Ting-Yi Wu

Low-complexity ML decoding for convolutional tail-biting codes

Recently, a maximum-likelihood (ML) decoding algorithm with two phases has been proposed for convolutional tailbiting codes. The first phase applies the Viterbi algorithm to obtain the trellis information, and then the second phase employs the algorithm A* to find the ML solution. In this work, we improve the complexity of the algorithm A* by using a new evaluation function. Simulations showed that the improved A* algorithm has over 5 times less average decoding complexity in the second phase when Eb/N0ges 4 dB.

An A*-Based Algorithm for Constructing Reversible Variable Length Codes with Minimum Average Codeword Length

Variable length codes (VLCs) are widely adopted in many compression standards due to their good coding efficiency on average codeword length. However, an inherent problem with a VLC is that an error of even one bit can cause serious error propagation and thus loss of synchronization at the receiver, which would lead to a series of non-correctly decoded symbols. Reversible variable length codes (RVLCs) were introduced to significantly mitigate this phenomenon. In this work, a method to find an optimal RVLC in terms of the minimum average codeword length is first formulated as a tree-searching problem, and then, instead of performing an exhaustive search, an A*-based construction algorithm is proposed to find an optimal RVLC. The proposed algorithm has been applied to several benchmarks for sources and has found respective optimal symmetric and asymmetric RVLCs.

Priority-first search decoding for convolutional tail-biting codes

Due to rapid interest on the applications of convolutional tail-biting to communication systems, several suboptimal algorithms have been proposed to achieve near-optimal Word error rate (WER) performances with circular Viterbi decoding approach. Among them, the wrap-around Viterbi algorithm (WAVA) proposed is the one with least decoding complexity. Very recently, a maximum likelihood (ML) decoding algorithm has been proposed. The scheme has two phases. The Viterbi algorithm is applied to the trellis of the convolutional tail-biting code and the information obtained in the first phase is used by algorithm A*, which is performed to all subtrellises, in the second phase. In this work, a new two-phase ML decoding algorithm is proposed. From the simulation results for the (2, 1, 12) convolutional tail-biting code, the proposed algorithm has 16 times less average decoding complexity in the second phase when compared to the one using algorithm A* and 15123 times less than that of the WAVA, respectively, when SNRb=4 dB.

Reliability-Based Decoding for Convolutional Tail-Biting Codes

In this work, we proposed a reliability-based enhancement for the decoding of convolutional tail-biting codes (CTBC) from the observations that the decoding does not have to start from the beginning of the received vector, and that the reliability of the received vector can be used to determine a good starting position of the decoding process. Simulations show that our reliability-based enhancement can be used together with existing decoding algorithms of the CTBC to improve either their error rate or complexity.

Soft-decision priority-first decoding algorithms for variable-length error-correcting codes

Joint source-channel decoding has recently received extensive attention due to the rise in the applications of multimedia wireless communication. Based on a code trellis rather than on a code tree, this work presents a maximum a posteriori (MAP) soft-decision priority-first decoding algorithm and its approximations for variable-length error-correcting codes. Simulation results indicate that for the code with average codeword length 6.269 bits and free distance 3, under moderate signal-to-noise ratio, one of the proposed algorithms almost reaches the lowest decoding complexity, and has nearly the same performance on symbol error probability as the MAP decoding.

On the Design of Variable-Length Error-Correcting Codes

A joint source-channel coding problem that combines the efficient compression of discrete memoryless sources with their reliable communication over memoryless channels via binary prefix-free variable-length error-correcting codes (VLECs) is considered. Under a fixed free distance constraint, a priority-first search algorithm is devised for finding an optimal VLEC with minimal average codeword length. Two variations of the priority-first-search-based code construction algorithm are also provided. The first one improves the resilience of the developed codes against channel noise by additionally considering a performance parameter Bdfree without sacrificing optimality in average codeword length. In the second variation, to accommodate a large free distance constraint as well as a large source alphabet such as the 26-symbol English data source, the VLEC construction algorithm is modified with the objective of significantly reducing its search complexity while still yielding near-optimal codes. A low-complexity sequence maximum a posteriori (MAP) decoder for all VLECs (including our constructed optimal code) is then proposed under the premise that the receiver knows the number of codewords being transmitted. Simulations show that the realized optimal and suboptimal VLECs compare favorably with existing codes in the literature in terms of coding efficiency, search complexity and error rate performance.

On the construction and MAP decoding of optimal variable-length error-correcting codes

In this paper, we present a novel algorithm that guarantees of finding a variable-length error-correcting code (VLEC) with minimal average codeword length for a fixed free distance dfree. We also propose a low complexity maximum a posterior (MAP) decoding algorithm for our codes under the premise that the receiver knows the number of codewords being transmitted. The resulting VLEC provides significant gains over other codes from the literature. When compared with separate source-channel tandem codes with identical dfree, such as a tandem code consisting of a Huffman source code concatenated with a (2, 1, 4) tail-biting convolutional channel code, our system has only a 0.3 dB performance loss at a bit error rate of 10−5 while requiring significantly less decoding complexity.

A Low-Complexity Maximum-Likelihood Decoder for Tail-Biting Convolutional Codes

Due to the growing interest in applying tail-biting convolutional coding techniques in real-time communication systems, fast decoding of tail-biting convolutional codes has become an important research direction. In this paper, a new maximum-likelihood decoder for tail-biting convolutional codes is proposed. It is named bidirectional priority-first search algorithm (BiPFSA) because priority-first search algorithm has been used both in forward and backward directions during decoding. Simulations involving the antipodal transmission of (2, 1, 6) and (2, 1, 12) tail-biting convolutional codes over additive white Gaussian noise channels shows that BiPFSA not only has the least average decoding complexity among the state-of-the-art decoding algorithms for tail-biting convolutional codes but can also provide a highly stable decoding complexity with respect to growing information length and code constraint length. More strikingly, at high SNR, its average decoding complexity can even approach the ideal benchmark complexity, obtained under a perfect noise-free scenario by any sequential-type decoding. This demonstrates the superiority of BiPFSA in terms of decoding efficiency.

An Efficient Tree Search Algorithm for the Free Distance of Variable-Length Error-Correcting Codes

We propose an efficient tree search algorithm for determining the free distance of variable-length error-correcting codes (VLECs). A main idea behind the algorithm is to structure all pairs of code word-concatenated sequences as a tree, in which we seek the pair of sequences that determine the free distance. In order to speed up the algorithm, we establish constraints that do not compromise optimality in determining the free distance. Experimental results on VLECs algorithmically constructed for the English alphabet show that our algorithm requires a considerably smaller number of bitwise distance computations and covers a much smaller number of tree nodes than Dijkstra’s algorithm operating over the pairwise distance graph while being a hundred times faster in terms of execution time.

The modified wrap-around Viterbi algorithm for convolutional tail-biting codes

Recently, two near-optimal decoding algorithms [Shao, R.Y., Lin, S., and Fossorier, M.P.C., 2003. Two decoding algorithms for tailbiting codes. IEEE transactions on communications, 51 (10), 1658–1665; Krishnan, K.M. and Shankar, P., 2006. Approximate linear time ML decoding on tail-biting trellises in two rounds. In IEEE international symposium on information theory, Seattle, WA, USA, pp. 2245–2249] have been proposed for convolutional tail-biting codes. Both algorithms iterate the Viterbi algorithm twice, but use different metrics in the second iteration. Simulations showed that the latter algorithm (Krishnan and Shankar 2006) improved on the earlier one (Shao et al. 2003) in word error rates at the price of additional storage consumption. In this work, we prove that with a proper modification to the earlier one, the two algorithms can be made to have exactly the same survivor path at each state in the trellis, and hence are equivalent in error performance. One can consequently adopt the modified algorithm to alleviate the need for extra storage consumption of the later algorithm and, at the same time, achieve equally good performance.