154 Part 2 KU Lectrures 3 and 4

# 154 Part 2 KU Lectrures 3 and 4 - Performance of Block...

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Coding 1 1/1/2007 Information Theory and Coding © K. Sam Shanmugan, 2007 Performance of Block Codes

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Coding 2 1/1/2007 Information Theory and Coding © K. Sam Shanmugan, 2007 Message BER : With Error Detection e With error detection, the decoder computes the syndrome, if the syndrome is ≠0 the decoder requests a retransmission or discards the frame e There are several methods of retransmission o Stop and wait method : Transmit a block and wait for ACK/NACK; If NACK, retransmit the block; otherwise transmit the next block o Go back m blocks ( Continuously retransmit; Only NCAKs are sent and if a NACK is received, transmit the last m blocks, m = round trip delay in blocks) o Use sequence numbering and retransmit only the blocks for which a NACK is sent o ACKS/NACKS may be piggy bagged onto messages in the reverse direction
Coding 3 1/1/2007 Information Theory and Coding © K. Sam Shanmugan, 2007 Message BER : With Error Detection Stop and Wait Method e Compute the relationship between r b and r c and use it in the message BER computation ( derived later) o Stop and wait method yields very low throughput if the round trip delay 2Δ is large. In applications where the round trip delay is small compared to the transmission time for a block [Ex: LAN], this is a simple method to use Block 1 Block 2 Block 2 Block 3 Block 1 Block 2 Block 2 Block 3 ACK NAK ACK ACK ) P - 1 include Otherwies small; is error word of y probabilit the Assume ( efficiency sion transmis the is 2 ; 2 error block c c c b r n n r n n n k r r + + = Δ One way delay

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Coding 4 1/1/2007 Information Theory and Coding © K. Sam Shanmugan, 2007 1 2 3 4 5 6 7 3 4 5 6 7 8 1 2 3 4 5 6 7 3 4 1 2 3 4 5 6 7 3 4 5 6 NACK ACK Message BER with Error Detection Continuous Retransmission ( No Sequence numbering) TX Blocks ACK/NACK Sent ACK/NACK Received Time Go back 4 blocks and retransmit Rx sends NACKS for these blocks that will be retransmitted Variation: sequence numbering and retransmitting only those blocks for which NACK is received ( when the round trip delay is large) small is blocks ted retransmit of number the if c b r n k r
Coding 5 1/1/2007 Information Theory and Coding © K. Sam Shanmugan, 2007 Message Bit Error Probability with Forward Error Correction e Assumptions: o Probability of channel bit error o Minimum distance = d min;; t= (d min -1)/2 Code words are incorrectly decoded when more than t errors per code block occurs; o When a code word is in correctly decoded, the number of bit errors per code block is j , and these errors can be assumed to be are uniformly distributed across the n bits in the code word o When q c <<1, the most likely number of uncorrected errors per block will be t+1 o The number of message bits that are in error = j( k/n) Hence the message bit error probability is given by [ ] t t q q j n P j n c j c n t j c we = - - + = none but , upto errors all correct can code the if holds ) 1 ( 1 = = b

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## This note was uploaded on 04/14/2008 for the course ECE 154C taught by Professor Shanmu during the Spring '07 term at UCSD.

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154 Part 2 KU Lectrures 3 and 4 - Performance of Block...

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