Near sphere packing bound communication: excellent block code with very small block size
Date Issued
2007
Date
2007
Author(s)
Wu, Yu-Peng
DOI
en-US
Abstract
After the publication of Shannon's paper in 1948 [13], a large amount of research was led to the construction of specific codes with good error-correcting capabilities
and development of efficient decoding algorithms for these codes. Until now, many good codes and corresponding decoding algorithms have been proposed. For short
or very short codeword lengths (hundreds of or less bits), several good codes (for example, the Golay code) for specific block size have been found. For moderate
or large codeword lengths (thousands of or more bits), turbo code and low density parity check (LDPC) code also show their excellent error correcting capability. But
for short or very short codeword lengths, there are no adjustable block sizes and high performance short codes with practical decoding (turbo or LDPC codes don't perform
well in this codeword lengths). Based on this reason, we aim to discover alternative high performance short codes with practical decoding and adjustable block sizes.
In this thesis, we provide a method, based on concepts of "decomposition of the input error space of convolutional code" and "denial of input", to find a family of good codes consisted of concatenated Cyclic redundancy code (CRC) and convolutional
code. This concatenated code own very simple encoding form. On the framework of this concatenated code, we also search the best code (from the viewpoint of having
the largest minimal distance) on some given conditions. Our result indicates that maximum likelihood (ML) decoding performance of this concatenated code with close to rate-0.4 can achieve near-SPB performance for codeword lengths ranging from 272 bits to 528 bits with 0.55 dB to 0.75 dB for a word error probability of 10^-4.
Furthermore, we also propose two decoders, "LVA followed by CRC correction decoder" and "LVA with built-in CRC constraint decoder", for this concatenated code.
The decoders take advantage of the error correction capability rather than the error detection capability of CRC and the concept of list decoding. Under our result, it
shows that "LVA with built-in CRC constraint decoder" can achieve optimal decoding of close to rate-0.4 codes of lengths up to 528 bits. This is the best reported decoding
performance so far for codeword lengths from 200 to 500 bits.
Keywords ─ concatenated code, CRC, convolutional code, decomposition of the input error space of convolutional code, denial of input, LVA followed by CRC correction decoder, LVA with built-in CRC constraint decoder
Subjects
連結碼
循環檢測碼
摺積碼
摺積碼輸入端空間的分解
否定輸入
循環檢測碼錯誤更正跟隨列舉維特比演算法解碼器
循環檢測碼限制嵌入列舉維特比演算法解碼器
concatenated code
CRC
convolutional code
decomposition of the input error space of convolutional code
denial of input
LVA followed by CRC correction decoder
LVA with built-in CRC constraint decoder
Type
thesis
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