Optimum symbol-by-symbol mean-square error channel coding
An (n,k) linear block code is used to convey k information digits, each having a numerical value attached, in such a way as to minimize the mean-square error of the individual information digits regardless of the other (k-1) positions. This criterion is used because it provides a graceful degradatio...
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| Vydané v: | IEEE transactions on information theory Ročník 25; číslo 4; s. 387 - 405 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
IEEE
01.07.1979
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | An (n,k) linear block code is used to convey k information digits, each having a numerical value attached, in such a way as to minimize the mean-square error of the individual information digits regardless of the other (k-1) positions. This criterion is used because it provides a graceful degradation in the coding performance when the channel temporarily becomes less reliable. Unambiguous encoding is employed, and the channel is assumed to obey a realistic additive property. An optimum pair of symbol encoding and decoding functions are derived, and it is shown that the optimum symbol encoding can be performed in a linear fashion. The related decoding role is the conditional mean estimator. Fourier transforms are central to the optimal design of both rules. The optimum symbol rules tire identical with the properly isolated parts of the optimum mean-square error rules when the code is used to carry the k Information digits considered as a single complete numerical entity, The same channel coding design is therefore optimum for a wide variety of Information configurations. Techniques for implementing the optimum symbol decoders are examined with special emphasis on memoryless channels where the storage requirements for the necessary weighting coefficients are drastically reduced. |
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| AbstractList | An(n,k)linear block code is used to conveykinformation digits, each having a numerical value attached, in such a way as to minimize the mean-square error of the individual information digits regardless of the other(k-1)positions. This criterion is used because it provides a graceful degradation in the coding performance when the channel temporarily becomes less reliable. Unambiguous encoding is employed, and the channel is assumed to obey a realistic additive property. An optimum pair of symbol encoding and decoding functions are derived, and it is shown that the optimum symbol encoding can be performed in a linear fashion. The related decoding role is the conditional mean estimator. Fourier transforms are central to the optimal design of both rules. The optimum symbol rules tire identical with the properly isolated parts of the optimum mean-square error rules when the code is used to carry the k Information digits considered as a single complete numerical entity, The same channel coding design is therefore optimum for a wide variety of Information configurations. Techniques for implementing the optimum symbol decoders are examined with special emphasis on memoryless channels where the storage requirements for the necessary weighting coefficients are drastically reduced. An (n,k) linear block code is used to convey k information digits, each having a numerical value attached, in such a way as to minimize the mean-square error of the individual information digits regardless of the other (k-1) positions. This criterion is used because it provides a graceful degradation in the coding performance when the channel temporarily becomes less reliable. Unambiguous encoding is employed, and the channel is assumed to obey a realistic additive property. An optimum pair of symbol encoding and decoding functions are derived, and it is shown that the optimum symbol encoding can be performed in a linear fashion. The related decoding role is the conditional mean estimator. Fourier transforms are central to the optimal design of both rules. The optimum symbol rules tire identical with the properly isolated parts of the optimum mean-square error rules when the code is used to carry the k Information digits considered as a single complete numerical entity, The same channel coding design is therefore optimum for a wide variety of Information configurations. Techniques for implementing the optimum symbol decoders are examined with special emphasis on memoryless channels where the storage requirements for the necessary weighting coefficients are drastically reduced. |
| Author | Redinbo, G. |
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| Cites_doi | 10.1109/TIT.1979.1056073 10.1109/TIT.1969.1054275 10.1007/978-3-642-66286-7 10.1016/S0019-9958(74)90451-3 10.1109/TIT.1972.1054869 10.1109/TIT.1967.1054054 10.1109/TIT.1974.1055221 10.1109/ICASSP.1978.1170448 10.1109/TIT.1976.1055617 10.1109/TIT.1973.1055035 10.1109/TIT.1970.1054489 10.1109/TIT.1971.1054615 10.1016/0097-3165(73)90079-4 10.1109/TIT.1976.1055634 10.1016/S0019-9958(78)90492-8 10.1016/S0019-9958(76)80012-5 |
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| References | ref13 fraleigh (ref21) 1976 ref23 ref15 ref14 ref20 ref11 clark (ref3) 1966 totty (ref4) 1969 ref17 ref16 apple (ref7) 1970 ref19 ref18 ref8 tsuruoka (ref10) 1976; 7 markel (ref1) 1976 ref9 ref6 ref5 gore (ref12) 1971; it 17 mitryayev (ref2) 1963; 8 rudin (ref22) 1967 |
| References_xml | – start-page: 468 year: 1966 ident: ref3 article-title: PCM transmission with minimum mean-square error publication-title: International Telemetry Conf Proc – year: 1967 ident: ref22 publication-title: Fourier Analysis on Groups – ident: ref18 doi: 10.1109/TIT.1979.1056073 – ident: ref5 doi: 10.1109/TIT.1969.1054275 – year: 1976 ident: ref21 publication-title: A First Course in Abstract Algebra – year: 1976 ident: ref1 publication-title: Linear Prediction of Speech doi: 10.1007/978-3-642-66286-7 – ident: ref20 doi: 10.1016/S0019-9958(74)90451-3 – year: 1970 ident: ref7 publication-title: Performance of PCM systems employing error correcting codes – ident: ref13 doi: 10.1109/TIT.1972.1054869 – ident: ref14 doi: 10.1109/TIT.1967.1054054 – ident: ref8 doi: 10.1109/TIT.1974.1055221 – ident: ref16 doi: 10.1109/ICASSP.1978.1170448 – ident: ref17 doi: 10.1109/TIT.1976.1055617 – volume: 7 start-page: 61 year: 1976 ident: ref10 article-title: Error correction by real number transformation of digital information publication-title: Systems Computers Controls – volume: 8 year: 1963 ident: ref2 article-title: Transmission of telemetry data by means of group codes publication-title: Radio Engineering and Electronics – ident: ref19 doi: 10.1109/TIT.1973.1055035 – ident: ref6 doi: 10.1109/TIT.1970.1054489 – volume: it 17 start-page: 214 year: 1971 ident: ref12 article-title: Cyclic codes with unequal-error-protection publication-title: IEEE Trans Inform Theory doi: 10.1109/TIT.1971.1054615 – ident: ref23 doi: 10.1016/0097-3165(73)90079-4 – ident: ref11 doi: 10.1109/TIT.1976.1055634 – ident: ref15 doi: 10.1016/S0019-9958(78)90492-8 – ident: ref9 doi: 10.1016/S0019-9958(76)80012-5 – start-page: 14-1 year: 1969 ident: ref4 article-title: Coding for mean-square error publication-title: Conf Rec IEEE Int Conf Communications |
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| Snippet | An (n,k) linear block code is used to convey k information digits, each having a numerical value attached, in such a way as to minimize the mean-square error... An(n,k)linear block code is used to conveykinformation digits, each having a numerical value attached, in such a way as to minimize the mean-square error of... |
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| StartPage | 387 |
| SubjectTerms | Additives Aggregates Block codes Decoding Fourier transforms Ions Mean square error methods Multiplexing Protection Symbols |
| Title | Optimum symbol-by-symbol mean-square error channel coding |
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