A lower bound on the distance profile for convolutional codes

James L. Massey

Upper and lower bounds for feedback decoding and definite decoding minimum distances of binary convolutional codes

Dmitri V. Truhachev, Kamil Sh. Zigangirov, Daniel J. Costello

Existence type lower bounds on the free distance of periodically time-varying LDPC convolutional codes and on the minimum distance of tail-biting LDPC convolutional codes are derived. It is demonstrated that the bound on free distance of periodically time-varying LDPC convolutional codes approaches the bound on free distance of general (nonperiodic) time-varying LDPC convolutional codes as the period increases. The proof of the bound is based on lower bounding the minimum distance of corresponding tail-biting LDPC convolutional codes, which is of interest in its own right.

Karin Engdahl, Michael Lentmaier, Kamil Sh. Zigangirov

Stefan Höst, Rolf Johannesson, Kamil Sh. Zigangirov +1 more

Aolin Liu, Bowen Feng, Chulong Liang +3 more

A novel rate-profiling design is proposed for polarization-adjusted convolutional (PAC) codes under list decoding, adopting a path probability perspective. Inspired by the concepts of Hamming distance and Hamming weight, the concepts of path probability distance (PPD) and path probability weight (PPW) are innovatively introduced to measure the disparity between the erroneous paths and the correct path for PAC codes under probabilistic decoding. An in-depth analysis of the recursion of node log-likelihood ratios (LLRs) in the factor graph is conducted, elucidating the derivation of a lower bound on the PPW as a consequential outcome. Utilizing the concept of the PPW, a rate-profiling design algorithm is proposed to establish the reliability ranking for the bit-channels of PAC codes. Simulation results demonstrate that PAC codes employing the proposed rate-profiling exhibit advantages over alternative rate-profiling and other state-of-the-art polar coding schemes across various block lengths and code rates under short decoding list sizes.

Karin Engdahl, Dmitri V. Truhachev, Kamil Sh. Zigangirov