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Mean Codeword Lengths And Their Correspondence With Entropy Measures

R.K.Tuli
2011 Zenodo  
codeword lengths.  ...  The objective of the present communication is to develop new genuine exponentiated mean codeword lengths and to study deeply the problem of correspondence between well known measures of entropy and mean  ...  length nor a monotonic increasing unction of mean codeword length.  ... 
doi:10.5281/zenodo.1327872 fatcat:4w6ydpzhtzcjrncndrgkdq6wt4

D-ary Bounded-Length Huffman Coding [article]

Michael B. Baer
2007 arXiv   pre-print
codes with a maximum difference between the longest and shortest codewords.  ...  Length-limited Huffman coding, useful for many practical applications, is one such variant, in which codes are restricted to the set of codes in which none of the n codewords is longer than a given length  ...  The code should be a prefix code, i.e., no codeword c i should begin with the entirety of another codeword c j .  ... 
arXiv:cs/0701012v2 fatcat:sjsxed6thjanjm3e2vc5hakacq

Optimal Compression for Two-Field Entries in Fixed-Width Memories [article]

Ori Rottenstreich, Yuval Cassuto
2017 arXiv   pre-print
After defining the problem formally, we solve it optimally with an efficient code-design algorithm.  ...  With an empirical study we show the success probabilities of the optimal codes for different distributions and memory widths.  ...  these pairs with a codeword of length L.  ... 
arXiv:1701.02900v1 fatcat:ahmfjf6qbzhehnm5favcienppa

Twenty (or so) Questions: D-ary Length-Bounded Prefix Coding [article]

Michael B. Baer
2007 arXiv   pre-print
limited fringe, that is, finding the best code among codes with a maximum difference between the longest and shortest codewords.  ...  Length-limited Huffman coding, useful for many practical applications, is one such variant, for which codes are restricted to the set of codes in which none of the n codewords is longer than a given length  ...  The overall code should be a prefix code, that is, no codeword c i should begin with the entirety of another codeword c j .  ... 
arXiv:cs/0602085v4 fatcat:hiftrhbsbvgyniso5t5re4rgv4

Reserved-Length Prefix Coding [article]

Michael B. Baer
2007 arXiv   pre-print
Consider situations in which one wishes to find an optimal code with the restriction that all codewords have lengths that lie in a user-specified set of lengths (or, equivalently, no codewords have lengths  ...  In addition, one modification of the approach solves any quasiarithmetic prefix coding problem, while another finds optimal codes restricted to the set of codes with g codeword lengths for user-specified  ...  This code has codewords of 13 different lengths, with an average length of about 8.78 bits.  ... 
arXiv:0801.0102v1 fatcat:oygdmfe7pbc6vnzpgc5rvgb4n4

Design of nonbinary error correction codes with a maximum run-length constraint to correct a single insertion or deletion error for DNA storage

Xiaozhou Lu, Sunghwan Kim
2021 IEEE Access  
Hence, the overall maximum run-length r of the output codeword is guaranteed to be three when the maximum run-length of the message sequence is three.  ...  For the proposed code, we design the fixed maximum run-length r in the parity sequence of the proposed code to be three.  ...  The output codeword is a sequence of the q-ary SIDEC code with the maximum run-length r constraint.  ... 
doi:10.1109/access.2021.3116245 fatcat:tlmkdo4icfgt5je3j6na4detwa

The meet operation in the imbalance lattice of maximal instantaneous codes: alternative proof of existence [article]

Stephan Foldes, D. Stott Parker, Sandor Radeleczki
2017 arXiv   pre-print
These codes are viewed as maximal antichains of a given size in the infinite binary tree of 0-1 words.  ...  An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size.  ...  It is well known that for every maximal instantaneous code there is a unique lex monotone maximal instantaneous code with the same multiset of codeword lengths. (See e.g.  ... 
arXiv:1702.06438v2 fatcat:pqtobclxdfhfhpgsbtu74cyk4a

Source Coding for Quasiarithmetic Penalties

M.B. Baer
2006 IEEE Transactions on Information Theory  
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items.  ...  Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with  ...  lengths of an infinite code C with codeword lengths l = { l 1 , l 2 , l 3 , . . .}.  ... 
doi:10.1109/tit.2006.881728 fatcat:xt3k4kihozcf5dcwrjx6ortcnu

Reed–Muller Codes Achieve Capacity on Erasure Channels

Shrinivas Kudekar, Santhosh Kumar, Marco Mondelli, Henry D. Pfister, Eren Sasoglu, Ridiger L. Urbanke
2017 IEEE Transactions on Information Theory  
Any sequence of Reed-Muller codes with block lengths n m → ∞, and rates R m → R, for R ∈ (0, 1), is capacity-achieving for the transmission over the BEC under bit-MAP decoding.  ...  Actually, we will prove something stronger: we will show that any code with "sufficient amount of symmetry" achieves capacity.  ...  Lemma 15 (Ω i Monotone). Consider the transmission of a binary linear code C of block length n over the BEC(ε).  ... 
doi:10.1109/tit.2017.2673829 fatcat:6n7y3cfk5fdwvh5rza4ytmrxdi

Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback

Wing Shing Wong, R.W. Brockett
1999 IEEE Transactions on Automatic Control  
communication channel with finite capacity.  ...  Index Terms-Finitely recursive coder-estimator sequence, hybrid systems, prefix code, state estimation.  ...  FIXED CODEWORD LENGTH SEQUENCES Coder-estimator sequences with fixed codeword length form an important sub-family.  ... 
doi:10.1109/9.763226 fatcat:3t52girfuvdofgi5wdvjvfucjq

Systems with finite communication bandwidth constraints. I. State estimation problems

Wing Shing Wong, R.W. Brockett
1997 IEEE Transactions on Automatic Control  
communication channel with finite capacity.  ...  Index Terms-Finitely recursive coder-estimator sequence, hybrid systems, prefix code, state estimation.  ...  FIXED CODEWORD LENGTH SEQUENCES Coder-estimator sequences with fixed codeword length form an important sub-family.  ... 
doi:10.1109/9.623096 fatcat:33nbx7mmvbc3jph3o6jsbcrwae

Zero-Error Capacity of $ P $ -ary Shift Channels and FIFO Queues

Mladen Kovacevic, Milos Stojakovic, Vincent Y. F. Tan
2017 IEEE Transactions on Information Theory  
Two channel models are introduced and their zero-error capacities and zero-error-detection capacities determined by explicit constructions of optimal codes.  ...  Model B is an abstraction of a single-server queue: 1) The transmitter sends packets from a P -ary alphabet through a queuing system with an infinite buffer and a First-In-First-Out (FIFO) service procedure  ...  Is C P ;K (n)•0 K the largest zero-error code of length n+K for the ShC(P ; K) (in the regime of communication with multiple codewords)?  ... 
doi:10.1109/tit.2017.2756667 fatcat:ap66e6jwcbdkfeiq7zxzidkxcq

Lossless Compression Performance of a Simple Counter-Based Entropy Coder

Armein Z. R. Langi
2011 ITB Journal of Information and Communication Technology  
The average codeword length of 1  code is      q i i i s P R 1 (10) It has been studied elsewhere [3] that this code is optimal for a (monotonically decreasing distribution) source with a first-order  ...  If the codeword table does not have to be transmitted, Huffman code is the shortest length code for statistically independent data.  ... 
doi:10.5614/itbj.ict.2011.5.3.2 fatcat:kqtq46hjcvhevprc3ya2f7iisq

Cross-layer design of LT codes and LDPC codes for satellite multimedia broadcast/multicast services

Zhenbang Wang, Zhenyong Wang, Xuemai Gu, Qing Guo
2013 Chinese Journal of Aeronautics  
With tradeoffs between the LT codes word lengths and the LDPC code rates, optimized cross-layer solutions are achieved with a binary search algorithm.  ...  The codewords generated from an LT encoder are divided into finite-length packets, which are encoded by an LDPC encoder subsequently.  ...  In the physical layer, an LDPC encoder with different code rates R c can generate various lengths of codewords.  ... 
doi:10.1016/j.cja.2013.07.010 fatcat:gr632tpfnvhurnueku5vwcbuzi

On a Relation Between Verifiable Secret Sharing Schemes and a Class of Error-Correcting Codes [chapter]

Ventzislav Nikov, Svetla Nikova
2006 Lecture Notes in Computer Science  
Let C be a code of length p, with set of forbidden distances ∆(C) and with d × p generator matrix G. Analogously let C be a code of length N , with set of forbidden distances ∆( C) and with Proof.  ...  Let C be an error-set correcting code of length N , with a set of forbidden distances ∆( C).  ...  This immediately gives the following requirements for the code in this retransmitting scenario. Theorem 6. Let C be an error-set correcting code of length N , with a set of forbidden distances ∆( C).  ... 
doi:10.1007/11779360_22 fatcat:i3yb4an6zza77cfvwrwifmvhjy
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