Minimal Trellis Decoder for Low-Complexity Hamming Code Decoding
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Solution Overview
Problem
The complexity of traditional trellis decoders for shortened Hamming codes, such as those used in Bluetooth radios, leads to high computational requirements and power consumption, which is a challenge for low-power communication systems.
Innovation Solution
A minimal trellis representation and permutation-based decoding technique is introduced, which reduces the number of states and branches in the trellis, thereby decreasing the complexity of the decoder and facilitating a reduction in power consumption and die size, by permuting the received codeword according to a specific permutation before applying Viterbi or other trellis search algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional trellis representation is used for decoding shortened Hamming codes, then decoding accuracy is maintained, but decoder complexity and power consumption increase
Solution Approach 1:
The patent segments the decoding process into two distinct parts: (1) a permutation operation that reorders the received codeword bits according to a predetermined permutation pattern, and (2) a simplified trellis decoding operation. This segmentation allows the complex trellis structure to be replaced with a simpler version that operates on the permuted input, thereby reducing decoder complexity while maintaining decoding accuracy through the combined effect of permutation and simplified decoding.
Solution Approach 2:
The patent applies a preliminary permutation operation to the received codeword before it enters the trellis decoder. This preliminary action reorders the bits in a specific pattern that transforms the decoding problem into an equivalent but simpler form. By performing this permutation beforehand, the subsequent trellis decoding requires fewer computational steps and comparisons, reducing overall decoder complexity while preserving the ability to achieve the same decoding accuracy.
2Reliability
If traditional trellis representation is used for decoding shortened Hamming codes, then decoding accuracy is maintained, but power consumption increases
Solution Approach 1:
The patent segments the decoding process into a permutation stage and a simplified trellis decoding stage. The permutation stage requires minimal computational resources, while the simplified trellis decoder performs fewer operations than a traditional decoder. This segmentation directly reduces the total number of computational operations, thereby lowering power consumption while maintaining the same decoding accuracy through the combined permutation and decoding operations.
Solution Approach 2:
The preliminary permutation operation prepares the input data in a form that is more efficient for the simplified trellis decoder to process. By reordering the bits before decoding, the subsequent decoding operations require fewer computational steps, which directly translates to reduced power consumption. The permutation itself is a simple reordering operation with minimal energy cost, making the overall process more energy-efficient while achieving the same decoding accuracy.
3Reliability
If traditional trellis representation is used for decoding shortened Hamming codes, then decoding accuracy is maintained, but the number of computational steps increases
Solution Approach 1:
The patent divides the decoding task into a permutation step and a simplified trellis decoding step. The permutation step is computationally trivial, and the simplified trellis decoder performs fewer state transitions and comparisons than a traditional decoder. This segmentation reduces the total number of computational steps required to achieve the same decoding accuracy, thereby improving computational efficiency and productivity.
Solution Approach 2:
The permutation operation is performed as a preliminary step that transforms the input data into a format that requires fewer computational operations for decoding. By reordering the bits according to a specific pattern before they enter the trellis decoder, the subsequent decoding process involves fewer state transitions, metric calculations, and comparisons. This preliminary transformation maintains decoding accuracy while significantly reducing the number of computational steps required.
Data Source
AI summary
A device including a minimal trellis decoder is disclosed. The device can receive an encoded codeword, which the minimal trellis decoder efficiently decodes. In a specific implementation, the device can include a Bluetooth receiver that, in operation, receives an encoded codeword from a Bluetooth transmitter, which is decoded by the minimal trellis decoder.