Minimal State-Space Representation of Convolutional Product Codes

Climent, Joan‐Josep; Napp, Diego; Pinto, Raquel; Requena, Verónica

doi:10.3390/math9121410

Cited by 1 publication

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References 42 publications

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“…The case we are interested in is that of submodules and I/S/O representations. I/S/O representations are useful because, among other reasons, they allow one to construct convolutional codes with desirable properties (such as observability and good distances), to define (algebraic) decoding algorithms, to study concatenated convolutional codes, and to study finite support 2D convolutional codes, periodically time-invariant convolutional codes and product convolutional codes ( [11][12][13][14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

2021

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In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

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