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Due to inevitable propagation delay involved in deep-space communication systems, very high cost is associated with the retransmission of erroneous segments. Quantization with linear index coding (QLIC) scheme is known to provide compression along with robust transmission of deep-space images, and thus the likelihood of retransmissions is significantly reduced. This paper aims to improve its spectral efficiency as well as robustness. First, multiple quantization refinement levels per transmitted source block of QLIC are proposed to increase spectral efficiency. Then, iterative multipass decoding is introduced to jointly decode the subsource symbol-planes. It achieves better PSNR of the reconstructed image as compared to the baseline one-pass decoding approach of QLIC.

The deep-space communication is more challenging than its near-Earth counterpart due to the associated huge intertransceiver propagation delay [

It is well-known that the state-of-the-art image compression standards (JPEG2000 and ICER) are sensitive to postdecoding residual errors [

In order to provide error resilient source transmission, a vast number of schemes are proposed in literature under the category of joint source-channel coding (JSCC) [

Indeed, QLIC is able to withstand significant SNR fluctuations while still preserving the visual quality of the image, but its spectral efficiency is inferior to the currently used deep-space image transmission system [

On the encoder side, QLIC [

On the decoder side, QLIC [

The main contributions of this paper are summarized below:

An efficient quantization scheme is proposed for QLIC to assign quantization precision to the transformed image considering relatively small blocks. The proposed scheme achieves better overall transmission bandwidth efficiency.

A multipass decoding scheme is proposed to utilize the redundancy left in the lower level symbol-planes in order to improve the BER of the higher level symbol-planes. The improved BER of the higher levels eventually results in improved reconstruction quality.

The rest of this paper is organized as follows: In Section

In this section, we briefly outline QLIC scheme, the optimization problem, the solution of which is used in Section

In classical separated source-channel coding systems the aim of the source coding is to reduce the redundancy from the source as much as possible and then the error protection is provided by the channel codes. In this way, controlled amount of redundancy is added to the transmitted data stream in order to protect it against channel induced errors. However, in QLIC, channel codes are used to provide compression as well as error protection. The source data after quantization is arranged into bit-planes and the bit-planes are directly mapped to the channel codewords. Consequently, the rate-budget assigned to each encoded bit-plane is directly proportional to the conditional entropy rate of the bit-plane given the higher level bit-planes. The direct mapping of the bit-planes has been shown to be more robust against channel induced errors [

Let us consider that an image after

Let

Dead-zone uniform scaler quantizer (DZUSQ)

Let

Let us consider that a successive refinement source-channel code exists which encodes all the subsources up to a particular refinement level such that the overall distortion is given by

Consequently, the refinement level

The solution of the above program is then used to quantize each subsource up to a refinement level of

(a) Multilayer encoding approach of QLIC. (b) Baseline one-pass multistage decoder. The higher significant bit-planes provide decoding decisions to the lower significant bit-planes.

The soft information can also be used instead of hard decisions; however, no significant improvement in performance was observed as mentioned in [

Different from JPEG2000 and ICER which use sophisticated context based probability models to derive the entropy coder, the pure compression performance of QLIC is derived by the solution of optimization problem in (

The high level and low level transform coefficients are usually not uniformly distributed within the subband due to various image features. The choice of

However, large block length is associated with a serious drawback. The optimization problem to find out the refinement levels considers each subsource as a single unit. Consequently, the solution assigns the same refinement level to all the transform coefficients within a subsource. However, due to different spatial location of high and low level coefficients within a subsource, this assignment of refinement levels is usually not optimal. For example, let us consider a

Binary map of a single subsource of an image from Mars exploration rover. The nonzero quantization indices are represented with white pixels.

A possible solution is to use small block lengths to find the quantization refinement levels. Figure

The pure compression performance of QLIC using ideal channel codes for an image taken from Mars exploration rover. The compression performance for short block lengths is superior to that of the large block lengths.

Another possible solution is to combine the promising features of both the block lengths; i.e., use small

The above scheme is straightforward but unable to improve the spectral efficiency in practice. Every segment associated with a subsource may have different range of transform coefficients. Therefore, the quantization step size

Therefore, we propose to use the overall dynamic range of the transform coefficients of a subsource to determine the quantization step size

(a) Typical index assignment after reduced refinement level. (b) Proposed approach of index assignment.

The above solution enables getting rid of redundant symbols-planes quite effectively and thus increases the overall spectral efficiency. However, there are also some associated drawbacks. Let us assume that

In order to overcome this issue, we propose to update the

The multilayer encoding approach of QLIC directly maps the symbols-planes to the channel codewords as shown in Figure

The nonuniversality of Raptor codes is well-known for general noisy channels [

Inspired by the work of [

The decoding threshold of Raptor codes for different channel capacities. The output degree distribution for all plots is optimized for SNR of 3dB. It appears that there is no big difference in the decoding thresholds of Raptor codes at various channel SNRs.

In this subsection, we present the simulation results depicting the spectral efficiency of QLIC using the multiple refinement levels approach. We also compare these results with the numerical simulations of [

Image taken from Mars exploration rover: MER1 [

A target PSNR of 49 dB is defined for the reconstructed image. The LL0 subband [

The (

The (+)-curve corresponds to the spectral efficiency for the case when small block length is used in the encoding process. The length of each segment

The (○)-curve corresponds to the spectral efficiency achieved by the proposed approach. We would like to highlight that, in order to obtain the spectral efficiency at various values of channel SNR, only Raptor codes optimized for 3 dB SNR are used. The gap between the proposed scheme (○)-curve and the baseline scheme (

The (

The spectral efficiency of QLIC at various SNR levels for MER-B image. The plots depict that the proposed QLIC scheme with multiple quantization precision per source block possesses superior spectral efficiency.

In this section, we first establish the importance of observed virtual correlation channel in multipass decoding. Then, we present the analysis of multipass decoding. It reveals that certain symbols recovered in the first decoding pass can only provide effective extrinsic information in the subsequent decoding passes. In particular, a reliably recovered symbol of a lower level can only provide effective extrinsic information, if its corresponding symbol of higher level was recovered with low reliability in the previous decoding pass. Therefore, we propose to utilize information from only those combinations of the bit-planes which results in the higher extrinsic information. The block diagram of the proposed multipass decoder is shown in Figure

Proposed multipass decoding approach.

During decoding, every level of the multistage decoder observes a composite channel. A fraction

The overall observed channel capacity at the

Let the multistage decoder at every decoding level provide the estimate

Now let us consider the transmission using QLIC for

The normalized average channel capacities

Let us define

The decoded output

Scenario 1:

Scenario 2: now consider that all the nodes recovered in the first decoding pass of

Multipass decoding approach depicting the decoding of two correlated sources

Consequently, let us define

According to (

The extrinsic LLR

Reconstructed PSNR of MER1 when channel SNR varies form its nominal value of 3 dB.

In case of more than two bit-planes, different amount of correlation exists between the combinations of the bit-planes. For example, in case of 3 bit-planes,

Therefore, it is likely that including symbols from every bit-plane without any criterion in calculating the extrinsic information may decrease

In this subsection, we compare the simulation results for the baseline one-pass and the multipass decoding approach. The simulation setup similar to the one explained in Section

(○)-curve shows the performance of one-pass decoding scheme as the channel degrades from its nominal value. The PSNR degrades gradually as the channel SNR decreases similar to the results of [

(

(

(+)-curve is similar to the (○)-curve. However, the proposed multiple refinement level encoder is used. The simulation results confirm that the robustness of QLIC is retained by using the multiple refinement levels per subsource.

(

In this paper, we propose to efficiently remove the redundant bit-planes for spectrally efficient linear index coding of images. Further, the bit-planes are arranged to preserve their significance, and hence the similar robustness performance is achieved even with higher spectral efficiency. Then, multipass decoding is used to iteratively decode the bit-planes. We show that the multipass decoding provides better gain by using extrinsic information from selected bit-planes.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by National Natural Science Foundation of China under Grant 61471022, and NSAF under Grant U1530117.