Lecture19-FA14.pdf - Digital Communications Lecture 22 Chapter 6 Channel Coding I Structured Sequences Linear Block Codes Error Detecting and Correcting

Lecture19-FA14.pdf - Digital Communications Lecture 22...

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Digital Communications Lecture # 22 Chapter 6: Channel Coding I Structured Sequences Linear Block Codes Error Detecting and Correcting Capability Cyclic Codes Block Codes
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Channel Coding Definition Channel coding refers to the class of signal transformation designed to improve communication performance by enabling the transmitted signals to better withstand effects of various channel impairments, such as noise, interference and fading.
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Channel Coding: Part 1
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6.2 Types of Error control Error detection and retransmission Forward error correction Terminal Connectivity Simplex Half duplex Full duplex Figure 6.6: Terminal connectivity classifications (a) Simplex (b) Half-duplex (c) Full-duplex
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Automatic Repeat Request ARQ vs. FEC ARQ is much simpler than FEC and need no redundancy. ARQ is sometimes not possible if A reverse channel is not available or the delay with ARQ would be excessive The retransmission strategy is not conveniently implemented (Video broadcasting) The expected number of errors, without corrections, would require excessive retransmissions
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Figure 6.7: Automatic Repeat Request (ARQ) (a) Stop and wait ARQ (b) Continuous ARQ with pullback (c) Continuous ARQ with selective repeat
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6.3 Structured Sequences Block codes Convolutional codes Turbo codes In case of block codes, encoder transforms each k- bit data block into a larger block of n- bits called code bits or or channel symbol The (n-k)- bits added to each data block are called redundant bits , parity bits or check bits They carry no new information Ratio of redundant bits to data bits: (n-k)/k is called redundancy of code Ratio of data bits to total bits, k/n is called code rate 6.3.2 Code Rate and Redundancy
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6.3.3 Parity-Check Codes Single-parity-Check Code Parity check codes use linear sums of the information bits, called parity symbols or parity bits, for error detection or correction. Even Parity Example:
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Rectangular Code Also called a product code, can be thought of as a parallel code structure. The rate of the code k/n is ( 1)( 1) MN k n M N = + + Figure 6.8: Parity checks for parallel structure
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6.3.4 Why Use Error-Correction Coding Figure 6.9:Comparison of typical coded versus uncoded error performance Trade-Off 1: Error Performance vs. Bandwidth (A to C rather than B) Trade-Off 2: Power versus Bandwidth (D to E) Trade-Off 3: Data Rate versus Bandwidth (D to F and than to E) Trade-Off 4: Capacity versus Bandwidth (like in CDMA)
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6.4 Linear block Codes 6.4.1 Vector Spaces The set of all binary n-tuples is called a vector space over the binary field of 0 and 1 Addition Multiplication 6.4.2 Vector Subspaces A subset S of the vector space is called a subspace if The all-zeros vector is in S The sum of any two vectors in S is also in S ( Closure property./Linear property) e.g. { 0000 0101 1010 1111 } (the code will be linear only if condition 2 satisfied) 0 1 1 1 0 1 1 1 0 0 0 0 = = = = 1 1 1 0 0 1 0 1 0 0 0 0 = = = =
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The subset chosen for the code should include as many as elements to reduce the redundancy but they should be as apart as possible to maintain good error performances Figure 6.10: Linear block-code structure
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6.4.3 A (6.3) Linear Block Code Examples
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