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Section Daily Prep 22
Today we will continue our discussion of cyclic codes and look at a particular decoding algorithm for them.
Subsection Learning Objectives
Subsubsection Basic Learning Objectives
Objectives
Before our class meeting, you should use the resources below to be able to learn the following. You should be reasonably fluent with these; we’ll answer some questions on them in class but not reteach them in detail.
Compute generator matrices for cyclic codes of the form
\((R \mid I_k)\) and parity-check matrices of the form
\((I_{n-k} \mid -\transpose{R})\text{.}\)
State and apply the result that we can choose a parity-check matrix so that the syndrome polynomial for a received word is the remainder on dividing the received polynomial by the generator.
Subsubsection Advanced Learning Objectives
Objectives
During our class meeting, we will work on learning the following. Fluency with these is not expected or required before class.
Derive the error-trapping algorithm for cyclic codes and the burst-error-trapping algorithm for cyclic codes.
Apply these algorithms to decoding problems for cyclic codes.
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Vanstone & van Oorschot, Sections 5.5-5.8, pp. 161-180
Figure 71. Reference Video for Cyclic Code Matrices
Subsection Important Terms
