Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes
Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relativel...
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| Abstract | Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity. |
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| AbstractList | Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity. Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity. |
| Author | Merhav, Neri Tamir (Averbuch), Ran |
| AuthorAffiliation | The Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion—Israel Institute of Technology, Technion City, Haifa 3200003, Israel; merhav@ee.technion.ac.il |
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| Cites_doi | 10.1109/TIT.2002.800480 10.1109/TIT.2019.2917175 10.1017/CBO9780511921889 10.1109/TIT.1982.1056514 10.1109/TIT.2020.2995136 10.1109/TIT.2017.2689787 10.1109/TIT.1982.1056524 10.1109/TIT.2018.2834503 10.1109/TIT.1981.1056281 10.1109/TIT.2015.2405537 10.1109/TIT.2014.2331952 10.1109/TIT.2019.2942624 10.1109/TIT.2012.2201346 10.1109/TIT.2019.2902387 10.1109/TIT.1980.1056166 10.1109/TIT.2019.2963392 10.3390/e19080389 10.1109/18.340465 10.1109/TIT.2011.2162178 10.1561/0100000052 10.1109/TIT.1973.1055037 10.1109/ALLERTON.2017.8262727 |
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| Keywords | typical random code variable-rate coding excess-rate exponent error exponent Slepian–Wolf coding |
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| References | Merhav (ref_5) 2020; 66 Ahlswede (ref_10) 1982; 28 Merhav (ref_4) 2019; 65 Merhav (ref_1) 2018; 64 Merhav (ref_7) 2020; 66 (ref_14) 1982; 28 (ref_11) 1981; 27 Kelly (ref_17) 2012; 58 ref_12 Nazari (ref_3) 2014; 60 Slepian (ref_8) 1973; 19 ref_22 Merhav (ref_6) 2020; 66 ref_21 Scarlett (ref_23) 2019; 65 Barg (ref_2) 2003; 48 ref_19 ref_9 Merhav (ref_20) 2017; 63 Oohama (ref_18) 1994; 40 (ref_15) 1980; 26 Weinberger (ref_13) 2015; 61 Kelly (ref_16) 2011; 57 Merhav (ref_24) 2009; 6 |
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| Title | Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes |
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