Timeliness in Lossless Block Coding

We examine lossless data compression from an average delay perspective. An encoder receives input symbols one per unit time from an i.i.d. source and submits binary codewords to a FIFO buffer that transmits bits at a fixed rate to a receiver/decoder. Each input symbol at the encoder is viewed as a status update by the source and the system performance is characterized by the status update age, defined as the number of time units (symbols) the decoder output lags behind the encoder input. An upper bound on the average status age is derived from the exponential bound on the probability of error in streaming source coding with delay. Apart from the influence of the error exponent that describes the convergence of the error, this upper bound also scales with the constant multiplier term in the error probability. However, the error exponent does not lead to an accurate description of the status age for small delay and small blocklength. An age optimal block coding scheme is proposed based on an approximation of the average age by converting the streaming source coding system into a D/G/1 queue. We compare this scheme to the error exponent optimal coding scheme which uses the method of types. We show that maximizing the error exponent is not equivalent to minimizing the average status age.