List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Low density parity check matrices for coding of correlated sources

Abstract: Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and a coding theorem of parity-check codes for general channels is proved.

Fast Sparse Superposition Codes Have Near Exponential Error Probability for $R

Abstract: For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. In a previous paper, we investigated decoding using the optimal maximum-likelihood decoding scheme. Here, a fast decoding algorithm, called the adaptive successive decoder, is developed. For any rate R less than the capacity C, communication is shown to be reliable with nearly exponentially small error probability. Specifically, for blocklength n, it is shown that the error probability is exponentially small in n/logn.

A parallel decoding scheme for turbo codes

Abstract: The recursive computations in the MAP-based decoding of turbo codes usually introduce a significant amount of decoding delay. In this paper, we present a method for reducing the decoding delay by means of segmenting a block into several sub-blocks, which are partially overlapped. The proposed sub-block segmentation scheme allows for the parallel decoding of each component code by using several sub-block decoders. The number of steps for the recursive computations in each sub-block decoder is reduced to O(N/W), where W is the number of segmented sub-blocks. The decoding delay is approximately one-Wth that of a conventional MAP-based turbo-coding system. The cost paid is a slight degradation in bit error rate performance and a reasonable increase in hardware complexity.

Soft-output decoding algorithms for continuous decoding of parallel concatenated convolutional codes

Abstract: We propose new decoding algorithms to be embedded in the iterative decoding strategy of parallel concatenated convolutional codes. They are derived from the optimum maximum-a-posteriori algorithm and permit a continuous decoding of the coded sequence without requiring trellis termination of the constituent codes. Two basic versions of the continuous algorithm and their suboptimum simplifications are described. Simulation results refer to the applications of the new algorithms to a highly efficient rate 1/3 concatenated code; they show performance only 0.6 dB worse than the Shannon limit.

Design of Length-Compatible Polar Codes Based on the Reduction of Polarizing Matrices

Abstract: Length-compatible polar codes are a class of polar codes which can support a wide range of lengths with a single pair of encoder and decoder. In this paper we propose a method to construct length-compatible polar codes by employing the reduction of the 2n × 2n polarizing matrix proposed by Arikan. The conditions under which a reduced matrix becomes a polarizing matrix supporting a polar code of a given length are first analyzed. Based on these conditions, length-compatible polar codes are constructed in a suboptimal way by codeword-puncturing and information-refreezing processes. They have low encoding and decoding complexity since they can be encoded and decoded in a similar way as a polar code of length 2n. Numerical results show that length-compatible polar codes designed by the proposed method provide a performance gain of about 1.0 - 5.0 dB over those obtained by random puncturing when successive cancellation decoding is employed.