convolution coding
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Transcript of convolution coding
Input sequence all ones will give encoded output as
Compare with all zero output sequence – Hamming distance is just 4
Catastrophic codes• Self loop with Input 1 but
output all zeros.• k – input bits not all
zeroes, but output all zeroes.
Decoding
• Symbol by symbol estimation - Max Aposteriori Probability (MAP) based Estimation. This is a Suboptimal procedure. The Probability of errors have been derived for various demodulation schemes based on distances in N- dimensional Euclidean space (Euclidean distances) for M - symbols.
• Maximum likelihood Sequence based Estimation procedure (MLSE). This is an optimal procedure. Received sequence consists of ‘mn’ bits. The ‘m’ branches, n code bits output per branch has 2^mn possible sequences. Need to select from a subset of 2^mk possible sequences for the Rate (k/n) code. Received sequence compared with this subset of sequence in the Trellis based on one of the two metrics
• Hamming distance (hard decision decoding)• Euclidean distance (Soft decision decoding)
Received sequence { 110110110010101100 }Trellis Path { 111 110 101 101 010 011 000 } and Info seq is { 11110 00 }
g1 = [1 0 1] , g2 = [1 1 1] , g3 = [ 1 1 1]
Encoder, STD, TFD, TF, Dfree? Is it catastrophic?
Path through the Trellis for 011011
Received CW sequence { 101001011110111} find the user sequence