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Decoding Cosets of First-Order Reed-Muller Codes


Green, Richard Rutherford (1969) Decoding Cosets of First-Order Reed-Muller Codes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wfs6-ej43.


Proper encoding of transmitted information can improve the performance of a communication system. To recover the information at the receiver it is necessary to decode the received signal. For many codes the complexity and slowness of the decoder is so severe that the code is not feasible for practical use. This thesis considers the decoding problem for one such class of codes, the comma-free codes related to the first-order Reed-Muller codes.

A factorization of the code matrix is found which leads to a simple, fast, minimum memory, decoder. The decoder is modular and only n modules are needed to decode a code of length 2n. The relevant factorization is extended to any code defined by a sequence of Kronecker products.

The problem of monitoring the correct synchronization position is also considered. A general answer seems to depend upon more detailed knowledge of the structure of comma-free codes. However, a technique is presented which gives useful results in many specific cases.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Applied Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Martel, Hardy Cross
Thesis Committee:
  • Unknown, Unknown
Defense Date:13 May 1969
Funding AgencyGrant Number
Tektronix Foundation FellowshipUNSPECIFIED
Record Number:CaltechTHESIS:03182016-151447208
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9626
Deposited On:21 Mar 2016 20:25
Last Modified:29 Apr 2024 21:09

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