Maximum likelihood (ML) decoding of linear block codes can be considered as an integer linear programming (ILP). Since it is an NP-hard problem in general, there are many researches about the algorithms to approximately solve the problem. One of the most popular algorithms is linear programming (LP) decoding proposed by Feldman et al. LP decoding is based on the LP relaxation, which is a method to approximately solve the ILP corresponding to the ML decoding problem. Advanced algorithms for solving ILP (approximately or exactly) include cutting-plane method and branch-and-bound method. As applications of these methods, adaptive LP decoding and branch-and-bound decoding have been proposed by Taghavi et al. and Yang et al., respectively. Another method for solving ILP is the branch-and-cut method, which is a hybrid of cutting-plane and branch-and-bound methods. The branch-and-cut method is widely used to solve ILP, however, it is unobvious that the method works well for the ML decoding problem. In this paper, we show that the branch-and-cut method is certainly effective for the ML decoding problem. Furthermore the branch-and-cut method consists of some technical components and the performance of the algorithm depends on the selection of these components. It is important to consider how to select the technical components in the branch-and-cut method. We see the differences caused by the selection of those technical components and consider which scheme is most effective for the ML decoding problem through numerical simulations.

This paper describes a least complex, high speed decoding method named multi-stage threshold decoding (MTD-DR). Each stage of MTD-DR is formed by the traditional threshold decoder with a special shift register, called difference register (DR). After flipping each information bit, DR helps to shorten the Hamming and the Euclidian distance between a received word and the decoded codeword for hard and soft decoding, respectively. However, the MTD-DR with self-orthogonal convolutional codes (SOCCs), type 1 in this paper, makes an unavoidable error group, which depends on the tap connection patterns in the encoder, and limits the error performance. This paper introduces a class of SOCCs type 2 which can breakdown that error group, as a result, MTD-DR gives better error performance. For a shorter code (code length = 4200), hard and soft decoding MTD-DR achieves 4.7 dB and 6.5 dB coding gain over the additive white Gaussian noise (AWGN) channel at the bit error rate (BER) 10-5, respectively. In addition, hard and soft decoding MTD-DR for a longer code (code length = 80000) give 5.3 dB and 7.1 dB coding gain under the same condition, respectively. The hard and the soft decoding MTD-DR experiences error flooring at high Eb/N0 region. For improving overall error performance of MTD-DR, this paper proposes parity check codes concatenation with soft decoding MTD-DR as well.

For decoding non-binary low-density parity-check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, the computations required at check nodes in the Log-SP algorithms are computationally intensive. What is worth, check nodes usually have higher degree than variable nodes. As a result, most of the time for decoding is used for check node computations, which leads to a bottleneck effect. In this paper, we propose a Log-SP algorithm in the Fourier domain. With this algorithm, the role of variable nodes and check nodes are switched. The intensive computations are spread over lower-degree variable nodes, which can be efficiently calculated in parallel. Furthermore, we develop a fast calculation method for the estimated bits and syndromes in the Fourier domain.

This letter proposes extended single parity check product codes and presents their empirical performances on a Gaussian channel by belief propagation (BP) decoding algorithm. The simulation results show that the codes can achieve close-to-capacity performance in high coding rate. The code of length 9603 and of rate 0.96 is only 0.77 dB away from the Shannon limit for a BER of 10-5.

In this paper, we derive a lower bound on the minimum decoding delay for convolutional network codes, which provides us with a guide line in the performance of decoding delay for convolutional network code decoders. The lower bound can be achievable by the sequential decoder introduced by E. Erez and F. Feder. Then we discuss the relationship between the network topology and the minimum decoding delay. Finally, we illustrate our results by an example.

A novel turbo coded modulation scheme, called the turbo-APPM, for deep space optical communications is proposed. The proposed turbo-APPM is a serial concatenation of turbo codes, an accumulator and a pulse position modulation (PPM), where turbo codes act as an outer code while the accumulator and the PPM act together as an inner code. The generator polynomial and the puncturing rule for generating turbo codes are chosen to lower the bit error rate. At the receiver, the joint iterative decoding is performed between the inner decoder and the outer turbo decoder. In the outer decoder, local iterative decoding for turbo codes is conducted. Simulation results are presented showing that the proposed turbo-APPM outperforms all previously proposed schemes such as LDPC-APPM, RS-PPM and SCPPM reported in the literature.

A continuous belief propagation (BP) decoding algorithm for a hybrid automatic repeat request (ARQ) system is proposed in this paper. The proposed continuous BP decoding algorithm utilizes the extrinsic information generated in the last iteration of the previous transmission for a continuous progression of the decoding through retransmissions. This allows the continuous BP decoding algorithm to accelerate the decoding convergence for codeword determination, especially when the number of retransmissions is large or a currently combined packet has punctured nodes. Simulation results verify the effectiveness of the proposed continuous BP decoding algorithm.

An improved soft-input soft-output (SISO) minimum mean-squared error (MMSE) detection method is proposed for joint coding and precoding OFDM systems under imperfect channel estimation. Compared with the traditional mismatched detection which uses the channel estimate as its exact value, the signal model of the proposed detector is more accurate and the influence of channel estimation error (CEE) can be effectively mitigated. Simulations indicate that the proposed scheme can improve the bit error rate (BER) performance with fewer pilot symbols.

This letter investigates the space-time block codes from quasi-orthogonal design as a tradeoff between high transmission rate and low decoding complexity. By studying the role orthogonality plays in space-time block codes, upper bound of transmission rate and lower bound of decoding complexity for quasi-orthogonal design are claimed. From this point of view, novel algorithms are developed to construct specific quasi-orthogonal designs achieving these bounds.

A (k,δ,ε)-locally decodable code C:Fqn FqN is an error-correcting code that encodes =(x1,x2,...,xn) ∈ Fqn to C() ∈ FqN and has the following property: For any ∈ FqN such that d(,C()) ≤ δ N and each 1 ≤ i ≤ n, the symbol xi of can be recovered with probability at least 1-ε by a randomized decoding algorithm looking at only k coordinates of . The efficiency of a (k,δ,ε)-locally decodable code C:Fqn FqN is measured by the code length N and the number k of queries. For a k-query locally decodable code C:Fqn FqN, the code length N was conjectured to be exponential of n, i.e., N=exp(nΩ(1)), however, this was disproved. Yekhanin [In Proc. of STOC, 2007] showed that there exists a 3-query locally decodable code C:F2n F2N such that N=exp(n1/log log n) assuming that infinitely many Mersenne primes exist. For a 3-query locally decodable code C:Fqn FqN, Efremenko [ECCC Report No.69, 2008] further reduced the code length to N=exp(nO((log log n/ log n)1/2)), and in general showed that for any integer r>1, there exists a 2r-query locally decodable code C:Fqn FqN such that N=exp(nO((log log n/ log n)1-1/r)). In this paper, we will present improved constructions for query-efficient locally decodable codes by introducing a technique of "composition of locally decodable codes," and show that for any integer r>5, there exists a 9 2r-4-query locally decodable code C:Fqn FqN such that N=exp(nO((log log n/ log n)1-1/r)).

In order to reduce the iterative decoding delay of convolutional turbo codes, this paper presents a concurrent decoding algorithm for the hardware implementation of turbo convolutional decoders. Different than a general turbo code, the hardware turbo decoder based on the proposed algorithm can update the priori information of message for each component code in a bit-by-bit manner as soon as it is generated by the other component code. The two component codes in a turbo code can thus be decoded concurrently, by using a single MAP decoder, subsequently reducing the decoding latency by approximately half while maintaining the bit error rate performance and a comparable hardware complexity, as a general turbo decoder.

An entropy decoding engine plays an important role in modern multimedia decoders. Previous researches that focused on the decoding performance paid a considerable attention to only one parameter such as the data parsing speed, but they did not consider the performance caused by a table configuration time and memory size. In this paper, we developed a novel method of entropy decoding based on the two step group matching scheme. Our approach achieves the high performance on both data parsing speed and configuration time with small memory needed. We also deployed our decoding scheme to implement an entropy decoding processor, which performs operations based on normal processor instructions and VLD instructions for decoding variable length codes. Several extended VLD instructions are prepared to increase the bitstream parsing process in modern multimedia applications. This processor provides a solution with software flexibility and hardware high speed for stand-alone entropy decoding engines. The VLSI hardware is designed by the Language for Instruction Set Architecture (LISA) with 23 Kgates and 110 MHz maximum clock frequency under TSMC 0.18 µm technology. The experimental simulations revealed that proposed processor achieves the higher performance and suitable for many practical applications such as MPEG-2, MPEG-4, H.264/AVC and AAC.

In this paper network coding based relay for multi-access channel is studied. In the system, two nodes send messages to a common access point (AP). A relay assists the two nodes by forwarding a network coded version of the messages. The AP performs joint channel and network decoding to recover the two original messages from three received signals. Two schemes, soft network coding (SoftNC) and turbo network coding (TurboNC), both focusing on bitwise exclusive or (XOR) based network coding, are proposed to salvage messages from erroneous signals. SoftNC is simple and backward compatible with existing protocol stack of wireless networks, and reduces packet errors by maximal ratio combining (MRC). TurboNC improves channel efficiency by letting the relay node transmit only parity check bits of the interleaved XORed message, where reliability is retained by iterative decoding. Simulation results show that compared with the network-layer path diversity scheme, both SoftNC and TurboNC greatly improve the reliability, and TurboNC also achieves a much higher throughput. The proposed schemes are suitable for improving the performance of wireless local area networks (WLAN).

Two decoding procedures combined with a belief-propagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after the BP decoding algorithm terminates. We derive a condition that our decoding algorithms can correct an erased bit which is uncorrectable by the BP decoding algorithm. We show by simulation results that the performance of our decoding algorithms is enhanced compared with that of the BP decoding algorithm with little increase of the decoding complexity.

In the modern day, MPEG-4 image compression technique have been commonly applied in various indoor wireless communication systems. The efficient system design mostly relies on the joint source channel coding algorithms, which aim to reduce the complexity of channel coding process, while maintaining the quality of the receiving images. In this paper, we design the MAP source-controlled channel decoders with both random and semirandom interleavers for Rician slow flat block-fading channels. The MAP-Viterbi decoder employs the residual redundancy from zerotree symbol sequences of MPEG-4 HFS packets. The interleaving processes are done after the overall channel coding process to combat the block-fading effects. The computer simulations summarize the system performance in terms of average WER and PSNR (dB). With the interleavers, the significant improvement in PSNR of about 15-17 dB is obtained for both ML and MAP decoding. Also in many cases, we obtain more improvement of about 0.2-0.4 dB for using MAP decoding with the interleavers.

We propose an iterative channel decoding scheme for two or more multiple correlated sources. The correlated sources are separately turbo encoded without knowledge of the correlation and transmitted over noisy channels. The proposed decoder exploits the correlation of the multiple sources in an iterative soft decision decoding manner for joint detection of each of the transmitted data. Simulation results show that achieved performance for the more than two sources is also close to the Shannon and Slepian-Wolf limit and large additional SNR gain is obtained in comparison with the case of two sources. We also verify through simulation that no significant penalty results from the estimation of the source correlation in the decoding process and the code with a low error floor achieves good performance for a large number of the correlated sources.

We propose a complexity-reducing algorithm for serial scheduled min-sum decoding that reduces the number of check nodes to process during an iteration. The check nodes to skip are chosen based on the reliability, a syndrome and a log-likelihood-ratio (LLR) value, of the incoming messages. The proposed algorithm is evaluated by computer simulations and shown to reduce the decoding complexity about 20% compared with a conventional serial scheduled min-sum decoding with small fractional decibel degradation in error correction performance.

A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.

In this letter, we analyze the convergence speed of layered decoding of block-type low-density parity-check codes and verify that the layered decoding gives faster convergence speed than the sequential decoding with randomly selected check node subsets. Also, it is shown that using more subsets than the maximum variable node degree does not improve the convergence speed.

An improved iterative minimum mean-squared error (MMSE) channel estimation method is proposed for joint coding and precoding OFDM systems. Compared with the traditional simplified estimator, the proposed scheme provides higher estimation quality with slight complexity increment at low signal-to-noise ratio (SNR) values. The performance of the iterative receiver including the proposed estimator approaches that of the perfect MMSE estimator without any simplification.