part_4_error_handling2

part_4_error_handling2 - CIS 6930 Powerline Communications...

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CIS 6930 Powerline Communications Richard Newman Spring 2010
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Error Handling - Outline Analysis Forward Error Correction Copy codes Block codes Convolutional codes Scrambling Concatenated codes Turbo-codes Low Density Parity Check (LDPC) Backward Error Correction (BEC) Stop-and-Wait ARQ Conclusions
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Analysis Measures Nature of errors detected/corrected Efficiency Efficiency: U = Uf Up Ue Uf = framing efficiency = D/(D+H) where D = Data length and H = Header length Up = protocol utilization Depends on protocol, propagation delay, transmission time Ue = error caused utilization efficiency = 1-P where P = frame error rate
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Error Correction Strategies Forward Error Correction Include sufficient redundancy in transmitted units that errors can be corrected Simplifies sender protocol – used in PHY Backward Error Correction Include sufficient redundancy in transmitted units that errors can be detected Retransmit damaged units More efficient – used in MAC and above Limitations Hamming Distance of code limits capabilities Always possible to “fool” receiver
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General ECC Considerations Systematic vs. non-systematic Systematic = data bits appear in coded stream Non-systematic = no data bits identifiable Hamming Distance H(x,y) = number of bits where x and y differ Code C = {x1, x2, . .., xN} set of valid codewords d = H(C) = min{H(x,y) | x and y are distinct codewords in C} Maximum detection ability = d-1 Maximum correction ability = (d-1)/2
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Forward Error Correction Block vs. continuous Block = set number of information symbols encoded into set number of code symbols Internal fragmentation Need for delimitation Continuous = stream of information symbols encoded into stream of code symbols Memory/constraint length – must “fill the pipeline” Linearity Sum of two code words is a code word Concatenation Combine two codes (inner and outer) to increase correction capabilities
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Forward Error Correction Efficiency = code rate Rate = k/n for (n,k) code k = “information bits” n = total bits t = n-k = redundant bits With continuous codes, need to account for “tail” - the number of bits in the memory
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Block Codes Copy codes LRC Hamming codes BCH Reed-Solomon LDPC
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Block Codes Copy Codes Simplest code Copy data bits r times to encode Use received copies to “vote” for input value Can survive a burst error if scrambled LRC – Longitudinal Redundancy Check Information bits arranged in p-1 by q-1 matrix Each row has parity bit at the end Each column has parity bit at the bottom n = pq, k = (p-1)(q-1), r = p+q-1 Detects single bit errors
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LRC Example 1 0 1 1 0 1 1 0 1 0 1 1 = information bits 1 0 1 1 _ 1 0 1 1 1 0 1 1 0 _ -> 0 1 1 0 0 1 0 1 1 _ 1 0 1 1 1 _ _ _ _ _ 0 1 1 0 0 <- LRC ^ VRC 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 = code word
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part_4_error_handling2 - CIS 6930 Powerline Communications...

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