A Class of Linear-Complexity, Soft-Decodable, High-Rate, "Good" Codes: Construction, Properties and Performance

ISIT 2001  
Washington D.C. 
June, 2001  
          J.Li,   K.R.Narayanan,  C.N.Georghades

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Abstract -- This paper proposes a class of high-rate codes which is a serial concatenation of a single-parity check turbo product code (TPC/SPC), interleaver and a rate-1 convolutional code. The proposed codes, which we call {\it product accumulate} codes, are linear time encodable and linear time decodable. We show that a TPC/SPC by itself is not a ``good'' code, a product accumulate code becomes a ``good'' code both in the ML (maximal likelihood) sense and under the practical iterative approach. In particular, the thresholds computed using density evolution show that these codes can perform within a few tenths of a dB from the capacity limits, for rates from 0.7 to 0.98. Simulation results confirm these claims.

Keywords -- serial / parallel concatenated codes, turbo product codes, Tanner graph, density evolution, union bounds, Galager bounds, Divsalar bounds, message-passing decoding, sum-product decoding, min-sum decoding