Distributed joint source-channel coding for relay systems exploiting source-relay correlation and source memory
- Xiaobo Zhou^{1}Email author,
- Meng Cheng^{1},
- Khoirul Anwar^{1} and
- Tad Matsumoto^{1, 2}
https://doi.org/10.1186/1687-1499-2012-260
© Zhou et al.; licensee Springer. 2012
Received: 1 March 2012
Accepted: 30 July 2012
Published: 16 August 2012
Abstract
In this article, we propose a distributed joint source-channel coding (DJSCC) technique that well exploits source-relay correlation as well as source memory structure simultaneously for transmitting binary Markov sources in a one-way relay system. The relay only extracts and forwards the source message to the destination, which implies imperfect decoding at the relay. The probability of errors occurring in the source-relay link can be regarded as source-relay correlation. The source-relay correlation can be estimated at the destination node and utilized in the iterative processing. In addition, the memory structure of the Markov source is also utilized at the destination. A modified version of the Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm is derived to exploit the memory structure of the Markov source. Extrinsic information transfer (EXIT) chart analysis is then performed to investigate convergence property of the proposed technique. Results of simulations conducted to evaluate the bit-error-rate (BER) performance and the EXIT chart analysis show that, by exploiting the source-relay correlation and source memory simultaneously, our proposed technique achieves significant performance gain, compared with the case where the correlation knowledge is not fully used.
Keywords
Introduction
Wireless mesh and/or sensor networks having great number of low-power consuming wireless nodes (e.g., small relays and/or micro cameras) have attracted a lot of attention of the society, and a variety of its potential applications has been considered recently[1]. The fundamental challenge of wireless mesh and/or sensor networks is how energy-/spectrum-efficiently as well as reliably the multiple sources can transmit their originating information to the multiple destinations. However, such multi-terminal systems have two practical limitations: (1) wireless channel suffers from various impairments, such as interference, distortions and/or deep fading, (2) signal processing complexity as well as transmitting powers has to be as low as possible due to the power, bandwidth, and/or size restrictions of the wireless nodes.
Cooperative communication techniques provide a potential solution to the problems described above, due to its excellent transmit diversity for fading mitigation[2]. One simple form of cooperative wireless communications is a single relay system, which consists of one source, one relay and one destination. The role of the relay is to provide alternative communication route for transmission, hence improving the probability of successful signal reception of source information sequence at the destination. In this relay system, the information sent from the source and the relay nodes are correlated, which in this article is referred to as source-relay correlation. Furthermore, the information collected at the source node contains memory structure, according to the dynamics that governs the temporal behavior of the originator (or sensing target). The source-relay correlation and the memory structure of the transmitted data can be regarded as redundant information which can be used for source compression and/or error correction in distributed joint source-channel coding (DJSCC).
There are many excellent coding schemes which can achieve efficient node cooperative communications, such as[3, 4], where decode-and-forward (DF) relay strategy is adopted and the source-relay link is assumed to be error free. In practice, when the signal-to-noise ratio (SNR) of the source-relay link falls below certain threshold, successful decoding at relay may become impossible. Besides, to completely correct the errors at the relay, strong codes such as turbo codes or low density parity check (LDPC) codes with iterative decoding are required, which will impose heavy computational burden at the relay. As a result, several coding strategies assuming that the relay cannot always decode correctly the information from the source have been presented in[5–7].
Joint source-channel coding (JSCC) has been widely used to exploit the memory structure inherent within the source information sequence. In the majority of the approaches to JSCC design, variable-length code (VLC) is employed as source encoder and the implicit residual redundancy after source encoding is additionally used for error correction in the decoding process. Some related study can be found in[8–11]. Also, there are some literatures which focus on exploiting the memory structure of the source directly, e.g., some approaches of combining hidden Markov Model (HMM) or Markov chain (MC) with the turbo code design framework are presented in[12–14].
In the schemes mentioned above, the exploitation of the source-relay correlation and the source memory structure have been addressed separately. Not much attention has been paid to relay systems exploiting the source-relay correlation and the source memory simultaneously. A similar study can be found in[15], where the memory structure of the source is represented by a very simple model, bit-flipping between the current information sequence and its previous counterpart, which is not reasonable in many practical scenarios. When the exploitation of the source memory having more generic structures, the problem of code design for relay systems exploiting jointly the source-relay correlation and the source memory structure is still open.
In this article, we propose a new DJSCC scheme for transmitting binary Markov source in a one-way single relay system, based on[7, 14]. The proposed technique makes efficient utilization of the source-relay correlation as well as the source memory structure simultaneously to achieve additional coding gain. The rest of this article is organized as follow. Section ‘System model’ introduces the system model. The proposed decoding algorithm is described in Section ‘Proposed decoding scheme’. Section ‘EXIT chart analysis’ shows the results of extrinsic information transfer (EXIT) chart analysis conducted to evaluate the convergence property of the proposed system. Section ‘Convergence analysis and BER performance evaluation’ shows the bit-error-rate (BER) performance of the system based on EXIT chart analysis. The simulation results for image transmission using the proposed technique is presented in Section ‘Application to image transmission’. Finally, conclusions are drawn in Section ‘Conclusion’ with some remarks.
System model
One-way single relay system
In this article, a single-source single-relay system is considered where all links are assumed to suffer from Additive White Gaussian Noise (AWGN). The relay system operates in a half-duplex mode. During the first time interval, the source node broadcasts the signal to both the relay and destination nodes. After receiving signals from the source, the relay extracts the data even though it may contain some errors, re-encodes, and then transmits the extracted data to the destination node in the second time interval.
where x and x_{ r } represent the symbol vectors transmitted from the source and the relay, respectively. Notations n_{ r } and n_{ d } represent the zero-mean AWGN noise vectors at the relay and the destination with variances${\sigma}_{r}^{2}$ and${\sigma}_{d}^{2}$, respectively. The SNR of the source-relay and relay-destination links with the three different relay location scenarios, as shown in Figure1, can be decided as: for location A, SNR_{ sr } = SNR_{ rd } = SNR_{ sd }; for location B, SNR_{ sr } = SNR_{ sd } + 21.19 dB and SNR_{ rd } = SNR_{ sd } + 4.4 dB; for location C, SNR_{ sr } = SNR_{ sd } + 4.4 dB and SNR_{ rd } = SNR_{ sd } + 21.19 dB.
Source-relay correlation
The source-relay correlation indicates the correlation between u and u_{ r }, which can be represented by a bit-flipping model, as shown in Figure2. u_{ r } can be defined as u_{ r } = u ⊕ e, where e is an independent binary random variable and ⊕ indicates modulus-2 addition. The correlation between u and _{ u r } is characterized by p_{ e }, where p_{ e } = Pr(e = 1) = Pr(u ≠ u_{ r })[6].
Markov source
where {μ_{ i }} is the stationary state probability.The memory structure of Markov source can be characterized by the state transition probabilities p_{1} and p_{2}, 0 < p_{1}p_{2} < 1, with which p_{1} = p_{2} = 0.5 indicates the memoryless source, while p_{1} ≠ 0.5 or p_{2} ≠ 0.5, and hence H(S) < 1 indicate source with memory.
Proposed decoding scheme
At the destination node, the received signals from the source and the relay are first converted to log-likelihood ratio (LLR) sequences L(y_{ sd }), L(y_{ rd }), respectively, and then decoded via two horizontal iterations (HI), as shown in Figure4. Then the extrinsic LLR s generated from D_{ s } and D_{ r } in the two HI s are further exchanged by several vertical iterations (VI) through an LLR updating function f_{ c }, of which role is detailed in the following section. This process is performed iteratively, until the convergence point is reached. Finally, hard decision is made based on the a posteriori LLR s obtained from D_{ s }.
LLR updating function
where N indicates the number of the a posteriori LLR pairs from the two decoders with sufficient reliability. Only the LLR s with their absolute values larger than a given threshold can be used in calculating${\widehat{p}}_{e}$.
where π_{0}(·) and${\pi}_{0}^{-1}(\xb7)$ denote interleaving and de-interleaving functions corresponding to π_{0}, respectively.${\mathbf{L}}_{{\mathbf{a},D}_{\mathbf{s}}}^{\mathbf{u}}$ and${\mathbf{L}}_{{\mathbf{e},D}_{\mathbf{s}}}^{\mathbf{u}}$ denote the a priori LLR s fed into, and extrinsic LLR s generated by D_{ s }, respectively, both for the uncoded bits. Similar definitions should apply to${\mathbf{L}}_{{\mathbf{a},D}_{\mathbf{r}}}^{\mathbf{u}}$ and${\mathbf{L}}_{{\mathbf{e},D}_{\mathbf{r}}}^{\mathbf{u}}$ for D_{ r }.
Joint decoding of Markov source and channel encoder C_{ s }
Representation of super trellis
At time instant t, the state of the source and the state of the C_{ s } can be regarded as a new state$({S}_{t}^{s},{S}_{t}^{c})$, which leads to the super trellis diagram. A simple example of combining binary Markov source with a recursive convolutional code (RSC) with generator polynominald (G_{ r },G) = (3,2)_{8} is depicted in Figure5. At each state$({S}_{t}^{s},{S}_{t}^{c})$, the input to the outer encoder is determined, given the state of the Markov source. Actually, the new trellis branches can be regarded as a combination corresponding to the branches of the Markov source and of the trellis diagram of C_{ s }. Hence, the new trellis branches represent both state transition probabilities of the Markov source and input/output characteristics of C_{ s }defined in its trellis diagram.
It should be noticed that a drawback of this approach is the exponentially growing number of the states in the super trellis. However, if C_{ s }is only a short memory convolutional code, the complexity increase is due mainly to the number of Markov source states. In fact, it is shown in Section ‘Convergence analysis and BER performance evaluation’ that, even with a memory-1 code used as C_{ s }can achieve excellent performance. Therefore, the complexity is largely the issue of source modeling depending on applications.
Modified BCJR algorithm for super trellis
In this section, we make modifications of the standard BCJR algorithm[18] for the decoding performed over the super trellis constructed in the previous section. Here, we ignore momentarily the serially concatenated structure, and only focus on the decoding process performed over the super trellis diagram. For a convolutional code with memory length v, there are 2^{ v } states in its trellis diagram, which is indexed by m m = 0,1,…,2^{ v }−1. The input sequence to the encoder u = u_{1}u_{2}…u_{ t }…u_{ L }, which is also a series of the states of Markov source, is assumed to have length L. The output of the encoder is denoted as x={x^{c 1}x^{c 2}}. The coded binary sequence is BPSK mapped and then transmitted over AWGN channels. The received signal is a noise-corrupted version of the BPSK mapped sequence, denoted as y={y^{c 1}y^{c 2}}. The received sequence from the time indexes t_{1} to t_{2} is denoted as${\mathbf{y}}_{{t}_{1}}^{{t}_{2}}={\mathbf{y}}_{{t}_{1}},{\mathbf{y}}_{{t}_{1}+1},\dots ,{\mathbf{y}}_{{t}_{2}}$.
where${B}_{t}^{k}$ denotes the sets of states$\left\{\right({S}_{t}^{s}=i,{S}_{t}^{c}=m\left)\right\}$ yielding the systematic output${x}_{t}^{c1}$ of the C_{ s }being k, k = 0,1.
E_{ t }(i,m) is the set of states {(u_{t−1},S_{t−1})} that have a trellis branch connected with state (u_{ t } = i,S_{ t } = m) in the super trellis.
Since the output encoder always starts from the state zero, while the probabilities for the Markov source starts from state “0” or state “1” is equal. Hence, the appropriate boundary condition for α is α_{0}(0,0) = α_{0}(1,0) = 1/2 and α_{0}(i,m) = 0,i = 0,1;m ≠ 0. Similarly, the boundary conditions for β is β_{ L }(i,m) = 1/2^{v + 1},i = 0,1;m = 0,1,…,2^{ v }−1.
representing the a priori LLR, the channel LLR and the extrinsic LLR, respectively. The same representation should apply to$\left\{{x}_{t}^{c2}\right\}$.
EXIT chart analysis
where${I}_{e,{D}_{s}}^{c}$ denotes the mutual information between the extrinsic LLR s,${L}_{e,{D}_{s}}^{c}$ generated from D_{ s }, and the coded bits of D_{ s }.${I}_{e,{D}_{s}}^{c}$ can be obtained by the histogram measurement[21]. Similar definitions can be applied to${I}_{a,{D}_{s}}^{c}$ and${I}_{e,{D}_{r}}^{u}$.
For the proposed DJSCC decoding scheme, both the source memory and the source-relay correlations are exploited in the iterative decoding process. The impact of the source memory and the source-relay correlations on D_{ s }, represented by the 3D EXIT planes, shown in light-blue, is presented in Figure7. We can observe that higher extrinsic information can be achieved (EXIT planes are lifted up) by exploiting the source memory and the source-relay correlations simultaneously, which will help decoder D_{ s } perfectly retrieve the source information sequence even at a low SNR_{ sd } scenario.
Convergence analysis and BER performance evaluation
A series of simulations was conducted to evaluate the convergence property, as well as BER performance of the proposed technique. The information sequences are generated from Markov sources with different state transition probabilities. The block length is 10000 bits, and 1000 different blocks were transmitted for the sake of keeping reasonable accuracy. The encoder used at the source and relay nodes, C_{ s } and C_{ r }, respectively, are both memory-1 half rate RSC with generator polynomials (G_{ r }G) = (3,2)_{8}. Five VI s took place after every HI, with the aim of exchanging extrinsic information to exploit the source-relay correlation. The whole process was repeated 50 times. All the three relay location scenarios were evaluated, with respect to the SNR of the source-destination link. The doping rates are set at K_{ s } = K_{ r } = 2 for location A, while K_{ s } = 1, K_{ r } = 16 for both the location B and C. The threshold for estimating${\widehat{p}}_{e}$[6] is set at 1.
Convergence behavior with the proposed decoder
Contribution of the source-relay correlation
Contribution of the source memory structure
BER performance comparison between DJSCC/SM and JSCTC
Markov source parameters | Gains over conventional P2P | ||||
---|---|---|---|---|---|
p _{ 1 } | _{ p 2 } | H ( S ) | JSCTC (dB) | DJSCC/SM (dB) | |
0.7 | 0.7 | 0.88 | 0.45 | 0.55 | |
0.8 | 0.8 | 0.72 | 1.29 | 1.5 | |
0.9 | 0.9 | 0.47 | 3.03 | 3.6 |
BER performance of the proposed technique
BER performance gains of the DJSCC over the technique that only exploits source-relay correlation
Markov source parameters | Relay locations | |||||
---|---|---|---|---|---|---|
p _{ 1 } | _{ p 2 } | H ( S ) | A (dB) | B (dB) | C (dB) | |
0.7 | 0.7 | 0.88 | 0.3 | 0.45 | 0.45 | |
0.8 | 0.8 | 0.72 | 1.2 | 1.4 | 0.9 | |
0.9 | 0.9 | 0.47 | 2.2 | 3.05 | 2.6 |
Application to image transmission
Conclusion
In this article, we have presented a DJSCC scheme for transmitting binary Markov source in a one-way relay system. The relay does not aim to completely eliminate the errors in the source-relay link. Instead, the relay only extracts and forwards the source information sequence to the destination, even though the extracted information sequence may contain some errors. Since the error probability of the source-relay link can be regarded as source-relay correlation, in our proposed technique, the LLR updating function is adopted to estimate and exploit the source-relay correlation. Furthermore, to exploit the memory structure of Markov source, the trellis of Markov source and that of the channel encoder at the source node are combined to construct a super trellis. A modified version of the BCJR algorithm has been derived, based on this super trellis, to perform joint decoding of Markov source and channel code at the destination. By exploiting the source-relay correlation and the memory structure of Markov source simultaneously, the proposed technique can achieve significant gains over the techniques that only exploit the source-relay correlation, which is verified through BER simulations as well as image transmission simulations.
Declarations
Acknowledgements
This research was supported in part by the Japan Society for the Promotion of Science (JSPS) Grant under the Scientific Research KIBAN, (B) No. 2360170, (C) No. 2256037, and in part by Academy of Finland SWOCNET project.
Authors’ Affiliations
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