Stationary queue-size distribution for variable complexity sequential decoders with large timeout

Abstract

Fano decoders are convolutional channel decoders having variable decoding complexity in changing channel conditions. Buffers are usually required by the Fano decoder to store data blocks due to non-deterministic decoding delays. In practice, however, a predetermined limit is typically set for the decoding time so that the Fano decoder is not allowed to devote more time than the limit in decoding any single data block. We assume that data blocks arrive to the decoder with an infinite buffer according to a Bernoulli process, and that the decoding time of the Fano decoder follows the Pareto distribution parameterized by the signal-to-noise ratio (SNR) of the channel. If the channel has a smaller SNR, it typically takes longer time to decode a nosier data block. It is known in theory that if the SNR is lower than a certain threshold, the variance of the decoding time can go to infinity. In practice, if the decoding time of a block exceeds this limit, the block is removed from the buffer, resulting in a failure in decoding. In this paper, we present a method to obtain the stationary queue size distribution numerically for large decoding time limits.