System-theoretic properties of convolutional codes over rings

2001 ◽  
Vol 47 (6) ◽  
pp. 2256-2274 ◽  
Author(s):  
F. Fagnani ◽  
S. Zampieri
Keyword(s):  
Convolutional Codes ◽  
Codes Over Rings

The Study of Coded CPM Schemes

2012 ◽  
Vol 198-199 ◽  
pp. 1408-1412
Author(s):  
Lin Bo Su ◽  
Jian Hua Chen ◽  
Ying Peng Hu
Keyword(s):  
Fading Channels ◽  
Convolutional Codes ◽  
Continuous Phase ◽  
Coded Modulation ◽  
Superior Performance ◽  
Continuous Phase Modulation ◽  
Codes Over Rings ◽  
Constant Envelope ◽  
Modulation Schemes ◽  
Serially Concatenated

Continuous Phase Modulation (CPM) schemes belong to a class of constant-envelope digital modulation schemes, the constant-envelope nature of the CPM signals makes them robust for the nonlinear and fading channels, and very useful for the satellite and/or the mobile radio channels. Comparing to PSK modulation, CPM modulation can not only provide spectral economy, but also exhibit a “coding gain”. CPM can be decomposed into a Continuous Phase Encoder (CPE) followed by a Memoryless Modulator (MM), this allows many new coded modulation schemes of combination of convolutional encoder and CPM modulator to be possible, such as serially-concatenated CPM (SC-CPM), SC-CPM with Convolutional Codes over Rings, pragmatic CPM (P-CPM), Concatenation of convolutional endocder and extended CE（CCEC）, etc. Some simulations show that these new CPM schemes can offer superior performance.

scholarly journals Some structural properties of convolutional codes over rings

1998 ◽  
Vol 44 (2) ◽  
pp. 839-845 ◽  
Author(s):  
R. Johannesson ◽  
Zhe-Xian Wan ◽  
E. Wittenmark
Keyword(s):  
Structural Properties ◽  
Convolutional Codes ◽  
Codes Over Rings

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

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2962
Author(s):  
Ángel Luis Muñoz Muñoz Castañeda ◽  
Noemí DeCastro-García ◽  
Miguel V. Carriegos
Keyword(s):  
Coding Theory ◽  
Convolutional Codes ◽  
Codes Over Rings ◽  
Input State ◽  
First Order ◽  
Convolutional Coding ◽  
Artinian Rings ◽  
Base Ring ◽  
Order Representation ◽  
Classical Construction

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.

Convolutional codes over rings for CPFSK signalling

1994 ◽  
Vol 30 (11) ◽  
pp. 832 ◽  
Author(s):  
N.A. Ugrelidze ◽  
S.A. Shavgulidze
Keyword(s):  
Convolutional Codes ◽  
Codes Over Rings
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