Low Complexity Maximum-Likelihood Decoding of Cyclic Codes

Tech ID: 31759 / UC Case 2020-186-0


UCLA researchers in the Department of Electrical and Computer Engineering have developed a low complexity decoding algorithm of cyclic codes with better performance and lower latency than current approaches.


Cyclic codes are error-correcting codes (ECC) used in many systems including: CD-ROMs, cellular communication, data communication technologies and flash memory. As technology nodes shrink and memory complexities increase, bit error rates continue to grow. Thus, there is a growing need for low complexity decoding algorithms to retrieve original data after error corrections.


UCLA researchers have developed a maximum likelihood (ML) decoding algorithm of cyclic codes with a reduced-complexity approach. This new approach possesses both better performance and lower latency for high-rate cyclic codes vs common bounded distance hard decoding approaches. The proposed decoding algorithm also supports complete hard decoding of Bose-Chaudhuri-Hocquenghem (BCH) codes, as opposed to the bounded distance decoding of the Berlekamp-Massey and Euclidean algorithms. This ML soft decoding algorithm, when used in high-rate BCH examples, has complexity similar to that of the Viterbi decoder used in communication devices today.


  • Flash Memory 
  • Data Communications 
  • Wireless Communications 
  • CD-ROMs 
  • ADSL/VDSL modem


  • Better performance and lower latency for the decoding of high-rate cyclic codes 
  • Supports complete hard decoding of BCH codes 
  • Complexity similar to Viterbi decoders used in communication devices

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Patent Status

Patent Pending


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Other Information


Maximum likelihood (ML) decoding, cyclic codes, error-correcting codes, hard and soft decoding algorithms, Bose-Chaudhuri-Hocquenghem (BCH) codes

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