TY - GEN
T1 - Fundamental limits of universal variable-to-fixed length coding of parametric sources
AU - Iri, Nematollah
AU - Kosut, Oliver
N1 - Funding Information:
This research was funded in part by the NSF under grant No. CCF-1422358.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - Universal variable-to-fixed (V-F) length coding of d-dimensional exponential family of distributions is considered. An achievable scheme is proposed, which consists of a dictionary to parse the source output stream. The previously-introduced notion of quantized type is employed for the dictionary construction. The quantized type class of a sequence is based on partitioning the space of minimal sufficient statistics into cuboids. The proposed dictionary consists of sequences in the boundaries of transition from low to high quantized type class size. Asymptotics of the -coding rate of the proposed coding scheme for large enough dictionaries is derived. In particular, we show that the third-order coding rate of the proposed scheme is H d/2 log log M/log M, where H is the entropy of the source and M is the dictionary size. We further provide a converse, showing that this rate is optimal up to the third-order term.
AB - Universal variable-to-fixed (V-F) length coding of d-dimensional exponential family of distributions is considered. An achievable scheme is proposed, which consists of a dictionary to parse the source output stream. The previously-introduced notion of quantized type is employed for the dictionary construction. The quantized type class of a sequence is based on partitioning the space of minimal sufficient statistics into cuboids. The proposed dictionary consists of sequences in the boundaries of transition from low to high quantized type class size. Asymptotics of the -coding rate of the proposed coding scheme for large enough dictionaries is derived. In particular, we show that the third-order coding rate of the proposed scheme is H d/2 log log M/log M, where H is the entropy of the source and M is the dictionary size. We further provide a converse, showing that this rate is optimal up to the third-order term.
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U2 - 10.1109/ALLERTON.2017.8262715
DO - 10.1109/ALLERTON.2017.8262715
M3 - Conference contribution
AN - SCOPUS:85047966221
T3 - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
SP - 31
EP - 37
BT - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
Y2 - 3 October 2017 through 6 October 2017
ER -