Abstract
The structural properties of a noncoherent coded system, which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection, is presented in this second part of a two-part paper, where the performance analysis was provided in Part I. These convolutional codes are referred to as nd-convolutional codes and they provide a general framework for various noncoherent coding systems, including differential systems, for several practical models of the carrier phase. The exponential rate in which the error probability decays to zero, derived in Part I of the paper, is used here to obtain the free equivalent distance of nd-codes, which is the single parameter dominating the error performance at large signal-to-noise ratios. The free equivalent distance is upper-bounded by the free nd-distance, which constitutes a more convenient and practical parameter to work with, and it is the basis for a computer search for optimal nd-codes. The resultant codes of the computer search are compared to codes which are optimal for coherent detection, and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd-distance. The ambiguity problem, inherent to noncoherent systems, is also treated in this paper in the general framework of nd-catastrophic codes, and necessary and sufficient conditions for catastrophic error propagation are identified.
| Original language | English |
|---|---|
| Pages (from-to) | 576-589 |
| Number of pages | 14 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 43 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1997 |
| Externally published | Yes |
Bibliographical note
Funding Information:Manuscript received June 30, 1995; revised May 16, 1996. This work was performed at the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, and was supported in part under the Chief Scientist Grant, Ministry of Communications. The material in this paper was presented in part at the ISSSE Symposium, Paris, France, July 1992, and at the 1993 International Symposium on Information Theory, San Antonio, TX, January 1993.
Funding
Manuscript received June 30, 1995; revised May 16, 1996. This work was performed at the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, and was supported in part under the Chief Scientist Grant, Ministry of Communications. The material in this paper was presented in part at the ISSSE Symposium, Paris, France, July 1992, and at the 1993 International Symposium on Information Theory, San Antonio, TX, January 1993.
| Funders | Funder number |
|---|---|
| Ministry of Communications | |
| Technion-Israel Institute of Technology, Haifa |
Keywords
- Catastrophic error propagation
- Differential detection
- Free distance
- Multiple symbol detection
- Nd-convolutional codes
- Nd-distance