|| A Discretization Approach to Compute–Forward
||Adriano Pastore, CTTC, Spain; Sung Hoon Lim, Hallym University, Korea (South); Chen Feng, University of British Columbia, Canada; Bobak Nazer, Boston University, United States; Michael Gastpar, EPFL, Switzerland|
||D5-S4-T1: Multiple Access Capacity II
||Friday, 16 July, 23:00 - 23:20
||Friday, 16 July, 23:20 - 23:40
We present a novel unified framework of compute-forward achievable rate regions for simultaneous decoding of multiple linear codeword combinations. This framework covers a wide class of discrete and continuous-input channels, and computation over finite fields, integers, and reals. The resulting rate regions recover several well-known achievability results, and in some cases extend them. The framework is built upon a recently established achievable rate region based on linear codes and joint typicality decoding. The latter is extended from finite fields to computation over the integers and, via a discretization approach, to computation over the reals with integer coefficients and continuous inputs. Evaluating the latter with Gaussian distributions, we obtain a closed-form rate region which generalizes the classic compute-forward rates originally derived by means of lattice codes by Nazer and Gastpar.