The PPM poisson channel: Finite-length bounds and code design

This work investigates the finite-length block error probability for the pulse position modulation (PPM) Poisson channel. Amongst, expressions for the Gallager random coding bound (RCB) and the Gaussian approximation of the converse theorem are derived. Likewise, we introduce an erasure channel (EC) approximation that allows the application of known EC bounds to the PPM Poisson channel by matching the channel capacities. We show that the derived benchmarks are not only simple to compute, but also accurate. Additionally, the design of protograph-based non-binary low-density parity-check (LDPC) codes for the (PPM) Poisson channel is addressed. The order q of the finite field is directly matched to the PPM order, so that no iterative message exchange between the decoder and the demodulator is required. The suggested design turns out to be robust w.r.t. different channel parameters, yielding performances within 0.5 dB from the theoretical benchmarks.

[1]  Dariush Divsalar,et al.  Accumulate repeat accumulate codes , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[2]  Igal Sason,et al.  On Universal LDPC Code Ensembles Over Memoryless Symmetric Channels , 2011, IEEE Transactions on Information Theory.

[3]  Aaron D. Wyner,et al.  Capacity and error exponent for the direct detection photon channel-Part I , 1988, IEEE Trans. Inf. Theory.

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

[5]  Marco Chiani,et al.  Protograph LDPC Codes Design Based on EXIT Analysis , 2007, IEEE GLOBECOM 2007 - IEEE Global Telecommunications Conference.

[6]  Marco Chiani,et al.  Non‐binary protograph low‐density parity‐check codes for space communications , 2012, Int. J. Satell. Commun. Netw..

[7]  J. Thorpe.  Low-Density Parity-Check (LDPC) Codes Constructed from Protographs , 2003 .

[8]  Richard C. Singleton,et al.  Maximum distance q -nary codes , 1964, IEEE Trans. Inf. Theory.

[9]  Gianluigi Ferrari,et al.  Does the Performance of LDPC Codes Depend on the Channel? , 2006, IEEE Transactions on Communications.

[10]  Marco Chiani,et al.  Bounds on the Error Probability of Block Codes over the q-Ary Erasure Channel , 2013, IEEE Transactions on Communications.

[11]  M. Fossorier,et al.  Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images , 2008, IEEE Transactions on Communications.

[12]  David Declercq,et al.  Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images , 2008, IEEE Transactions on Communications.

[13]  Robert J. McEliece,et al.  Practical codes for photon communication , 1981, IEEE Trans. Inf. Theory.

[14]  Sae-Young Chung,et al.  On the construction of some capacity-approaching coding schemes , 2000 .

[15]  Surrogate-channel design of universal LDPC codes , 2006, IEEE Communications Letters.

[16]  Marco Chiani,et al.  A robust pulse position coded modulation scheme for the Poisson channel , 2014, 2014 IEEE International Conference on Communications (ICC).

[17]  J. R. Clark.  Optical communications , 1977, Proceedings of the IEEE.

[18]  Jon Hamkins,et al.  Deep-Space Optical Communications Downlink Budget: Modulation and Coding , 2003 .

[19]  J. L. Massey,et al.  Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel , 1981, IEEE Trans. Commun..

[20]  Aaron D. Wyner,et al.  Capacity and error-exponent for the direct detection photon channel-Part II , 1988, IEEE Trans. Inf. Theory.

[21]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[22]  David Burshtein,et al.  Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels , 2005, IEEE Transactions on Information Theory.

[23]  Masahito Hayashi,et al.  Information Spectrum Approach to Second-Order Coding Rate in Channel Coding , 2008, IEEE Transactions on Information Theory.

[24]  Dariush Divsalar,et al.  EXIT Function Aided Design of Iteratively Decodable Codes for the Poisson PPM Channel , 2010, IEEE Transactions on Communications.