Fig. 1 Proposed end-to-end quantum communication system with adaptive
coding for image transmission.
In this study, images with varying spatial information (SI)
characteristics are used as an information source. These images are
first compressed using either the JPEG or HEIF source encoding methods,
converting them into classical bitstreams. For channel coding, polar
codes with rates of 2/3, 1/2, 1/3 and 1/4 are considered and these
channel coding rates are adaptively changed based on the channel
conditions. To maintain a similar bandwidth, source coding rates
(quality levels) are adjusted in the source coding process. By varying
the quality level in response to different channel coding rates, the
overall bitrate remains constant across the channel. Once the classical
bitstreams are channel encoded, they are converted into qubit
superposition states and these qubit states are then transmitted through
the quantum communication channel. At the receiver, quantum measurement
operators are applied to convert the received qubit states back into
classical bits. After this, the appropriate channel decoding process is
performed, corresponding to the applied polar coding rate. Finally, the
recovered classical bitstream undergoes source decoding (JPEG or HEIF),
reconstructing the final images. The following subtopics explain the
details of each part of the proposed framework.
Information Source : In our experiment, a set of eleven images
from the Microsoft Common Objects in Context (COCO) dataset [12] is
used as the source of data, serving as foundational test images for the
study. These images represent a range of spatial features that are
considered essential for demonstrating the impact of the proposed
framework.
Source Encoder : The selected images are compressed using two
different source encoding methods: HEIF and JPEG. JPEG is widely used
for lossy compression of digital images, while HEIF offers better
compression efficiency and higher image quality. To evaluate the
proposed system in a bandwidth-restricted environment, the HEIF and JPEG
source coding rates are adjusted according to the channel coding rates,
ensuring that the system’s throughput remains nearly constant. After
compression, the images are converted to classical bitstreams, sequences
of binary data ready for further processing.
Channel Encoder : For channel coding, polar codes are employed
with specific rates: 2/3, 1/2, 1/3, and 1/4. Polar codes are a type of
error correction code that is known for its capacity-achieving
properties and can efficiently handle noise in communication channels.
The different rates indicate varying levels of redundancy and
error-correcting capabilities, which influence the robustness of the
encoded data.
Quantum Encoder : The Hadamard gate is a fundamental quantum
operation that creates superposition states, where classical bits are
transformed into qubits superposition. This transformation allows the
classical information to be transmitted through a quantum communication
channel. This process is similar to the method that we proposed in our
previous work [11].
Channel : The qubits superposition states are then sent through
the quantum communication channel. Unlike classical channels, quantum
channels are characterized by the properties of quantum mechanics. But
in this process, we use a simple channel model to simulate the quantum
channel with varying signal-to-noise ratios (SNR), based on the concept
that the behaviour of quantum channels under different SNR conditions
can be evaluated using a classical channel with equivalent SNR
conditions up to a certain level of noise [13].
Quantum Decoder : At the receiver’s end, quantum measurement
operators are applied to the received qubit states as described in
[11]. These operators collapse the qubit superposition states back
into classical bits. Measurement in quantum mechanics is the process by
which quantum information is retrieved from qubits and converted into a
format that can be processed by classical systems.
Channel Decoder : The classical bits recovered from quantum
measurement are then subjected to channel decoding processes that
correspond to the polar coding rates used during encoding. This step
involves applying the appropriate decoding algorithm to correct any
errors and reconstruct the bitstream accurately.
Source Decoder : Finally, the recovered classical bitstream
undergoes source decoding using the same method employed during the
source encoding phase (JPEG or HEIF). This step reconstructs the final
images from the bitstreams, effectively reversing the compression and
encoding processes to retrieve the images as they were before
transmission.
To demonstrate the proposed quantum communication system for image
transmission, we analyse the average performance of the input images
across different SNR conditions and coding rates. By dynamically varying
the channel noise, we select the optimal channel coding rate for a given
channel SNR of the adaptive coding system.
To ensure a fair comparison with the proposed adaptive coding based
quantum communication system, an equivalent classical communication
system is employed using the same channel coding rates and binary
phase-shift keying (BPSK) modulation. This approach helps maintain
consistent bandwidth across both methods. The Peak Signal-to-Noise Ratio
(PSNR) and Structural Similarity Index Measure (SSIM) values are
computed for images reconstructed using both adaptive coding based
quantum and the classical communication systems. These metrics provide
quantitative measures of image quality, allowing for a direct comparison
of performance between the two systems. By analysing the PSNR and SSIM
results, the study assesses the effectiveness of the proposed adaptive
coding based quantum communication system relative to the equivalent
classical system, identifying advantages in terms of image quality and
overall performance.
Results and Discussion: This research focuses on comparing the
performance of adaptive coding based quantum communication systems with
adaptive coding based classical communication systems. The results
reveal significant insights into how each system adapts to varying SNR
levels, particularly in terms of image quality and error resilience.
Furthermore, both HEIF and JPEG image formats are analysed to understand
their performance in these communication systems.
The analysis of PSNR for the HEIF image format, as shown in Figure 2,
reveals that adaptive coding offers substantial benefits in preserving
signal quality across varying SNR levels. Both quantum (Q) and classical
(C) systems exhibit notable improvements when adaptive coding is
employed, outperforming their non-adaptive counterparts. Notably, the
adaptive coding based quantum system exhibits significantly higher PSNR
values compared to the adaptive coding based classical system,
particularly in the lower SNR range (below 16 dB). This trend is
particularly evident, as the proposed quantum communication system
achieves a rapid increase in PSNR starting around 4 dB SNR, indicating
its robust performance under noisy conditions.
The results also show that the highest PSNR values achieved with high
polar coding rates are lower than those obtained with low polar coding
rates due to the bandwidth-restrictive conditions imposed during
implementation. However, adaptive coding implementations in both quantum
and classical communications can mitigate this issue by switching to
higher quality values when the channel SNR improves, as the required
optimum polar coding rate decreases.
Therefore, as the SNR increases beyond 16 dB, both systems achieve high
PSNR values, reaching up to 65 dB. Notably, the earlier rise in PSNR for
the proposed quantum system at low SNR (4-12 dB) demonstrates its
capability to maintain high-quality transmission under less-than-ideal
conditions.