EXIT Analysis#

plot_exit_chart([mi_a, mi_ev, mi_ec, title])

Plots an EXIT-chart based on mutual information curves [tenBrinkEXIT].

get_exit_analytic(pcm, ebno_db)

Calculates analytic EXIT curves for a given parity-check matrix.

plot_trajectory(plot, mi_v, mi_c[, ebno])

Plots the trajectory of an EXIT-chart.

The LDPC BP decoder allows to track the internal information flow (extrinsic information) during decoding via callbacks. This can be plotted in so-called EXIT Charts [tenBrinkEXIT] to visualize the decoding convergence.

../../../../_images/exit.png

This short code snippet shows how to generate and plot EXIT charts:

# parameters
ebno_db = 2.5 # simulation SNR
batch_size = 10000
num_bits_per_symbol = 2 # QPSK
num_iter = 20 # number of decoding iterations

pcm_id = 4 # decide which parity check matrix should be used (0-2: BCH; 3: (3,6)-LDPC 4: LDPC 802.11n
pcm, k, n , coderate = load_parity_check_examples(pcm_id, verbose=True)

noise_var = ebnodb2no(ebno_db=ebno_db,
                      num_bits_per_symbol=num_bits_per_symbol,
                      coderate=coderate)

# init callbacks for tracking of EXIT charts
cb_exit_vn = EXITCallback(num_iter)
cb_exit_cn = EXITCallback(num_iter)

# init components
decoder = LDPCBPDecoder(pcm,
                        hard_out=False,
                        cn_update="boxplus",
                        num_iter=num_iter,
                        v2c_callbacks=[cb_exit_vn,], # register callbacks
                        c2v_callbacks=[cb_exit_cn,],) # register callbacks

# generates fake llrs as if the all-zero codeword was transmitted over an AWNG channel with BPSK modulation
llr_source = GaussianPriorSource()


# generate fake LLRs (Gaussian approximation)
# Remark: the EXIT callbacks require all-zero codeword simulations
llr_ch = llr_source([batch_size, n], noise_var)

# simulate free running decoder (for EXIT trajectory)
decoder(llr_ch)

# calculate analytical EXIT characteristics
# Hint: these curves assume asymptotic code length, i.e., may become inaccurate in the short length regime
Ia, Iev, Iec = get_exit_analytic(pcm, ebno_db)

# and plot the analytical exit curves

plt = plot_exit_chart(Ia, Iev, Iec)

# and add simulated trajectory (requires "track_exit=True")
plot_trajectory(plt, cb_exit_vn.mi.numpy(), cb_exit_cn.mi.numpy(), ebno_db)

Remark: for rate-matched 5G LDPC codes, the EXIT approximation becomes inaccurate due to the rate-matching and the very specific structure of the code.

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