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Two Step SOVA-Based Decoding Algorithm for Tailbiting Codes

Jorge Ortin, Paloma Garcia, Fernando Gutierrez, Antonio Valdovinos

TL;DR

This work tackles the decoding complexity of tailbiting convolutional codes, where maximum-likelihood decoding is prohibitive due to needing $2^{M}$ separate initial/final state evaluations. It introduces the two-step Viterbi algorithm (TSVA), first performing a modified Soft-Output Viterbi Algorithm to estimate a most likely trellis state, then executing a circular Viterbi pass constrained to that state. Results in AWGN and WSSUS OFDM channels show TSVA achieving near-ML BLER with a fixed, low computational load, outperforming fixed CVA approaches, and reducing decoding-time variability. The approach offers a practical, deterministic decoder suitable for real-time mobile systems such as WiMAX/LTE that employ tailbiting codes.

Abstract

In this work we propose a novel decoding algorithm for tailbiting convolutional codes and evaluate its performance over different channels. The proposed method consists on a fixed two-step Viterbi decoding of the received data. In the first step, an estimation of the most likely state is performed based on a SOVA decoding. The second step consists of a conventional Viterbi decoding that employs the state estimated in the previous step as the initial and final states of the trellis. Simulations results show a performance close to that of maximum-likelihood decoding.

Two Step SOVA-Based Decoding Algorithm for Tailbiting Codes

TL;DR

This work tackles the decoding complexity of tailbiting convolutional codes, where maximum-likelihood decoding is prohibitive due to needing separate initial/final state evaluations. It introduces the two-step Viterbi algorithm (TSVA), first performing a modified Soft-Output Viterbi Algorithm to estimate a most likely trellis state, then executing a circular Viterbi pass constrained to that state. Results in AWGN and WSSUS OFDM channels show TSVA achieving near-ML BLER with a fixed, low computational load, outperforming fixed CVA approaches, and reducing decoding-time variability. The approach offers a practical, deterministic decoder suitable for real-time mobile systems such as WiMAX/LTE that employ tailbiting codes.

Abstract

In this work we propose a novel decoding algorithm for tailbiting convolutional codes and evaluate its performance over different channels. The proposed method consists on a fixed two-step Viterbi decoding of the received data. In the first step, an estimation of the most likely state is performed based on a SOVA decoding. The second step consists of a conventional Viterbi decoding that employs the state estimated in the previous step as the initial and final states of the trellis. Simulations results show a performance close to that of maximum-likelihood decoding.
Paper Structure (4 sections, 2 equations, 3 figures)

This paper contains 4 sections, 2 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Algorithm Description
  3. Simulation Results
  4. Conclusion

Figures (3)

  • Figure 1: State decision error of the (3,1,6) tailbiting code with generators (171,133,165) as a function of the window size with different SNRs and block sizes over an AWGN channel.
  • Figure 2: Block Error Rate (BLER) of the (96,48) and the (120,40) tailbiting codes over the AWGN channel decoded by various algorithms with soft decision decoding.
  • Figure 3: Block Error Rate (BLER) of the (96,48) and the (120,40) tailbiting codes over the ITU Vehicular A channel decoded by various algorithms with soft decision decoding.