Tighter Bounds on the Capacity of Finite-State Channels Via Markov Set-Chains

Abstract

Abstract-The theory of Markov set-chains is applied to derive upper and lower bounds on the capacity of finite-state channels that are tighter than the classic bounds by Gallager. The new bounds coincide and yield single-letter capacity characterizations for a class of channels with the state process known at the receiver, including channels whose long-term marginal state distribution is independent of the input process. Analogous results are established for finite-state multiple access channels.

Capacity Analysis of Discrete Energy Harvesting Channels

“…It turns out that in many cases we are interested in, W becomes a finite state channel (FSC). The capacity of a general FSC is studied in [18], [24], both of which give two series as the capacity upper and lower bounds, in terms of the mutual information between the input and output for each block size N . When the FSC is indecomposable 5 , the upper and lower bounds both converge to the capacity.…”

“…When the FSC is indecomposable 5 , the upper and lower bounds both converge to the capacity. However, these bounds are not very useful for us: i) since C is less than or equal to C, the lower bounds are genuine, but the upper bounds are not meaningful; ii) the computational complexity of such bounds is exponential in N ; iii) the bounds in [18] are too loose for small N and their convergence is slow (see [24]); iv) the bounds in [24] are supposed to be tighter, but the computation is not easy for a general N .…”

“…In other words, conditioned on (X n , S n ), the pair (Y n , S n+1 ) is independent of all prior inputs, outputs, and states 24 . If we define the new output Y n of the channel as the output-state pair (Y n−1 , S n ) with P xn y n , y n+1 = P xn ( (y n−1 , s n ), (y n , s n+1 ) ) p(y n s n+1 | x n s n ),…”

“…23 As in the main text, the state index is increased by 1 compared to the original definition in [18]. 24 Actually from (43), (Yn, Sn+1) is also conditionally independent of the future inputs, i.e., the channel is causal. It is also implicitly assumed when computing the block conditional probability in [18] (equation (4.6.1)).…”

Capacity of Diffusion based Molecular Communication Networks over LTI-Poisson Channels

“…MAC MLN in [33]); that is, we set or reset the channel using k consecutive inputs. Other related work which considers networks with more general models of memory than LTI [31], [33], [35], [47] take on a different approach. That is, the outer bound derivation begins with an n-letter expression which often resembles the capacity region of the memoryless case.…”