Monotonicity in Sum Rate Maximization for Finite Blocklength Interference Channel

This paper investigates the sum rate maximization problem of finite blocklength code (FBC) rate in an interference channel (IC) with strict blocklength constraints. Sum rate maximization using classical first-order approximation can be globally solved by the mixed monotonic programming, which explores its hidden monotonicity. However, under blocklength constraints, more accurate second-order rate approximation is required. To do this, we adopt a shell codebook with latency reducing treating-interference-as-noise decoder, which has higher second- order FBC rates than that using conventional Gaussian codebook. However, our second-order normal-approximation FBC rate suffers from a backoff term called shell dispersion, which not only complicates the rate formula but also makes desired mixed monotonicity difficult to prove. In a general K-user IC, we modify the original shell dispersion term to enable the desired mixed monotonicity to have a slightly lower FBC rate. Two mixed- monotonic functions provided for proposed second-order FBC rates, correspond to two different hidden monotonicities in the rate formulas respectively. Finally, in two-user case K = 2, we can prove the desired mixed monotonicity for FBC sum rate which uses the original shell dispersion term. Simulation results verify that our second-order FBC sum rate maximization can be globally solved and provide a 59 percent rate prediction improvement over the first-order one, with nearly same iterations.