Modul:   MAT076  Neuchatel - St.Gallen - Zurich Seminar in Coding Theory and Cryptography

Overview of Classes of MDP Convolutional Codes and Their Erasure Decoding Algorithms

Vortrag von Yves Krähenbühl

Datum: 27.09.23  Zeit: 16.15 - 17.00  Raum: Y27H25

Convolutional codes are a class of codes particularly well-suited for data transmission over erasure channels, commonly used in multimedia traffic over the internet. This thesis compares three erasure decoding algorithms for convolutional codes: The forward and backward decoding algorithm, the low delay decoding algorithm for modules, and the low delay decoding algorithm for linear systems. Our primary focus is on comparing these algorithms in terms of their delays, computational complexities, and erasure recovery capabilities. Additionally, we discuss various classes of MDP convolutional codes, highlighting their advantageous properties in achieving an optimal performance with the three erasure decoding algorithms. Through two simulations, we assess the performance of the decoding algorithms over different erasure channel models simulating practical scenarios. In a first simulation, we evaluate the recovery capability of the algorithms using their respective optimal convolutional code classes and compare them with MDS linear block codes of the same rate. The results show that convolutional codes consistently match or even outperform MDS block codes over the different channel models. In a second simulation, we use longer received codewords relative to the largest sliding window of a convolutional code, revealing that the recovery process is influenced not only by the quantity of erasures but also by their distribution. Notably, early erasures have a minimal influence on the remainder of the decoding process. This thesis provides valuable insights into the selection and optimization of erasure decoding algorithms for convolutional codes, offering practical implications for multimedia data transmission over the internet.