LDPC Packet Interleaving to Avoid Minimum Stopping Sets
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Solution Overview
Problem
The performance of erasure correction using LDPC codes is limited by the combination of variable nodes forming a 'minimum stopping set' in the parity check matrix, leading to difficulties in correcting packet erasures, especially when packets corresponding to these nodes are lost, resulting in decoding failures.
Innovation Solution
An encoding apparatus that includes a padding section to add known packets, an interleaving section to reorder the packet sequence, and an erasure correction coding section to perform LDPC coding, allowing for adjustment of the coding rate and improved erasure correction by assigning known packets to positions influencing erasure correction performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LDPC coding is performed without reordering packets, then encoding/decoding processing can be performed within a practical period at a practical operation cost, but erasure correction performance is limited by minimum stopping sets in the parity check matrix
Solution Approach 1:
The patent applies preliminary action by reordering packets before LDPC encoding to prevent minimum stopping sets from forming in the encoded packet sequence. The encoding apparatus includes a reordering section that permutes packets according to a predetermined pattern before they enter the LDPC encoder, and a restorer section that reverses this reordering after decoding. This preliminary reordering ensures that even if erasures occur, they are unlikely to align with minimum stopping sets, thereby improving erasure correction performance without changing the fundamental LDPC coding structure.
2Reliability
If known packets are added to positions corresponding to variable nodes forming minimum stopping sets, then decoding failure frequency is reduced, but the amount of redundant data increases
Solution Approach 1:
The patent applies parameter changes by modifying the positions of packets in the sequence through reordering, rather than adding extra known packets. By changing the positional parameters of existing packets according to a predetermined permutation pattern, the system ensures that packets corresponding to variable nodes in minimum stopping sets are replaced with known packets without increasing the total data quantity. This approach maintains the same code length while improving decoding reliability.
Data Source
AI summary
Disclosed are an encoding device and a decoding device which can effectively reduce the decoding failure frequency in LDPC encoding/decoding. A loss correction encoding device (120) includes a padding unit (121) which adds a padding packet to an information packet sequence; an interleave unit (122) which rearranges the padding packet and the information packet; and a loss correction encoding unit (123) which performs loss correction encoding for the packet string after the interleave. The interleave unit (122) rearranges the padding packet and the information packet according to variable nodes constituting a minimum stopping set of the inspection matrix which defines a low-density parity inspection code. The interleave unit (122) uses such a rearrangement pattern that avoids a loss correction failure by the minimum stopping set of the LDPC inspection matrix so as to reduce the probability of the loss correction failure by the minimum stopping set.