### Deterministic list codes for state-constrained arbitrarily varying channels

**Authors:**

Sarwate, Anand

Gastpar, Michael
**Technical Report Identifier:** EECS-2007-6
**January 8, 2007**

**Abstract:** The capacity for the discrete memoryless arbitrarily varying channel (AVC) with cost constraints on the jammer is studied using deterministic list codes under both the maximal and average probability of error criteria. For a cost function *l*(.) on the state set and constraint Lambda on the jammer, the achievable rates are upper bounded by the random coding capacity *Cr*(Lambda). For maximal error, the rate *R* = *Cr*(Lambda) - epsilon is achievable using list codes with list size *O*(epsilon^-1). For average error, an integer *L*_sym(Lambda), called the symmetrizability, is defined. It is shown that any rate below *Cr*(Lambda) is achievable under average error using list codes of list size *L* > *L*_sym. An example is given for a class of discrete additive AVCs.