TY - GEN
T1 - Graph-based Encoders and their Achievable Rates for Channels with Feedback
AU - Sabag, Oron
AU - Huleihel, Bashar
AU - Permuter, Haim H.
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/15
Y1 - 2018/8/15
N2 - This paper investigates graph-based encoders for the unifilar finite-state channel (FSC) with feedback. A recent paper introduced the Q-graph as a tool for the recursive quantization of channel outputs on a directed graph. The Q- graph approach yielded single-letter lower and upper bounds on the feedback capacity of unifilar FSCs, termed here Q-LB and Q-UB, respectively. The current paper provides two computable optimization problems for the Q-LB and the Q-UB. The first, for the Q-LB, aims to find the graph-based encoder with the highest achievable rate. Specifically, for a structured cooperation between the encoder and the decoder, that is given by a particular Q-graph, the optimization problem maximizes the Q-LB over all input distributions. The resultant graph-based encoder from the optimization problem has a corresponding posterior matching scheme that achieves the Q-LB. The second optimization problem provides a formulation of the Q-UB as a convex optimization problem. Numerical results of the Q-LB and the Q-UB are presented for the Ising channel and a simplified version of a fading channel. The numerical results are then translated into analytical expressions for graph-based encoders and their achievable rates.
AB - This paper investigates graph-based encoders for the unifilar finite-state channel (FSC) with feedback. A recent paper introduced the Q-graph as a tool for the recursive quantization of channel outputs on a directed graph. The Q- graph approach yielded single-letter lower and upper bounds on the feedback capacity of unifilar FSCs, termed here Q-LB and Q-UB, respectively. The current paper provides two computable optimization problems for the Q-LB and the Q-UB. The first, for the Q-LB, aims to find the graph-based encoder with the highest achievable rate. Specifically, for a structured cooperation between the encoder and the decoder, that is given by a particular Q-graph, the optimization problem maximizes the Q-LB over all input distributions. The resultant graph-based encoder from the optimization problem has a corresponding posterior matching scheme that achieves the Q-LB. The second optimization problem provides a formulation of the Q-UB as a convex optimization problem. Numerical results of the Q-LB and the Q-UB are presented for the Ising channel and a simplified version of a fading channel. The numerical results are then translated into analytical expressions for graph-based encoders and their achievable rates.
UR - http://www.scopus.com/inward/record.url?scp=85052434146&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2018.8437602
DO - 10.1109/ISIT.2018.8437602
M3 - Conference contribution
AN - SCOPUS:85052434146
SN - 9781538647806
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1121
EP - 1125
BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018
PB - Institute of Electrical and Electronics Engineers
T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018
Y2 - 17 June 2018 through 22 June 2018
ER -