TY - JOUR
T1 - A note on the ∈-overflow probability of lossless codes
AU - Nomura, Ryo
AU - Matsushima, Toshiyasu
AU - Hirasawa, Shigeichi
PY - 2007/12
Y1 - 2007/12
N2 - In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the e-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ∈. Then we show that the e-achievability of variable-length codes is essentially equivalent to the e-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of e-achievability for some restricted sources given ∈.
AB - In this letter, we generalize the achievability of variable-length coding from two viewpoints. One is the definition of an overflow probability, and the other is the definition of an achievability. We define the overflow probability as the probability of codeword length, not per symbol, is larger than ηn and we introduce the e-achievability of variable-length codes that implies an existence of a code for the source under the condition that the overflow probability is smaller than or equal to ∈. Then we show that the e-achievability of variable-length codes is essentially equivalent to the e-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of e-achievability for some restricted sources given ∈.
KW - Error probability
KW - Fixed-length codes
KW - Overflow probability
KW - Variable-length codes
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U2 - 10.1093/ietfec/e90-a.12.2965
DO - 10.1093/ietfec/e90-a.12.2965
M3 - Article
AN - SCOPUS:68249161028
VL - E90-A
SP - 2965
EP - 2970
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 12
ER -