Juntan Zhang

Shuffled iterative decoding

Shuffled versions of iterative decoding of low-density parity-check codes and turbo codes are presented. The proposed schemes have about the same computational complexity as the standard versions, and converge faster. Simulations show that the new schedules offer better performance/complexity tradeoffs, especially when the maximum number of iterations has to remain small.

A modified weighted bit-flipping decoding of low-density Parity-check codes

In this letter, a modified weighted bit-flipping decoding algorithm for low-density parity-check codes is proposed. Improvement in performance is observed by considering both the check constraint messages and the intrinsic message for each bit.

Shuffled belief propagation decoding

In this paper, we propose a shuffled version of the belief propagation (BP) algorithm for the decoding of low-density parity-check (LDPC) codes. We show that when the Tanner graph of the code is acyclic and connected, the proposed scheme is optimal in the sense of MAP decoding and converges faster (or at least no slower) than the standard BP algorithm. Interestingly, this new version keeps the computational advantages of the forward-backward implementations of BP decoding. Both serial and parallel implementations are considered. We show by simulation that the new schedule offers better performance/complexity trade-offs.

Two-dimensional correction for min-sum decoding of irregular LDPC codes

Two-dimensional (2-D) correction schemes are proposed to improve the performance of conventional min-sum (MS) decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization is presented to obtain the optimal 2-D factors. Both density evolution analysis and simulation show that the proposed method provides a comparable performance as belief propagation (BP) decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of BP decoding. With respect to conventional MS and 1-D normalized MS decodings, the 2-D normalized MS offers a better performance. The 2-D offset MS decoding exhibits a similar behavior.

Iterative Decoding With Replicas

Replica shuffled versions of iterative decoders for low-density parity-check (LDPC) codes and turbo codes are presented. The proposed schemes can converge faster than standard and plain shuffled approaches. Two methods, density evolution and extrinsic information transfer (EXIT) charts, are used to analyze the performance of the proposed algorithms. Both theoretical analysis and simulations show that the new schedules offer good tradeoffs with respect to performance, complexity, latency, and connectivity

Improved min-sum decoding of LDPC codes using 2-dimensional normalization

A two-dimensional post normalization scheme is proposed to improve the performance of conventional min-sum (MS) and normalized MS decoding of irregular low density parity check codes. An iterative procedure based on parallel differential optimization algorithm is presented to obtain the optimal two-dimensional normalization factors. Both density evolution analysis and specific code simulation show that the proposed method provides a comparable performance as belief propagation decoding while requiring less complexity. Interestingly, the new method exhibits a lower error floor than that of belief propagation decoding in the high SNR region. With respect to standard MS and one-dimensional normalized MS decodings, the two-dimensional normalized MS offers a considerably better performance.

Reduced latency iterative decoding of LDPC codes

Reduced latency versions of iterative decoders of low-density parity-check codes are analyzed in this paper. The proposed schemes converge faster than standard approaches. Two methods, density evolution and EXIT charts, are used to analyze the performance of the proposed algorithms. Both theoretical analysis and simulations show that the new schedules offer good performance versus complexity and latency trade-offs.

Low-Latency Decoding of EG LDPC Codes

We describe simple iterative decoders for low-density parity-check codes based on Euclidean geometries, suitable for practical very-large-scale-integration implementation in applications requiring very fast decoders. The decoders are based on shuffled and replica-shuffled versions of iterative bit-flipping (BF) and quantized weighted BF schemes. The proposed decoders converge faster and provide better ultimate performance than standard BF decoders. We present simulations that illustrate the performance versus complexity tradeoffs for these decoders. We can show in some cases through importance sampling that no significant error floor exists.

Reduced latency turbo decoding

Reduced latency versions of iterative decoding of turbo codes are analyzed in this paper. The proposed schemes converge faster than the standard and plain shuffled approaches. EXIT chart is used to analyze the performance of the proposed algorithms. Both theoretical analysis and simulation results show that the new schedules offer better performance/complexity trade-offs.

Mean field and mixed mean field iterative decoding of low-density parity-check codes

In this paper, the mean field (MF) and mixed mean field (MMF) algorithms for decoding low-density parity-check (LDPC) codes are considered. The MF principle is well established in statistical physics and artificial intelligence. Instead of using a single completely factorized approximated distribution as in the MF approach, the mixed MF algorithm forms a weighted average of several MF distributions as an approximation of the true posterior probability distribution. The MF decoding algorithm for linear block codes is derived and shown to be an approximation of the a posteriori probability (APP) decoding algorithm. The MF approach is then developed in the context of iterative decoding and presented as an approximation of the popular belief propagation decoding method. These results are extended to iterative decoding with the MMF algorithm. Simulation results show that the MF and MMF decoding algorithms yield a good performance-complexity tradeoff, especially when employed for decoding LDPC codes based on finite geometries.