Reduced-Complexity Syndrome-Based TTCM Decoding

Abstract

Abstract-The iterative decoder of Turbo Trellis Coded Modulation (TTCM) exchanges extrinsic information between the constituent TCM decoders, which imposes a high computational complexity at the receiver. Therefore we conceive the syndrome-based block decoding of TTCM, which is capable of reducing the decoding complexity by disabling the decoder, when syndrome becomes zero. Quantitatively, we demonstrate that a decoding complexity reduction of at least 17% is attained at high SNRs, with at least 20% and 45% reduction in the 5 th and 6 th iterations, respectively.Index Terms-Syndrome decoding, TTCM, error trellis, block syndrome decoding, iterative decoding.

Distributed Source–Channel Coding Using Reduced-Complexity Syndrome-Based TTCM

“…The syndrome-based MAP decoder of [5] is employed in our BSD-TTCM decoder. In contrast to the conventional MAP decoder, which relies upon the codeword trellis, the syndrome-based MAP counterpart operates on the basis of the error trellis constructed using the syndrome former H T .…”

“…By contrast, separate channel codes, such as turbo and LDPC codes, impose a bandwidth expansion for accommodating the parity bits. An error trellis-based Block Syndrome Decoder (BSD) (TTCM-BSD) was designed for TTCM in [5], where the state probabilities of the trellis directly depend on the channel errors, rather than on the coded sequence. Hence, for high SNRs or for highly correlated sources, the syndrome decoder would be more likely to experience a syndrome of all zeros because of the predominantly near-error-free transmissions.…”

“…The BSD divides the received sequence into erroneous and error-free blocks according to their syndrome, and only the erroneous blocks are decoded by the BSD decoder, while a straightforward symbol-to-bit hard-demapper would be applied to the error-free blocks. In comparison to the conventional TTCM decoder, the TTCM-BSD of [5] was capable of achieving in excess of 20% complexity reduction at high SNRs.…”

“…Against this background, we propose a Distributed Joint Source and TTCM (DJSTTCM) coded scheme relying on the reducedcomplexity BSD decoder of [5], for transmission over Rayleigh fading MAC. Additionally, our iterative decoder is capable of accurately estimating the time-variant cross-over probability pe, hence enhancing the attainable Bit Error Ratio (BER) performance of the scheme.…”

“…Next, a precorrection sequenceê k is needed for updating any predicted errors in the hard-demapped sequence, where this sequence is set to zero during the first iteration. Then, the syndrome s is computed for estimating the corrected symbol stream r with the aid of the syndrome former matrix H T as [5]:…”