Determine the cutoff rate for the channel

Question

Response to the following problem:

A discrete-time additive non-Gaussian noise channel is described by the input-output relation

y_i = x_i + n_i

where ni represents a sequence of iid noise random variables with probability density function

p(n) = (1/2)e^-|n|

and xi can take ±1 with equal probability, where i represents the time index.

1. Determine the cutoff rate R0 for this channel.

2. Assume that this channel is used with optimal hard decision decoding at the output. What is the crossover probability of the resulting BSC channel?

3. What is the cutoff rate in part 2?