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 ε-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 ε. Then we show that the ε-achievability of variable-length codes is essentially equivalent to the ε-achievability of fixed-length codes for general sources. Moreover by using above results, we show the condition of ε-achievability for some restricted sources given ε.

Moving-picture transmission through narrow band and high bit error rate communication channels, such as a mobile communication channel, requires improved compression rate and enhanced error resilience. Variable-length codes are one of the essential techniques of compressing digital video information. This technique is used in various video coding schemes although a bit error in the channel impairs the synchronization of variable-length codewords, resulting in propagation of the error. With a hybrid video coding method in particular, which combines motion-compensation and transform coding, once an error is detected in the coded data, subsequent data cannot be decoded. Consequently, even an error-free portion of any data received must be discarded. To minimize the influence of an error in a channel on coded video data, this paper proposes a new video coding syntax which makes the best use of the self synchronizing characteristic of variable-length Huffman codes. Owing to the Huffman code's characteristic, the proposed coding syntax enables a decoder to decode the data portion that cannot be decoded, due to an error, by the conventional syntax without adding any redundancy. Computer simulation has verified the effectiveness of this proposed syntax in video coding with a very low bitrate and erroneous communication channel.