One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

This paper presents a successive cancellation (SC) decoding of polar codes modified for insertion/deletion/substitution (IDS) error channels, in which insertions and deletions are described by drift values. The recursive calculation of the original SC decoding is modified to include the drift values as stochastic variables. The computational complexity of the modified SC decoding is O (D3) with respect to the maximum drift value D, and O (N log N) with respect to the code length N. The symmetric capacity of polar bit channel is estimated by computer simulations, and frozen bits are determined according to the estimated symmetric capacity. Simulation results show that the decoded error rate of polar code with the modified SC list decoding is lower than that of existing IDS error correction codes, such as marker-based code and spatially-coupled code.

Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.

In this paper we look at the serial concatenation of short linear block codes with a rate-1 recursive convolutional encoder, with a goal of designing high-rate codes with low error floor. We observe that under turbo-style decoding the error floor of the concatenated codes with extended Hamming codes is due to detectable errors in many cases. An interleaver design addressing this is proposed in this paper and its effectiveness is verified numerically. We next examine the use of extended BCH codes of larger minimum distance, resulting in an improved weight spectrum of the overall code. Reduced complexity list decoding is used to decode the BCH codes in order to obtain low decoding complexity for a negligible loss in performance.

List decoding is a process by which a list of decoded words is output instead of one. This works for a larger noise threshold than the traditional algorithms. Under some circumstances it becomes useful to be able to find out the actual message from the list. List decoding is assumed to be successful, meaning, the sent message features in the decoded list. This problem has been considered by Guruswami. In Guruswami's work, this disambiguation is done by sending supplementary information through a costly, error-free channel. The model is meaningful only if the number of bits of side information required is much less than the message size. But using deterministic schemes one has to essentially send the entire message through the error free channel. Randomized strategies for both sender and receiver reduces the required number of bits of side information drastically. In Guruswami's work, a Reed-Solomon code based hash family is used to construct such randomized schemes. The scheme with probability utmost ε reports failure and returns the whole list. The scheme doesn't output a wrong message. Also, in Guruswami's work some theoretical bounds have been proved which lower bound the bits of side information required. Here we examine whether the gap between the theoretical bounds and existing schemes may be narrowed. Particularly, we use the same scheme as in Guruswami's work, but use hash families based on Hermitian curve and function fields of Garcia-Stichtenoth tower and analyze the number of bits of side information required for the scheme.

This paper presents an iterative algorithm for decoding product codes based on syndrome decoding of component codes. This algorithm is devised to achieve an effective trade-off between error performance and decoding complexity. A simplified list decoding algorithm, which uses a modified syndrome decoding method, for linear block codes is devised to deliver soft outputs for iterative decoding of product codes. By adjusting the size of the list, the decoder can achieve a proper trade-off between decoding complexity and performance. Compared to the other iterative decoding algorithms for product codes, the proposed algorithm has lower complexity while offers at least the same performance, which is demonstrated by analyses and simulations. The proposed algorithm has been simulated for BPSK and 16-QAM modulations over both the additive white Gaussian noise (AWGN) and Raleigh fading channels. This paper also presents an efficient scheme for applying product codes and their punctured versions. This scheme can be implemented with variable packet size and channel data block.