nnc_air: Information rates of the noisy nanopore channel

nnc_air is a software package that we release as supplementary material for the results in [1]. The package is capable of efficiently computing information rates of the noisy nanopore channel (NNC) [1] for an arbitrary Markov source. The Markov source can be heuristically optimised using the generalised Blahut-Arimoto algorithm (GBAA) [2], [3], which is included in this package.

This package is able to reproduce the results in [1], and additionally the results in [2], [3].

air_sim: Estimating information rates

Choosing the model parameters

The NNC is specified by the channel mapping f, the adjacency matrix A, the Gaussian noise level sigma, and the duration distribution P_K. In this package, we choose f and P_K using CSV files in the directory root/air_sim/name_of_model. The adjacency matrix is specified by the Markov distribution P, which is also chosen using a CSV file in the same directory. The noise level sigma is chosen as a range of values in the root/air_sim/kernel.cu script, which we detail in the next section.

To estimate information rates of an ISI channel with AWGN, make the contents of P_K.csv equal to 1. Alternatively, see the later section on GBAA.

Choosing the simulation parameters

The simulation parameters in the root/air_sim/kernel.cu script are:

• Block length m.
• sigma_min, sigma_max, and delta to simulate sigma for the range of values sigma_min:delta:sigma_max.
• Channel mapping f read from CSV root/air_sim/name_of_model/f.csv.
• Duration probabilities P_K read from CSV root/air_sim/name_of_model/P_K.csv.
• Markov distribution P read from CSV root/air_sim/name_of_model/P.csv.
• Intervals intervals.
• The data is saved to root/air_sim/data/data.csv.

By default, the intervals are chosen to be those specified in [1] using an epsilon eps equal to 1e-10 in the function bd_int(). Use the function periodic_markers() for computing information rates with markers.

Note that any change in channel parameters or simulation parameters must be updated from within the script.

gbaa_sim: Optimising the Markov source

The Markov source of the aforementioned NNC can be heuristically-optimised using GBAA on an NNC that has been synchronised, which is a finite-state channel (FSC). Specifically, the synchronised NNC is a faded ISI channel, with fading according to P_K (fading channel-state information known at the receiver), and AWGN noise according to sigma.

Choosing the model parameters

The parameters f and A are specified using a .mat file (e.g., root/gbaa_sim/scrappie_graph.mat). The duration distribution P_K and noise level sigma are specified in the root/gbaa_sim/gbaa_nnc_fading.m script.

Choosing the simulation parameters

The simulation parameters in the root/gbaa_sim/gbaa_nnc_fading.m script are:

• Block length m.
• The range of values for sigma in sigma_vals.
• The duration distribution P_K.
• The maximum number of iterations max_iters by GBAA.
• The early stopping condition parameter eps. If the information rates in consecutive iterations differ less than eps, then GBAA is stopped.
• The data is saved to root/gbaa_sim/optimised_P.mat.

Running

The following is a step-by-step guide for running the scripts root/air_sim/kernel.cu and root/gbaa_sim/gbaa_nnc_fading.m. When using complex models in the NNC, such as the nanopore in air_sim/nanopore_model/, we recommend running these scripts on a cluster. Hence, the following guides are based on a Linux environment.

For a cluster using the Slurm workload manager, run the job scripts air_sim.sh and gbaa_sim.sh using sbatch. Otherwise, follow the guides below.

air_sim

The script root/air_sim/kernel.cu is a so-called CUDA kernel that can only run on an NVIDIA GPU with CUDA installed.

1. Install CUDA (e.g., CUDA Version 11.7).
2. Ensure that the root directory is correctly specified within the script.
3. Run the commands:

cd air_sim
nvcc kernel.cu -o kernel -std=c++11
./kernel

gbaa_sim

The script root/gbaa_sim/gbaa_nnc_fading.m is a standard MATLAB program that should run on an any relatively new version of MATLAB.

1. Install MATLAB (e.g., MATLAB R2021a).
2. Run the commands:

export MATLABROOT=/usr/local/matlab/r2021a
cd gbaa_sim
mcc -mv gbaa_nnc_fading.m -o gbaa_nnc_fading -a ./GBAA
echo 10 | ./run_gbaa_nnc_fading.sh  $MATLABROOT

Alternatively, you may use the MATLAB GUI.

References

[1] McBain, B., Viterbo, E., Saunderson, J. (2023). Information rates of the noisy nanopore channel. IEEE Transactions on Information Theory (submitted).

[2] Kavcic, A. (2001). On the capacity of Markov sources over noisy channels. GLOBECOM'01. IEEE Global Telecommunications Conference.

[3] Vontobel, P., Kavcic, A., Arnold, D.-M., and Loeliger, H.-A. (2008). A generalized Blahut-Arimoto algorithm. IEEE Transactions on Information Theory.