Truncated tree codes for streaming data: Infinite-memory reliability using finite memory

We present a finite-memory code construction for streaming data systems. In our model a sequence of independent and identically distributed messages arrives at the transmitter according to a deterministic arrival process. Each message must be estimated by the decoder after a fixed delay. Prior work on this model relied on the use of semi-infinite tree-codes with growing encoder and decoder memory. We show that the same reliability that was attained in those constructions, which was based on an error-exponent analysis, can also be obtained by a finite-memory construction. In our construction both encoder and decoder have finite memory, although the instantaneous constraint length of the code (and of the decoding process) is time-varying in a periodic manner. The closer to capacity one wants to operate, the greater the memory our construction requires to match the infinite-memory results. For a given rate and delay it is straightforward to solve for the memory required to attain the same reliability as the earlier strategies.