Optimal Puncturing Ratios and Energy Allocation for Multiple Parallel Concatenated Codes
Artikel i vetenskaplig tidskrift, 2009

We propose a systematic design framework for optimal, low-complexity punctured multiple parallel concatenated codes (MPCCs), based on minimizing the convergence threshold using extrinsic information transfer (EXIT) charts. As the convergence threshold is related to the area between the two EXIT curves, the corresponding optimization problem is equivalent to a curve-fitting problem. The EXIT curves are determined by the respective EXIT functions of the constituents, which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams. The design task is therefore to find the optimal combination of constituents, puncturing ratios, and energy allocation for matching the EXIT curves. A search over all rate-one convolutional codes of memory length four or less is performed, identifying 98 classes of codes with unique EXIT functions out of a total of 310 codes. Low-complexity MPCCs with up to four constituents are found, where the convergence thresholds are observed to be within 0.1 dB or less of the fundamental minimum signal-to-noise ratio (SNR) corresponding to the binary phase-shift keying (BPSK) capacity for code rates 1/3 <= R <= 7/8. Further allowing for unequal energy allocation, the convergence thresholds for lower code rates are similarly improved.

parity-check codes

Code search

extrinsic information transfer (EXIT)

iterative decoding

parallel concatenated codes

energy allocation






Fredrik Brännström

Signaler och system, Kommunikationssystem, informationsteori och antenner, Kommunikationssystem

Lars K. Rasmussen

Kungliga Tekniska Högskolan (KTH)

University of South Australia

Alex J. Grant

University of South Australia

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 55 2062-2077


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