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In this paper, we make use of channel symmetry properties to determine the capacity region of three types of two-way networks: 1) two-user memoryless two-way channels (TWCs); 2) two-user TWCs with memory; and 3) three-user multiaccess/degraded broadcast (MA/DB) TWCs. For each network, symmetry conditions under which a Shannon-type random coding inner bound (under independent non-adaptive inputs) is tight are given. For two-user memoryless TWCs, prior results are substantially generalized by viewing a TWC as two interacting state-dependent one-way channels. The capacity of symmetric TWCs with memory, whose outputs are functions of the inputs and independent stationary and ergodic noise processes, is also obtained. Moreover, various channel symmetry properties under which the Shannon-type inner bound is tight are identified for three-user MA/DB TWCs. The results not only enlarge the class of symmetric TWCs whose capacity region can be exactly determined but also imply that interactive adaptive coding, not improving capacity, is unnecessary for such channels. [ABSTRACT FROM AUTHOR]

Permutation and multipermutation codes in the Ulam metric have been suggested for use in non-volatile memory storage systems such as flash memory devices. In this paper we introduce a new method to calculate permutation ball sizes in the Ulam metric using Young Tableaux and prove the non-existence of non-trivial perfect permutation codes in the Ulam metric. We then extend the study to multipermutations, providing upper and lower bounds on multipermutation Ulam ball sizes and resulting upper and lower bounds on the maximal size of multipermutation codes in the Ulam metric. [ABSTRACT FROM AUTHOR]