A wide-sense time-invariant block code in its parity check matrix exhibits more than one parity check polynomial periodically repeating. Quasi-cyclic codes are revisited from this point of view. Reordered forms of quasi-cyclic codes are treated. Shortening or lengthening, with respect to the quasi-cyclic condition, are possible here only with steps of integer periods. The concept of code duality is extended. Code puncturation is described for quasi-cyclic codes. Constant-length shortening and constant-length puncturation are dual operations by which an information symbol is transformed into a control symbols and vice versa. Modified lengthening and modified H-extension are discussed also for quasi-cyclic codes. Encoder circuits, state diagrams and trellises are finally outlined.
LDPC Code Parity Check Code Word Cyclic Code Convolutional Code
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