Design and Analysis of Successive Decoding With Finite Levels for the Markov Channel

This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels (FSMCs) where there is no a priori state information at the transmitter or the receiver. The design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level. The interleaver design criteria may be the achievable rate or the extrinsic information transfer (EXIT) chart, depending on the receiver type. For random interleavers, the optimization problem is solved efficiently using a pilot-utility function, while for deterministic interleavers, a good construction is given using empirical rules. Simulation results demonstrate that the new successive decoding scheme combined with irregular low-density parity-check (LDPC) codes can approach the identically and uniformly distributed (i.u.d.) input capacity on the Markov-fading channel using only a few levels.

[1]  Thomas E. Fuja,et al.  LDPC Codes for Fading Channels: Two Strategies , 2006, AAECC.

[2]  Hans-Andrea Loeliger,et al.  On the information rate of binary-input channels with memory , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[3]  Robert F. H. Fischer,et al.  Multilevel codes: Theoretical concepts and practical design rules , 1999, IEEE Trans. Inf. Theory.

[4]  S. Brink.  Convergence of iterative decoding , 1999 .

[5]  Teng Li,et al.  Capacity and coding for flat fading channels without channel state information , 2005, IEEE Wireless Communications and Networking Conference, 2005.

[6]  Teng Li,et al.  Successive Decoding for Finite State Markov Modelled Flat Fading Channels , 2006, 2006 IEEE International Symposium on Information Theory.

[7]  Harish Viswanathan,et al.  Optimal placement of training for frequency-selective block-fading channels , 2002, IEEE Trans. Inf. Theory.

[8]  Xiao Ma,et al.  Binary intersymbol interference channels: Gallager codes, density evolution, and code performance bounds , 2003, IEEE Transactions on Information Theory.

[9]  Pravin Varaiya,et al.  Capacity, mutual information, and coding for finite-state Markov channels , 1996, IEEE Trans. Inf. Theory.

[10]  Laurent Mevel,et al.  Exponential Forgetting and Geometric Ergodicity in Hidden Markov Models , 2000, Math. Control. Signals Syst..

[11]  Teng Li,et al.  A Successive Decoding Strategy for Channels With Memory , 2005, IEEE Transactions on Information Theory.

[12]  Paul H. Siegel,et al.  Determining and Approaching Achievable Rates of Binary Intersymbol Interference Channels Using Multistage Decoding , 2007, IEEE Transactions on Information Theory.

[13]  Xiao Ma,et al.  Matched information rate codes for Partial response channels , 2005, IEEE Transactions on Information Theory.

[14]  Teng Li,et al.  Approaching capacity on correlated fading channels with unknown state , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[15]  Richard D. Wesel,et al.  Joint iterative channel estimation and decoding in flat correlated Rayleigh fading , 2001, IEEE J. Sel. Areas Commun..

[16]  Hideki Imai,et al.  A new multilevel coding method using error-correcting codes , 1977, IEEE Trans. Inf. Theory.

[17]  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).

[18]  Stephan ten Brink,et al.  Extrinsic information transfer functions: model and erasure channel properties , 2004, IEEE Transactions on Information Theory.

[19]  Laurent Mevel,et al.  Basic Properties of the Projective Product with Application to Products of Column-Allowable Nonnegative Matrices , 2000, Math. Control. Signals Syst..

[20]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[21]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[22]  A. Sridharan.  Broadcast Channels , 2022 .

[23]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[24]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[25]  Matthew C. Valenti,et al.  Iterative channel estimation and decoding of pilot symbol assisted turbo codes over flat-fading channels , 2001, IEEE J. Sel. Areas Commun..

[26]  Emre Telatar,et al.  Mismatched decoding revisited: General alphabets, channels with memory, and the wide-band limit , 2000, IEEE Trans. Inf. Theory.

[27]  Andrew W. Eckford,et al.  Analysis and design of low density parity check codes for non-coherent block fading channels , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[28]  Andrew C. Singer,et al.  Turbo equalization: principles and new results , 2002, IEEE Trans. Commun..

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

[30]  Achilleas Anastasopoulos,et al.  Analysis and design of LDPC codes for time-selective complex-fading channels , 2005, IEEE Transactions on Wireless Communications.

[31]  L. Arnold,et al.  Evolutionary Formalism for Products of Positive Random Matrices , 1994 .

[32]  N. Varnica,et al.  Iteratively decodable codes for bridging the shaping gap in communication channels , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[33]  Frank R. Kschischang,et al.  On Designing Good LDPC Codes for Markov Channels , 2007, IEEE Transactions on Information Theory.

[34]  Krishna R. Narayanan,et al.  A BCJR-DFE Based Receiver for Achieving Near Capacity Performance on Inter Symbol Interference Channels , 2004 .

[35]  Aleksandar Kavcic,et al.  Optimized low-density parity-check codes for partial response channels , 2003, IEEE Communications Letters.

[36]  Qinghua Li,et al.  An iterative receiver for turbo-coded pilot-assisted modulation in fading channels , 2001, IEEE Communications Letters.