Information Capacity of BSC and BEC Permutation Channels

In this paper, we describe and study the permutation channel model, which constitutes a discrete memoryless channel (DMC) followed by a random permutation block that reorders the output codeword of the DMC. This model naturally emerges in the context of communication networks, and coding theoretic aspects of such channels have been widely studied. In contrast to the bulk of this literature, we analyze the information theoretic aspects of the model by defining an appropriate notion of permutation channel capacity. We consider two special cases of the permutation channel model: the binary symmetric channel (BSC) and the binary erasure channel (BEC). We establish the permutation channel capacity of the BSC, and prove bounds on the permutation channel capacity of the BEC. Somewhat surprisingly, our results illustrate that permutation channel capacities are generally agnostic to the parameters that define the DMCs. Furthermore, our achievability proof yields a conceptually simple, computationally efficient, and capacity achieving coding scheme for the BSC permutation channel.