Simulation-Based Computation of Information Rates for Channels With Memory

Abstract

Abstract-The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/channel trellis. This method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite-state approximations. Further upper and lower bounds can be computed by reduced-state methods.

Optimizing Information Rate Bounds for Channels with Memory

“…Practical examples of channels with memory include the correlated time-varying flat-fading channel (FFC) in wireless communication systems [1] and the partial response channel in magnetic and optical recording, as well as in communications over band-limited channels with inter-symbol interference (ISI) [2]. Although the information rate of such channels is generally formulated [3], the direct computation of the information rate has remained an open problem [1], [3].…”

“…Alternative strategies have been proposed in the literature for efficient stochastic and numerical computation of the information rate of finite-state machine channels (FSMCs) [3]- [6]. These techniques work efficiently only for finite-state channels with not too many states and so it is natural to try to come up with efficiently (stochastically) computable upper and lower bounds on the information rate.…”

“…These techniques work efficiently only for finite-state channels with not too many states and so it is natural to try to come up with efficiently (stochastically) computable upper and lower bounds on the information rate. Such upper and lower bounds were proposed in [3], [7] and were based on the introduction of an auxiliary channel. The lower bound in [3], [7] happens to be a special case of the generalized mutual information (GMI) lower bound for mismatched decoding [8].…”

“…Such upper and lower bounds were proposed in [3], [7] and were based on the introduction of an auxiliary channel. The lower bound in [3], [7] happens to be a special case of the generalized mutual information (GMI) lower bound for mismatched decoding [8]. The bound signifies achievable information rates when the receiver is equipped with the maximum likelihood (ML) decoding algorithm matched to the auxiliary channel model and hence, usually mismatched to the original channel (over which the actual communication takes place).…”

“…The main contribution of this paper is to optimize the parameters of the auxiliary FSMC model in order to tighten information rate bounds introduced in [3], [7]. In our approach we fix the number of FSMC states and optimize other FSMC parameters, i.e.…”