Turbo codes with symmetric and asymmetric component codes defined over finite fields of integers

Barros, Jose da Silva; Filho, Renato Baldini

doi:10.1049/iet-com.2009.0047

Cited by 1 publication

(1 citation statement)

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“…To accommodate such demand, nonbinary convolutional codes have been proposed to replace binary convolutional codes in many applications [3][4][5]. For example, non-binary turbo codes, which employ nonbinary convolutional codes as component codes, achieve lower error floor and better performance at the waterfall region compared with binary turbo codes [6]. Additionally, non-binary convolutional codes suit situations where bandwidth-efficient higher order (non-binary) modulation schemes are used, as well as situations where non-coherent modulation schemes are used, such as frequency-shift keying [7].…”

Section: Introductionmentioning

confidence: 99%

Duality of channel encoding and decoding—Part II: rate‐1 non‐binary convolutional codes

You

Liew

et al. 2016

Trans. Emerging Tel. Tech.

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This is the second part of a series of papers on a revisit to the bidirectional Bahl-Cocke-JelinekRaviv (BCJR) soft-in-soft-out (SISO) maximum a posteriori probability (MAP) decoding algorithm.Part I revisited the BCJR MAP decoding algorithm for rate-1 binary convolutional codes and proposed a linear complexity decoder using shift registers in the complex number field. Part II proposes a low complexity decoder for rate-1 non-binary convolutional codes that achieves the same error performance as the bidirectional BCJR SISO MAP decoding algorithm. We observe an explicit relationship between the encoding and decoding of rate-1 convolutional codes in GF (q). Based on this relationship, the BCJR forward and backward decoding are implemented by dual encoders using shift registers whose contents are vectors of complex numbers. The input to the dual encoders is the probability mass function (pmf) of the received symbols and the output of the dual encoders is the pmf of the information symbols. The bidirectional BCJR MAP decoding is implemented by linearly combining the shift register contents of the dual encoders for forward and backward decoding. The proposed decoder significantly reduces the computational complexity of the bidirectional BCJR MAP algorithm from exponential to linear with constraint length of convolutional codes. To further reduce complexity, fast Fourier transform (FFT) is applied. Mathematical proofs and simulation results are provided to validate our proposed decoder. Index TermsBCJR MAP decoding, computational complexity, convolutional codes, dual encoder.

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