Comment on Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes

Source Coding With Side Information Using List Decoding

The problem of source coding with side information (SCSI) is closely related to channel coding. Therefore, existing literature focuses on using the most successful channel codes namely, LDPC codes, turbo codes, and their variants, to solve this problem assuming classical unique decoding of the underlying channel code. In this paper, in contrast to classical decoding, we have taken the list decoding approach. We show that syndrome source coding using list decoding can achieve the theoretical limit. We argue that, as opposed to channel coding, the correct sequence from the list produced by the l…

An algebraic approach to source coding with side information using list decoding

Existing literature on source coding with side information (SCSI) mostly uses the state-of-the-art channel codes namely LDPC codes, turbo codes, and their variants and assume classical unique decoding. In this paper, we present an algebraic approach to SCSI based on the list decoding of the underlying channel codes. We show that the theoretical limit of SCSI can be achieved in the proposed list decoding based framework when the correlation between the source and side information is $q$-ary symmetric. We argue that, as opposed to channel coding, the correct sequence from the list produced by th…

乘积码覆盖空间译码的软输出

Soft-Output from Covered Space Decoding of Product Codes

本文提出覆盖空间软输出（SOCS）译码器，利用列表译码器探索的空间更准确地估计后验可靠性，在turbo乘积译码中相比Chase-Pyndiah译码获得高达0.25 dB的增益。

Joint Successive Cancellation List Decoding for the Double Polar codes

As a new joint source-channel coding scheme, the double polar (D-Polar) codes have been proposed recently. In this letter, a novel joint source-channel decoder, namely the joint successive cancellation list (J-SCL) decoder, is proposed to improve the decoding performance of the D-Polar codes. We merge the trellis of the source polar code and that of the channel polar code to construct a compound trellis. In this compound trellis, the joint source-channel nodes represent both of the information bits and the high-entropy bits. Based on the compound trellis, the J-SCL decoder is designed to recov…

Permutation Polynomial Interleavers: An Algebraic-Geometric Perspective

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are important because they admit analytical designs and simple, practical hardware implementation. The spread factor of an interleaver is a common measure for turbo coding applications. Maximum-spread interleavers are interleavers whose spread factors achieve the upper bound. An infinite sequence of quadratic permutation polynomials over integer rings that generate maximum-spread interleavers is presented. New properties of permutation polynomial interleavers are investigated from …

A Tree Search Method for Iterative Decoding of Underdetermined Multiuser Systems

Application of the turbo principle to multiuser decoding results in an exchange of probability distributions between two sets of constraints. Firstly, constraints imposed by the multiple-access channel, and secondly, individual constraints imposed by each users' error control code. A-posteriori probability computation for the first set of constraints is prohibitively complex for all but a small number of users. Several lower complexity approaches have been proposed in the literature. One class of methods is based on linear filtering (e.g. LMMSE). A more recent approach is to compute approximat…

Reduce the Complexity of List Decoding of Polar Codes by Tree-Pruning

Polar codes under cyclic redundancy check aided successive cancellation list (CA-SCL) decoding can outperform the turbo codes and the LDPC codes when code lengths are configured to be several kilobits. In order to reduce the decoding complexity, a novel tree-pruning scheme for the \mbox{SCL/CA-SCL} decoding algorithms is proposed in this paper. In each step of the decoding procedure, the candidate paths with metrics less than a threshold are dropped directly to avoid the unnecessary computations for the path searching on the descendant branches of them. Given a candidate path, an upper bound o…

Low-Latency Successive-Cancellation List Decoders for Polar Codes with Multi-bit Decision

Polar codes, as the first provable capacity-achieving error-correcting codes, have received much attention in recent years. However, the decoding performance of polar codes with traditional successive-cancellation (SC) algorithm cannot match that of the low-density parity-check (LDPC) or turbo codes. Because SC list (SCL) decoding algorithm can significantly improve the error-correcting performance of polar codes, design of SCL decoders is important for polar codes to be deployed in practical applications. However, because the prior latency reduction approaches for SC decoders are not applicab…

类极化码的近最优广义译码

Near-Optimal Generalized Decoding of Polar-like Codes

本文提出一种基于码本概率近似的广义译码框架，兼容所有SC类译码方法，在SCL译码下优于现有Forney广义译码近似，并使动态RM码在BLER和UER上超越CRC级联极化码。