Efficient algorithms for discrete universal denoising for channels with memory

Abstract

The paper is focused on the problem of discrete universal denoising: one estimates the input sequence to a discrete channel based on the observation of the entire output signal, and without assuming any particular knowledge on the statistical properties of the input sequence. A 2k + 1 sliding window denoiser (DUDE) has recently been introduced, and its asymptotic optimality was proven in the case of memoryless channels and additive channels with memory. However, DUDE is computationally infeasible for large values of its context parameter k. The purpose of this paper is to further investigate DUDE in the case of channels with memory. First, for the important family of binary additive channels, we propose H-DUDE, a computationally feasible implementation of DUDE. It modifies the DUDE algorithm to exploit the property of the block transition probability matrix to be diagonalized by the Hadamard transform. H-DUDE accommodates large values of k, and we demonstrate this for the particular case of the finite-memory contagion channel. Second, we apply DUDE for a non-additive channel model that was previously used in the design of stack filters to show its favorable performance