Product Accumulate Codes: A Class of Capacity-Approaching, Low Complexity Codes

IEEE Trans Inform Theory  
submitted  
2001  
          J.Li,   K.R.Narayanan,  C.N.Georghades

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Abstract -- This paper proposes a novel class of provably good codes which are a serial concatenation of a single-parity check turbo product code (TPC/SPC), an interleaver and a rate-1 recursive convolutional code. The proposed codes, termed as product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself is not a "good" code; however, a product accumulate code is a "good" code both in the ML (maximum likelihood) sense and under iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code; however, with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's simple bound and thresholds under density evolution show that these codes are capable of performance within a few tenths of a dB away from the Shannon limit. Simulation results confirm these claims and show that these codes provide similar performance to turbo codes but with significantly lesser decoding complexity and without an error floor. Hence, we propose PA codes to be a class of prospective codes with good-performance, low decoding complexity, and regular structure, uniformly for all rates from 1/2 and higher.

Keywords -- product accumulate codes, turbo product codes (TPC), serial concatenation, hybrid concatenation, iterative decoding, message-passing decoding, sum-product decoding, min-sum decoding, density evolution, Divsalar simple bound, union bound, interleaving gain, distance spectrum, code graph, "good" codes