Digital Link—B

Chapter 7 explained the detection and hypothesis testing problems, Huffman codes and the situation where errors are independent and Gaussian. In this chapter, we prove the optimality of the Huffman code in Sect. 8.1 and the Neyman–Pearson Theorem in Sect. 8.2. Section 8.3 discusses the theory of jointly Gaussian random variables that is used to analyze the modulation schemes of Sect. 7.5 . Section 8.4 uses the results on jointly Gaussian random variables to explain hypothesis tests that arise when analyzing data. That section discusses the chi-squared test and the F-test. Section 8.5 is devoted to the LDPC codes that are widely used in high-speed communication links. These codes augment a group of bits to be transmitted over a noisy channel with additional bits computed from those in the group. When it receives the bits, when the augmented bits are not consistent, the receiver attempts to determine the bits that are most likely to have been corrupted by noise.

Modified HuffBit Compress Algorithm – An Application of R

The databases of genomic sequences are growing at an explicative rate because of the increasing growth of living organisms. Compressing deoxyribonucleic acid (DNA) sequences is a momentous task as the databases are getting closest to its threshold. Various compression algorithms are developed for DNA sequence compression. An efficient DNA compression algorithm that works on both repetitive and non-repetitive sequences known as “HuffBit Compress” is based on the concept of Extended Binary Tree. In this paper, here is proposed and developed a modified version of “HuffBit Compress” algorithm to compress and decompress DNA sequences using the R language which will always give the Best Case of the compression ratio but it uses extra 6 bits to compress than best case of “HuffBit Compress” algorithm and can be named as the “Modified HuffBit Compress Algorithm”. The algorithm makes an extended binary tree based on the Huffman Codes and the maximum occurring bases (A, C, G, T). Experimenting with 6 sequences the proposed algorithm gives approximately 16.18 % improvement in compression ration over the “HuffBit Compress” algorithm and 11.12 % improvement in compression ration over the “2-Bits Encoding Method”.