NB-LDPC Coding in OTFS Links for Low Error Floors
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Solution Overview
Problem
Traditional error correction codes in wireless communication systems, such as those used in next-generation wireless networks, face challenges in achieving low bit error rates (BER) while maintaining computational efficiency, especially in devices with limited power resources like IoT devices and machine-to-machine communication devices.
Innovation Solution
The implementation of non-binary low-density parity-check (LDPC) codes with binary and non-binary entries, combined with orthogonal time-frequency space (OTFS) modulation, which formulates a parity-check matrix to reduce error triggering events and achieve extremely low error floors, such as 10−11 or 10−12, without significantly increasing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional error correction codes are used in wireless communication systems, then the system can achieve basic error correction functionality, but the bit error rate cannot be reduced below certain thresholds while maintaining computational efficiency
Solution Approach 1:
The patent changes the fundamental parameter of the error correction code from binary to non-binary (q-ary where q > 2). This parameter change allows the system to achieve lower bit error rates (10^-11 or 10^-12) while maintaining computational efficiency through the structured parity-check matrix design with cyclic permutation blocks
Solution Approach 2:
The patent creates a composite code structure by combining non-binary LDPC codes with OTFS modulation. The parity-check matrix H is constructed as a composite of cyclic permutation matrices and zero matrices, creating a structured code that achieves both low error rates and computational efficiency
2Reliability
If non-binary low-density parity-check codes are implemented to achieve extremely low error floors, then reliability is significantly improved, but computational resources are consumed
Solution Approach 1:
The patent segments the parity-check matrix into smaller cyclic permutation matrices and zero matrices. This segmentation allows the decoder to process the code in manageable blocks, reducing the computational energy required while achieving extremely low error floors of 10^-11 or 10^-12
Solution Approach 2:
By changing from binary to non-binary representation with carefully selected field size q, the patent reduces the number of iterations needed for decoding convergence, thereby reducing computational energy consumption while achieving the target error floors
3Reliability
If conventional binary LDPC codes are used, then the system maintains simple implementation, but error triggering events occur more frequently compared to non-binary codes
Solution Approach 1:
The patent changes the algebraic structure from binary GF(2) to non-binary GF(q) where q > 2. This parameter change fundamentally reduces error triggering events by providing better distance properties in the code space, while the cyclic structure maintains implementation simplicity
Solution Approach 2:
The cyclic permutation matrix structure serves multiple functions simultaneously: it provides the mathematical structure for non-binary operations, enables efficient implementation through reuse of the same matrix pattern, and achieves the desired error performance. This multi-functionality reduces the practical complexity increase
Data Source
AI summary
Methods, systems and devices for forward error correction in orthogonal time frequency space (OTFS) communication systems using non-binary low-density parity-check (NB-LDPC) codes are described. One exemplary method for forward error correction includes receiving data, encoding the data via a non-binary low density parity check (NB-LDPC) code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, modulating the encoded data to generate a signal, and transmitting the signal. Another exemplary method for forward error correction includes receiving a signal, demodulating the received signal to produce data, decoding the data via a NB-LDPC code, wherein the NB-LDPC code is characterized by a matrix with binary and non-binary entries, and providing the decoded data to a data sink.