Interpolation by convolutional codes, overload distortion, and the erasure channel

This paper investigates how closely randomly generated binary source sequences can be matched by convolutional code codewords. What distinguishes it from prior work is that a randomly chosen subsequence with density /spl lambda/ is to be matched as closely as possible. The so-called marked bits of the subsequence could indicate overload quantization points for a source sample generated from the tails of a probability distribution. They might also indicate bits where the initial estimate is considered reliable, as might happen in iterated decoding. The capacity of a convolutional code to interpolate the marked subsequence might be viewed as a measure of its ability to handle overload distortion. We analyze this capacity using a Markov chain whose states are sets of subsets of trellis vertices of the convolutional code. We investigate the effect of memory on the probability of perfect interpolation and calculate the residual rate on the unmarked bits of the binary source sequence. We relate our interpolation methodology to sequence-based methods of quantization and use it to analyze the performance of convolutional codes on the pure erasure channel.