On hierarchical joint source-channel coding with degraded side information
We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the o...
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| Published in: | IEEE transactions on information theory Vol. 52; no. 3; pp. 886 - 903 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York, NY
IEEE
01.03.2006
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and the channel statistics |
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| AbstractList | We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and the channel statistics. We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and t- - he channel statistics We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and the channel statistics. [PUBLICATION ABSTRACT] We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and the channel statistics |
| Author | Merhav, N. Steinberg, Y. |
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| Keywords | Performance evaluation Block code joint source-channel coding Multistage method Source coding successive refinement Necessary and sufficient condition Refinement method Two channel system Lossy medium Joint source channel coding side information (SI) Implementation Markov chain Memoryless channel systematic coding Wyner-Ziv problem Wyner Ziv problem Hierarchical coding Memoryless source |
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| SubjectTerms | Applied sciences Channel coding Channels Coding Coding, codes Data processing Decoders Decoding Degradation Descriptions Distortion measurement Encoders Exact sciences and technology Feedback Hierarchical coding Information technology Information, signal and communications theory joint source-channel coding Markov analysis Memoryless systems Optimization Output feedback Performance loss side information (SI) Signal and communications theory Source coding Statistical distributions successive refinement Sufficient conditions systematic coding Telecommunications and information theory Theorems Wyner-Ziv problem |
| Title | On hierarchical joint source-channel coding with degraded side information |
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