On the symmetric information rate of CPM in the finite blocklength regime

Continuous phase modulation (CPM) is a family of bandwidth-efficient signaling schemes with memory. In this paper we introduce a simulation-based method to compute a lower bound, namely the dependence testing (DT) bound, on the maximum achievable rate of general CPM schemes under finite blocklength, probability of error, and equiprobable input distribution constraints. The proposed method utilizes a posteriori probabilities (APPs) of the state transitions on the trellis that models the CPM modulator. The bound on the maximum achievable rate is then used to lower bound the spectral efficiency of CPM schemes under the finite blocklength constraint. For the numerical results, we focus on minimum-shift keying (MSK) modulation, and compute the DT bound for MSK as a function of the signal-to-noise ratio (SNR). We simulate a serially concatenated convolutional code (SCCC) using MSK as the inner code, which performs within 1.1 dB of the DT bound theoretical curve for various coding rates.

[1]  Shyam Ranganathan,et al.  General CPM and its capacity , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[2]  Bixio Rimoldi,et al.  A decomposition approach to CPM , 1988, IEEE Trans. Inf. Theory.

[3]  Michael Rice,et al.  PAM representation of ternary CPM , 2008, IEEE Transactions on Communications.

[4]  Yasuo Hirata,et al.  High-Rate Punctured Convolutional Codes for Soft Decision Viterbi Decoding , 1984, IEEE Trans. Commun..

[5]  Tor Aulin,et al.  Digital Phase Modulation , 1986, Applications of Communications Theory.

[6]  Wei Zeng,et al.  Simulation-Based Computation of Information Rates for Channels With Memory , 2006, IEEE Transactions on Information Theory.

[7]  H. Vincent Poor,et al.  Channel Coding Rate in the Finite Blocklength Regime , 2010, IEEE Transactions on Information Theory.

[8]  F. Pollara,et al.  Serial concatenation of interleaved codes: performance analysis, design and iterative decoding , 1996, Proceedings of IEEE International Symposium on Information Theory.

[9]  Cenk Sahin,et al.  The capacity of SOQPSK-TG , 2011, 2011 - MILCOM 2011 Military Communications Conference.

[10]  Dariush Divsalar,et al.  A soft-input soft-output APP module for iterative decoding of concatenated codes , 1997, IEEE Communications Letters.

[11]  Pierre A. Laurent,et al.  Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP) , 1986, IEEE Trans. Commun..

[12]  Carl-Erik W. Sundberg,et al.  A Class of Reduced-Complexity Viterbi Detectors for Partial Response Continuous Phase Modulation , 1984, IEEE Trans. Commun..

[13]  Arne Svensson,et al.  Viterbi Detectors with Reduced Complexity for Partial Response Continuous Phase Modulation , 1981 .

[14]  John Cocke,et al.  Optimal decoding of linear codes for minimizing symbol error rate (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[15]  Sergio Benedetto,et al.  Capacity-Achieving CPM Schemes , 2008, IEEE Transactions on Information Theory.

[16]  Paul H. Siegel,et al.  On the achievable information rates of finite state ISI channels , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).