Concatenated Codes

Concatenated Codes

§ Two levels of coding
   Achieves performance of very long code rates while maintaining
   shorter decoding complexity
§  Overall rate is product of individual code rates
§Codeword error occurs if both codes fail.
§Error probability is found by first evaluating the error probability of
  “inner” decoder and then evaluating the error probability of  “outer”
   decoder.
§ Interleaving is always used with concatenated coding
Block Diagram of Concatenated Coding Systems




Practical Application : Coding for CD

•Each channel is sampled at 44000 samples/second
•Each sample is quantized with 16 bits
Uses a concatenated RS code
§ Both codes constructed over GF(256) (8-bits/symbol)
§ Outer code is a (28,24) shortened RS code
§ Inner code is a (32,28) extended RS code
§In between coders is a (28,4) cross-interleaver
§ Overall code rate is r = 0.75
§
Most commercial CD players don’t exploit full power of the error correction coder 
Practical Application: Galileo Deep Space Probe
§  Uses concatenated coding
§ Inner code rate is ½, constraint length 7 convolutinal encoder
§Outer Code (255,223) RS code over GF(256) – corrects any burst errors from convolutional codes
§ Overall Code Rate is r= 0.437
§ A block interleaver held 2RS Code words
§ Deep space channel is severely energy limited but not bandwidth limited
 

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