A New Approach to Construction and Decoding of Linear Block Codes Based on Polar Codes

Abstract

In the field of channel coding theory, there are two main branches. The first is related to the design and construction of codes capable of facilitating identification of errors at the receiver despite potential alterations during transmission; this is known as the encoding operation. The second branch focuses on developing mechanisms for correcting errors caused by the transmission channel, by devising valid and suitable algorithms; this is known as the decoding operation. The authors have delved into both aspects. In the first part, a novel method for constructing good linear codes is studied. It is based on the Hadamard matrix, which shares the same structure as the kernel of polar codes, and on the generator matrix of several existing linear codes. In the second part, a new decoding algorithm is proposed. This involves adapting the SSCL polar code decoder to decode the codes designed in the first part, as well as some of the most well-known block codes.