Tail-Biting Convolutional Code Decoding With Partial Viterbi Trace-Back
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Solution Overview
Problem
Existing decoding methods for tail-biting convolutional codes face high computational complexity due to uncertainty in starting and ending states, leading to compromised decoder performance.
Innovation Solution
A sub-optimum decoding scheme using the Viterbi algorithm, where forward and backward metrics are calculated to trace back paths from the ending state to the initial state, balancing decoding performance and complexity by initializing all beginning states equally and calculating metrics within a predetermined period.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If tail biting is used for trellis termination without additional bits, then rate loss is avoided, but computational complexity increases due to uncertainty of beginning and ending states
Solution Approach 1:
The decoding process is segmented into two distinct phases: a forward Viterbi decoding phase that processes the entire trellis diagram, and a backward Viterbi decoding phase that processes only a predetermined period (K stages) from the end. This segmentation allows the complex tail-biting problem to be broken into manageable parts, reducing overall computational complexity while maintaining code rate efficiency.
Solution Approach 2:
The forward Viterbi decoding is performed as a preliminary action before the backward decoding. By pre-calculating the forward metrics and identifying the most likely ending state, the subsequent backward decoding only needs to process a limited time period, significantly reducing the computational burden compared to exhaustive search methods.
2Measurement precision
If forward and backward Viterbi metrics are calculated with trace-back process, then decoding accuracy is improved, but computational complexity increases
Solution Approach 1:
Instead of performing complete backward Viterbi decoding over the entire trellis duration, the invention applies partial action by limiting the backward decoding to only the last K stages. This partial processing achieves sufficient decoding accuracy for tail-biting codes while avoiding the excessive computational complexity of full backward decoding.
Solution Approach 2:
The invention extracts and processes only the critical portion of the trellis diagram - specifically the last K stages - for backward decoding. By taking out and focusing only on this essential segment, the method achieves accurate path convergence without the computational burden of processing the entire trellis in both directions.
3Productivity
If all beginning states are initialized equally without forcing to known state, then rate loss is avoided, but decoder performance becomes compromised
Solution Approach 1:
The initialization approach is made dynamic by allowing all states to be potentially valid at the beginning (unlike conventional methods that force a known state), while the dual-phase Viterbi decoding with trace-back dynamically identifies the actual beginning state through path convergence. This dynamic approach maintains code rate efficiency while achieving reliable decoding performance.
Data Source
AI summary
A method for decoding tail-biting convolutional codes is disclosed. In the method, all beginning states of a trellis diagram are initialized. Forward Viterbi metrics are calculated for the trellis diagram. A trace-back process is performed from an ending state of the trellis diagram at a first time instance to a first state where all surviving paths converge at a second time instance. Backward Viterbi metrics are calculated for a predetermined period of time from the first state at the second time instance to a second state at a third time instance. A trace-back process is performed from a designated state, which is equal to the second state, at the first time instance to determine a most likely path for the convolutional codes in the trellis diagram.