Graduate Thesis Or Dissertation

 

Balanced codes Public Deposited

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  • Balanced codes, in which each codeword contains equally many 1's and 0's, are useful in such applications as in optical transmission and optical recording. When balanced codes are used, the same number of 1's and 0's pass through the channel after the transmission of every word, so the channel is in a dc-null state. Optical channels require this property because they employ AC-coupled devices. Line codes, in which codewords may not be balanced, are also used as dc-free codes in such channels. In this thesis we present the research that leads to the following results: 1- Balanced codes These have higher information rate than existing codes yet maintain similar encoding and decoding complexities. 2- Error-correcting balanced codes In many cases, these give higher information rates and more efficient encoding and decoding algorithms than the best-known equivalent codes. 3- DC-Free coset codes A new technique to design dc-free coset codes was developed. These codes have better properties than existing ones. 4- Generalization of balanced codes -- Balanced codes are generalized in three ways among which the first is the most significant: a) Balanced codes with low dc level These codes are designed based on the combined techniques used in (1) and (3) above. A lower dc-level and higher transitions density is achieved at the cost of one extra check bit. These codes are much more attractive, to optical transmission, than the bare-bone balanced codes. b) Non-Binary Balanced Codes Balanced codes over a non-binary alphabet. c) Semi-Balanced Codes -- Codes in which the number of 1's and 0's in every code word differs by at most a certain value. 5- t-EC/AUED coset codes These are t error correcting/all unidirectional error detecting codes. Again the technique in (3) above is used to design t-EC/AUED coset codes. These codes obtain higher information rate than the best-known equivalent codes and yet maintain the same encoding/decoding complexity.
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