Chinese scholars have made progress in the research of distributed source coding

Fig.
1 Schematic diagram of the comparison of traditional source coding and distributed source coding principles: (A) traditional source coding (symmetrical); (B) distributed source coding (symmetrical); (C) traditional source coding (asymmetric); (D) Distributed source coding (asymmetric)

Fig.
2 Schematic diagram of symbol-interval mapping rules for multivariate distributed arithmetic codes: (A) equidistant increments; (B) Equidistant staggering

Figure 3 Comparison of the performance of multivariate distributed arithmetic codes with different code lengths and distributed source coding based on channel codes (LDPC codes) at 1/2 code rate (the short code length is 75 256-yuan symbols, which is equivalent to 600 bits; The length of the long code is 355 256 meta symbols, equivalent to 2840 bits) :(A) short code error rate; (B) Long code frame error rate; (C) shortcode Manhattan residuals; (D) Long code Manhattan residuals

With the support of the National Natural Science Foundation of China (grant number: 62141101), Professor Fang Yong of Chang'an University has made progress
in the research of distributed source coding 。 The research results were published in the journal IEEE Transactions on Information Theory on December 22, 2022 under the title "Q-ary Distributed Arithmetic Coding for Uniform Q-ary Sources
" 。 Article link: https://ieeexplore.
ieee.
org/stamp/stamp.
jsp?tp=&arnumber=9944690
.
Source code link: https://github.
com/fy79/Qary-DAC
.

In recent years, voice, image, video and other types of data have exploded growth, in order to eliminate the redundancy of these data to improve the effectiveness of communication, the source coding technology according to the statistical characteristics of the source symbol sequence to transform it into the shortest possible code word sequence, so that the encoded code element load the largest amount of information, while without distortion (or with the smallest possible distortion) to restore the original symbol sequence
。 The traditional centralized source coding is mainly based on the point-to-point information theory of single source-single host, and is committed to establishing the theoretical boundary of rate distortion of single node source coding, and exploring the actual coding scheme
that can reach these theoretical boundaries 。 In practical application scenarios such as intelligent traffic dense monitoring system and resident gene database coexisting with multiple nodes, the original data of multiple nodes has a high temporal and spatial correlation, if the traditional centralized source coding is still used, the source encoders of each node need to communicate with each other to obtain each other's information, and there are problems such as
high encoder complexity, large equipment power consumption, and high layout cost 。 Compared with the traditional centralized coding method, the distributed source coding method can independently encode multiple nodes with information related to each other, without the need for mutual communication between nodes, and then restore the original data of multiple nodes in the decoding end by joint decoding, and transfer the computational complexity from the coding end to the decoding end (server), thus solving the problems of the traditional centralized source coding method (Figure 1).

Since the prediction residuals between related sources can be modeled as additive noise of the virtual channel, distributed source coding is essentially equivalent to the channel coding problem on the virtual channel, so the implementation of existing distributed source coding is usually based on various channel codes (such as turbo code, LDPC code and polar code).

。 The main problem of the implementation of distributed source coding based on channel code is model inaccuracy: channel code is usually optimized based on the additive white Gaussian noise (AWGN) channel model, so it is optimal in the sense of Euclidean distance.
However, for actual sources of interest, such as video signals, the prediction residuals tend to follow the Laplace distribution rather than the Gaussian distribution
.
At this time, the optimal channel code in the sense of Euclidean distance cannot meet the optimal in the sense of Manhattan distance at the same time, so the implementation of distributed source coding based on channel code cannot reach the theoretical limit
of lossless distributed source coding given by the Slepian-Wolf theorem.

In order to narrow the gap between the actual performance of the existing distributed source coding implementation based on channel code and the theoretical limit of the Slepian-Wolf theorem, Professor Fang Yong studied the multivariate distributed arithmetic code, and its main innovative idea is to directly use the Manhattan distance as a measurement tool to design the optimal codec
scheme in the sense of Manhattan distance 。 He has rigorously proved that as the length of the block tends to infinity, the total bitrate loss of the multivariate distributed arithmetic code stream of each packet tends to a finite constant, so the average bitrate loss of a single symbol tends to zero, that is, the performance of the multivariate distributed arithmetic code can reach the theoretical limit
.
The core of the design of multivariate distributed arithmetic code is the symbol-interval mapping rule, so he proposed the equidistant interleaved symbolic-interval mapping rule (Figure 2), which solved the optimal decoding problem
of Laplace-related sources by segmenting the coset space according to the Manhattan distance 。 At 1/2 bit rate, when the code length is 75 256-tuple symbols (equivalent to 600 bits) and 355 256-tuple symbols (equivalent to 2840 bits), the frame error rate of the multivariate distributed arithmetic code is only about half that of the LDPC code-based distributed source encoding implementation (Figures 3A and 3B), while the advantages of the multivariate distributed arithmetic code are even more significant on the indicator of the Manhattan residual (Figures 3C and 3D).

。 The above work shows that the multivariate distributed arithmetic code solves the problem that the current implementation method of distributed source coding based on channel code cannot reach the theoretical limit, and is an excellent candidate scheme for realizing the distributed coding of multiple related sources
.

The research results of the project provide a theoretical basis and new solution
ideas for effectively reducing the computing power requirements of the coding terminal in the application scenarios of multi-node source coding.