Near sphere packing bound communication: excellent block code with very small block size

• Main Authors: Yu-Peng Wu, 吳宇鵬
• Other Authors: Da-Shan Shiu
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/23125082386241781379

碩士 === 臺灣大學 === 電信工程學研究所 === 95 === 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