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IEEE COMMUNICATIONS LETTERS, VOL. 21, NO. 11, NOVEMBER 2017
Reliability-Oriented Decoding Strategy for LDPC Codes-Based D-JSCC System Yibo Lyu, Shaohua Hong, Member, IEEE, Lin Wang, Senior Member, IEEE, and Zixiang Xiong, Fellow, IEEE Abstract— In this letter, a reliability oriented decoding strategy (RODS) for low density parity check codes-based distributed joint source and channel coding system is proposed. During each local decoding iteration, the reliability of each variable node is evaluated based on the sign of received log-likelihood ratios (LLRs) and its oscillation situation. Then, by employing reliability-oriented updating operation, the negative influence of those inaccurate messages is suppressed. Moreover, extra operations are performed on a group of most unreliable source nodes so that more accurate posteriori LLRs can be obtained. During global iteration, offset operation is performed to reduce error propagation. The simulation results illustrate that the proposed RODS outperforms other decoding algorithms at the aspects of error correction performance and convergence speed, especially when the correlation between distributed sources is low. Index Terms— AWGN channel, belief propagation (BP), distributed joint source and channel coding (D-JSCC), decoding strategy, low density parity check (LDPC) codes.
I. I NTRODUCTION
I
N WIRELESS sensor network (WSN), sensor nodes are planted in a particular area to collect data. Hence, the data acquired by those nodes are usually correlated. Simultaneously, taking the power limitation of those tiny sensor nodes into account, distributed source coding (DSC) is a good candidate technique for WSN [1], [2]. By exploiting the correlation between the data coming from different nodes through joint decoding operation, DSC system can dramatically reduce power consumption. In practice, DSC system is converted to distributed joint source and channel coding (D-JSCC) system if correlated source signals are transmitted over noisy channel. In order to enhance the performance of D-JSCC system, turbo codes and low density parity check (LDPC) codes which have strong anti-noise ability are adopted. There have been several works investigating the D-JSCC systems using LDPC codes. In [3], irregular repeat accumulate (IRA) code based D-JSCC system is introduced. In [4]–[6], the methods of designing irregular LDPC codes for D-JSCC system have been discussed. By using different degree distributions for source variable nodes and parity variable nodes, the performance of D-JSCC system is enhanced. Manuscript received June 5, 2017; revised July 29, 2017; accepted August 19, 2017. Date of publication August 24, 2017; date of current version November 9, 2017. This work was supported by the National Natural Science Foundation of China under Grant 61671395. The associate editor coordinating the review of this letter and approving it for publication was C. Feng. (Corresponding author: Shaohua Hong.) Y. Lyu, S. Hong, and L. Wang are with the Department of Communication Engineering, Xiamen University, Fujian 361005, China (e-mail:
[email protected]). Z. Xiong is with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA, and also with Monash University, Clayton, VIC 3800, Australia (e-mail:
[email protected]). Digital Object Identifier 10.1109/LCOMM.2017.2743698
For LDPC codes based D-JSCC system, belief propagation (BP) algorithm is applied to recover source bits. But the performance of BP algorithm is limited by short cycles that commonly exist in short length LDPC codes, the codeword length of which is smaller than 2000 bits. This is the reason why the D-JSCC system requires long LDPC codes to achieve good performance. However, in WSN the codeword length is generally constrained to short due to the limitation of complexity, delay and power consumption [4]. Therefore, the performance of D-JSCC system using short codes should be improved in practical applications. In order to reduce error message accumulation caused by the existing cycles, two reweighted BP algorithms, named as uniformly reweighted BP (URW-BP) and variable factor appearance probability BP (VFAP-BP) algorithms, are discussed in [7] and [8]. Moreover, several residual based decoding strategies, such as residual BP (RBP) and node-wise RBP (NW-RBP) algorithms, are investigated in [9]. By dynamically arranging decoding schedules, RBP and NW-RBP algorithms can converge faster than BP algorithm over additive white Gaussian noise (AWGN) channel. In [10], residual ordered layer BP (ROLBP) algorithm is designed for iterative receiver over block fading channel. The research results suggest that by considering the properties of the multilevel iterative system, a novel decoding strategy can provide better performance. Hence, for the purpose of further improving the performance of D-JSCC system, a reliability oriented decoding strategy (RODS) is introduced in this letter. By reducing the negative influence of the error messages and providing more accurate side information for joint decoder, RODS can outperform other algorithms at the aspects of error correction ability and convergence speed. II. D-JSCC S YSTEM AND T RADITIONAL J OINT D ECODING S TRATEGY Let S1 = [s1 (1), . . . , s1 (L)] and S2 = [s2 (1), . . . , s2 (L)] present two correlated L-bit i.i.d binary source sequences. The correlation between those two sources are abstracted and modeled as binary symmetric channel. Pr[s1 ( j ) = s2 ( j )] = p (1 ≤ j ≤ L) presents the cross-over probability and the corresponding log-likelihood ratio (LLR) is L p = log[(1 − p)/ p]. At the transmitter, S1 and S2 are separately encoded by two LDPC codes. Let Nk denote the codeword length, then the code rate is rk = L/Nk , k = {1, 2}. Besides parity bits, only K information bits of S1 are transmitted through channel 1, meanwhile, the rest L − K information bits of S2 are transmitted through channel 2, when 0 ≤ K ≤ L. Hence, the rate pair of this D-JSCC system is (R1 , R2 ), where R1 = (N1 + K − L)/L and R2 = (N2 − K )/L (channel uses/source-bits).
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LYU et al.: RODS FOR LDPC CODES-BASED D-JSCC SYSTEM
Fig. 1.
Data frame structure and block diagram of D-JSCC system.
In this letter, binary phase shift keying (BPSK) modulation scheme is selected and the modulated signals are transmitted over AWGN channel. Let yk be the received signals from channel k = {1, 2}. Then the initial channel LLR is L ch,k = log(yk /2σk2 ), where σk2 is the noise variance, k = {1, 2}. At the receiver, joint LDPC decoder is applied which takes correlated source information as side information. Because the performance of D-JSCC system can be improved by recalculating side information [6], the whole decoding procedure is divided into two serial stages in this letter, that is, local and global iteration stages. At local iteration stage, a recovered codeword Cˆ is obtained. If the check equation Cˆ H T is established, local decoding stops, otherwise, local decoding continues to work until the maximum number of local iteration is reached. After local iteration stage, if both check equations Cˆ 1 H1T and Cˆ 2 H2T are established, the whole D-JSCC decoding procedure stops, otherwise, side information are recalculated at global iteration. The data frame structure and block diagram of this system are depicted in Fig. 1. L s,k ( j ), k = {1, 2}, is the side information, which can be calculated by following equation [2], [4]. 1 + exp(L p + L k ( j )) (1) L s,k ( j ) = log exp(L p ) + exp(L k ( j )) where L k ( j ) is the posteriori LLR coming from the j -th correlated source bits. Let L In,k ( j ) be the initial LLR of the variable node v j . If v j is just a parity variable node, then L In,k ( j ) = L ch,k ( j ); if v j is a source variable node, then L In,k ( j ) = L ch,k ( j ) + L s,k ( j ); and if v j is punctured source bit then L In,k ( j ) = L s,k ( j ), k = {1, 2}. One observes that the side information calculation plays an important role in joint decoder, and inaccurate side information can cause severe error propagation. Given L p , if the posteriori LLR L k , k = {1, 2}, is incorrect, the side information calculation is inaccurate. Hence, the performance of D-JSCC system can be improved by employing a decoding strategy, which can provide more accurate posteriori LLRs to calculate side information and suppress the negative effects of inaccurate side information. III. T HE P ROPOSED R ELIABILITY O RIENTED D ECODING S TRATEGY Let L v ( j, i ) present the LLR sent from v j to ci and L c (i, j ) denote the LLR transmitted in the opposite direction.
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N (v j ) denotes the set of the neighbor check nodes of v j and N (v j )\i is the set of the neighbor check nodes of v j excluding the i -th check node ci . N (ci ) and N (ci )\ j have similar definitions, respectively. L In ( j ) is the initial LLR of v j , L( j ) is the posteriori LLR of this node and the corresponding value at the l-th local iteration is L l ( j ). Let Uv ( j ) denote the unreliable scale of v j . The value of Uv ( j ) ∈ {0, 1, 2} is set by following criteria: 1) If v j is oscillating, that is sign(L l ( j )) = sign(L l−1 ( j )) and simultaneously sign(L l−1 ( j )) = sign(L l−2 ( j )), set Uv ( j ) = 2. 2) If criterion 1 is not satisfied and there exists ci ∈ N (v j ) having sign(L c (i, j )) = sign(L In ( j )), set Uv ( j ) = 1. 3) If two criteria listed above are not satisfied, set Uv ( j ) = 0. The variable node oscillation happening suggests that there are two or more cycles through this node, meanwhile, accurate and inaccurate messages arrive at it. Therefore, those oscillating nodes can be defined as the least reliable nodes. Criterion 2 suggests that variable nodes are not oscillating but that they have received error LLRs. In this moment, they are also treated as unreliable. From the viewpoint of decoding algorithm, those unreliable nodes (fulfill criteria 1 and 2) are bad for recovering correct codeword due to sending inaccurate messages. Learning from the URW-BP and VFAP-BP algorithms, the negative effects of error messages accumulation caused by existing short cycles can be reduced by multiplying reweighted factors, whose values are between 0 and 1. The whole updating rules are given by ⎡ ⎤ , i ) L ( j v ⎦ , (2) tanh L c (i, j ) = 2 tanh−1 ⎣ 2 j ∈N (ci )\ j β(i , j )L c (i , j ) + L In ( j ), (3) L v ( j, i ) = i ∈N (v j )\i
L( j ) =
β(i, j )L c (i, j ) + L In ( j ),
(4)
i∈N (v j )
where 0 ≤ β(i, j ) ≤ 1 is the reweighted factor. The value of β(i, j ) is determined by the structure properties of LDPC codes and the unreliable scale of L c (i, j ), which is defined as Uc (i, j ). From (2), the value of L c (i, j ) depends on ci received extrinsic LLRs, thus the value of Uc (i, j ) is determined by those LLRs. Taking the unreliable scale of v j into account, Uc (i, j ) = max(Uv ( j )), j ∈ N (ci )\ j . Let
dv,max
dc,max l−1 and ρ(x) = l−1 be the λ(x) = l=1 λl x l=1 ρl x polynomials of variable nodes and check nodes, respectively. The edge connectivity expectation is the first moment M E =
dv,max λl E[1/l] = l=1 l . Considering the connectivity expectation and the corresponding variance, the second moment
dv,max λl 2 E = E[1/l ] = l=1 is utilized. It can be easily l2 found that 0 < E ≤ 1. Therefore, the reweighted factor β(i, j ) is calculated by β(i, j ) = 1.0 − Uc (i, j )α
(5)
where the parameter α is set as α = E /2 to make 0 ≤ β(i, j ) ≤ 1. One observes that if L c (i, j ) has the lowest
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IEEE COMMUNICATIONS LETTERS, VOL. 21, NO. 11, NOVEMBER 2017
reliability, then β(i, j ) has minimum value (1−2α), vice versa. Since Uc (i, j ) is iteratively updated, the value of β(i, j ) varies. After updating all variable nodes, if the stopping rules are not satisfied, an extra local iteration, which is shown in lines 13-23 of Algorithm 2, will be performed on the group of most unreliable source variable nodes to correct inaccurate posteriori LLRs. Let A1 with g1 elements be the set of source variable nodes that fulfill the criterion 1, and A2 with g2 be the set of the source variable nodes which satisfy the criterion 2. Define the number of unsatisfied parity check equations of a variable node as P ≥ 0. After variable nodes update, the nodes in sets A1 and A2 are sorted by their P in descending order. Let B with g = |B| ≤ L/20 elements present the group of the most unreliable source nodes. If g1 ≥ g, then the first g nodes in A1 are picked out to form B. If g1 < g, all the nodes in A1 and the first (g − g1) nodes in set A2 are used to form B. Due to the reliability evaluation and extra local iteration performed on those nodes in B, RODS requires a little more complexity. After local decoding stage, the posteriori LLRs of all source bits and the set B are updated. Then the side information L s,k , k = {1, 2} can be calculated by (1). In order to further suppress error propagation, offset operation of the unreliable side information is performed during global iteration. If sk ( j ), k = {1, 2} belongs to B, the corresponding L s,k ( j ) is modified by L s,k ( j ) = L s,k ( j ) − sign(L k ( j ))α.
(6)
The key steps for the proposed RODS are described above. The two stages of RODS in pseudo-code are given by Algorithm 1 and Algorithm 2, respectively. Algorithm 1 Global Iteration 1: if stopping rules of global iteration are satisfied then 2: Finish the whole decoding procedure 3: else 4: Obtain the most unreliable source variable nodes set B 5: Calculate side information by using (1) 6: for every source bit s( j ) ∈ B do 7: Modify the side information by using (6) 8: end for 9: Operate Local Iteration; 10: end if
IV. S IMULATION R ESULTS In this section, the simulation results are presented to demonstrate the performance achieved by employing proposed decoding strategy for short LDPC codes based D-JSCC system. Three groups of protographs LDPC codes are used in this letter, which are obtained by progressive edgegrowth (PEG) algorithm based on base matrices shown in Fig. 2. The codes of groups A and B are derived from BkI , k = {1, 2} with lifting factors 50 and 100, respectively. The codes of group C are derived from BkI I , k = {1, 2} with lifting factor 64. As a result, the codeword length of groups A, B, and C are 500 bits, 1000 bits, and 1024 bits,
Algorithm 2 Local Iteration 1: Initialization: all L c = 0, all L v = L In and all Uv = 0; 2: for every check node ci and v j ∈ N (ci ) do 3: Calculate L c (i, j ) by using (2); 4: end for 5: for every variable node v j and ci ∈ N (v j ) do 6: Calculate L v ( j, i ) by using (3); 7: Calculate posteriori LLR of v j by using (5); 8: Update Uv ( j ); 9: end for 10: if stopping rules of local decoding are satisfied then 11: Finish Local Decoding Iteration; 12: else 13: for every v j ∈ B do 14: for every ci ∈ N (v j ) do 15: Calculate L c (i, j ) by using (2); 16: end for 17: for every ci ∈ N (v j ) do 18: Calculate L v ( j, i ) by using (3); 19: end for 20: Calculate posteriori LLR of v j by using (5); 21: Update Uv ( j ); 22: end for 23: Go back to line 2; 24: end if respectively. The maximum number of local iteration is 10 and the one of global iteration is 5. The bit error rate (BER) performance of D-JSCC system with different decoding algorithms over AWGN channel is depicted in Fig. 3, where the codes of group A are used. Fig. 3 shows that URW-BP(β = 1 − 2α), VFAP-BP, ROLBP algorithms and RODS can improve the performance of D-JSCC system at waterfall and error floor regions. Moreover, more significant gain can be obtained by using RODS, especially when the correlation between two distributed sources is low. The performance comparison between RODS with and without side information offset operation suggests that the offset operation can further improve the performance of D-JSCC system at waterfall region. However, as the value of E b /N0 increases, the improvement becomes slight. Those curves also demonstrate that NW-RBP algorithm is not suitable for D-JSCC system. NW-RBP algorithm prioritizes the update of a check node with the lowest reliability during each iteration. Since a group of source information bits are punctured in D-JSCC system, the messages sent from those source variable nodes to check nodes are lack of channel information. Therefore, prioritizing such neighbor check nodes leads to performance degradation. Similar phenomenon has been discussed in [10]. Fig. 4 shows the iteration behavior of D-JSCC system, where the codes of group A are used for p = 0.05 and E b /N0 = 5.0d B. Fig. 4(a) shows the mutual information (MI) between the source bits and corresponding LLRs, which is calculated by the method in [11]. The MI ascending curves show that RODS can provide more MI than BP algorithm, thereby having better performance and faster convergence speed. It can
LYU et al.: RODS FOR LDPC CODES-BASED D-JSCC SYSTEM
Fig. 2.
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The base matrices of employed protograph LDPC codes.
Fig. 5 shows the BER performance of D-JSCC system with different rate pairs for p = 0.05. In this simulation, LDPC codes which belong to groups B and C are used. These curves demonstrate that proposed RODS can still improve the performance of D-JSCC system with different rate pairs. V. C ONCLUSION
Fig. 3. The BER performance comparisons of D-JSCC system over AWGN channel. (Codes of group A, R1 = R2 = 13/14).
In order to improve the performance of the short LDPC codes based D-JSCC system, a reliability oriented decoding strategy (RODS) is proposed in this letter. By using reliability based dynamic reweighted updating operation and performing extra operations on those least reliable source nodes, RODS can have more accurate side information to aid in recovering source sequences. As a result, RODS outperforms other decoding algorithms at the aspects of BER performance and convergence speed with slight computation complexity increased. In future work, density evolution (DE) or extrinsic information transfer (EXIT) algorithms are used to theoretically evaluate the performance and further design protograph LDPC codes to improve the performance. R EFERENCES
Fig. 4. Iteration behavior of D-JSCC system. (E b /N0 = 5.0d B, p = 0.05).
Fig. 5. The BER performance comparisons of D-JSCC system over AWGN channel with different system rate pairs. ( p = 0.05).
be found that the MI curves can also be used to justify the choice of α. Fig. 4(b) depicts the convergence speed of algorithms. The curves illustrate that RODS has the fastest convergence speed.
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