Decoding Aspects of Product Convolutional Codes and Guaranteeing Product Distance

James L. Massey

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

Alexander Barg, Gilles Zémor

We introduce a MinSum-based list decoder for product codes and analyze its performance. We show that it can guarantee successful list decoding for decoding radii that lie above half the code's minimum distance.

Nguyen Thi Hong Nhung, Pham Xuan Nghia, The Cuong Dinh +2 more

Lijuan Xing, Zhuo Li, Bai Bao-Ming +2 more

The research on quantum convolutional codes is aimed at protecting a flow of information over long distance communications. The polynomial representation of a quantum state is defined. Based on the Calderbank-Shor-Steane(CSS)-type construction of quantum codes, a new method for encoding and decoding of CSS-type quantum convolutional codes is presented and corresponding networks are described. The basis state of the code is transformed into the product of an information polynomial by the generator polynomial. Then networks can be realized by operations of polynomial multiplication. Finally, inspired by classical convolutional decoding idea, a quantum Viterbi algorithm with linear complexity is put forward.

Kamil Sh. Zigangirov, Harro Osthoff

Ferdinand Blomqvist