| Paper ID | D2-S7-T2.1 |
| Paper Title |
Two-Stage Coding over the Z-Channel |
| Authors |
Nikita Polyanskii, Skolkovo Institute of Science and Technology, Russia |
| Session |
D2-S7-T2: Combinatorial Coding Theory |
| Chaired Session: |
Wednesday, 14 July, 00:00 - 00:20 |
| Engagement Session: |
Wednesday, 14 July, 00:20 - 00:40 |
| Abstract |
A new Z-channel coding problem is addressed in this paper. Suppose that the encoder transmits $n$ binary symbols $(x_1,\ldots,x_n)$ one-by-one over the Z-channel, in which a 1 is received if and only if a 1 is transmitted. At some designated moment, say $n_1$, the encoder uses noiseless feedback and adjusts further encoding strategy based on the partial output of the channel $(y_1,\ldots,y_{n_1})$. The goal is to transmit error-free as much information as possible under the assumption that the total number of errors inflicted by the Z-channel is limited by $\tau n$, $0<\tau<1$. As the main contribution, we precisely characterize when exponential-sized (or positive-rate) codes exist for this model. Our proof relies on the concepts of list-decodable codes and high-error low-rate codes.
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