be represented by 00000. * Let 1 be represented by 00111. * The code block is five bits long. * The number of bits that are different between each allowed code word is 3. Therefore the Hamming distance is 3. * If 00110, 00101, or 00011 is received at the receiver then a bit error occurred. * This code can detect up to three bit error per block and can correct one bit bit error *
- 21. * Hamming code correct single bit errors * Example: Consider D=[1001] the minimum number of parity bits is 3. (2n ≥ m+n+1 where m is the length of D and n is the smallest of parity bits that makes the relationship true) * Let P1 = (2,4,5), P2 = (4,5,6), P3 = (5,6,2) and use odd parity. P1 1 P2 0 0 1 P3 1 2 34 567 0 1 0 0 0 1 1 Transmitted *
- 22. * Detects and corrects bursts of errors * Utilizes Interleaving * Used in extensively CDs and Cell Phone Transmission 0 1 0 <- 1st Word 0 0 1 <- 2nd Word 0 1 1 <- 3rd Word *
- 23. *
- 24. * Example: TDMA Example * Cell phone A and cell phone B, A would be given a certain amount of time to transmit. * After that time B is transmitted and the process is repeated * (ABABABABAB……) *
- 25. * Example: CDMA Example of a computer network Endpoint 1 (computer) Let 0 equal 0110 Let 1 equal 1001 Endpoint 2 (computer) Let 0 equal 0011 Let 1 equal 1100 * If the system router transmits 01101001, both endpoints receive the information. However, endpoint 1 knows the router is communicating with it because the XNOR and sum of the data equals 4 or 0. 0110|1001 <- Transmitted 0110|1001 <- Stored Codeword 1111|1111 <- 4|4 *

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