A lower bound on the minimum Euclidean distance of trellis-coded modulation schemes
Abstract
A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity. The bound is used to compare trellis codes combined with phase-shift keying, pulse amplitude modulation, and quadrature amplitude-shift keying modulation. This random coding bound is the first lower bound on the free distance of trellis codes, is tighter than any upper bound for large constraint lengths, and predicts the asymptotic performance of TCM when the complexity of the code becomes large. The bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length.
- Publication:
-
IEEE Transactions on Information Theory
- Pub Date:
- September 1988
- Bibcode:
- 1988ITIT...34.1011R
- Keywords:
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- Bandwidth;
- Channels (Data Transmission);
- Modulation;
- Phase Shift Keying;
- Pulse Communication;
- Signal To Noise Ratios;
- Binary Codes;
- Convolution Integrals;
- Pulse Amplitude Modulation;
- Satellite Communication;
- Telephones;
- Communications and Radar