V.C. da Rocha

On the entropy bound for optimum homophonic substitution

A proof is given of the fact that, for optimum binary prefix-free homophonic coding, the entropy of a homophone is less than 2 bits greater than that of its antecedent regardless of the alphabet size for this antecedent.

On the iterative decoding of binary product codes over the binary erasure channel

Iterative decoding in two dimensions over the binary erasure channel is investigated when identical linear binary cyclic codes are employed in each dimension. Decoding of the overall code is simplified by employing iterative decoding with cyclic permutations for the component code in each dimension. Decoding complexity versus performance can be traded as a function mainly of the number of minimum weight codewords selected from the dual of each component code. Using results from computer simulations, a comparative analysis is presented of various iterative decoding algorithms in two dimensions applied to simple codes, specifically the product codes (961,676,9), (225,49,25) and (961,256,49).

Multi-edge type unequal error protecting low-density parity-check codes

Irregular low-density parity-check (LDPC) codes are particularly well-suited for transmission schemes that require unequal error protection (UEP) of the transmitted data due to the different connection degrees of its variable nodes. However, this UEP capability is strongly dependent on the connection profile among the protection classes. This paper applies a multi-edge type analysis of LDPC codes for optimizing such a connection profile according to the performance requirements of each protection class. This allows the construction of UEP-LDPC codes where the difference between the performance of the protection classes can be adjusted and with an UEP capability that does not vanish as the number of decoding iterations grows.

Turbo block codes for the binary adder channel

A novel coding scheme for collaborative coding multiple access is introduced for practical application, which permits improving performance with the use of turbo decoding

Multi-edge framework for unequal error protecting LT codes

A multi-edge framework for unequal error protecting (UEP) LT codes is derived by distinguishing between the edges connected to each protection class. Under the framework introduced, two existing techniques for the design of unequal error protecting LT codes can be evaluated and explained in a unified way. Furthermore, a simple and flexible design technique is proposed for UEP LT codes with good performance.

Maximum entropy rate of Markov sources for systems with non-regular constraints

Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained system is limited by the combinatorial capacity of the system if the constraints define a regular language. In the present work, it is shown that this is not an inherent property of regularity but holds in general. To show this, constrained systems are described by generating functions and random walks on trees.

A secret-key cipher based on linear complementary codes

A secret-key cryptosystem is proposed where the key is derived from the linear complements of a given linear block code. >A secret-key cryptosystem is proposed where the key is derived from the linear complements of a given linear block code.<<ETX>>

A hybrid iterative decoder for LDPC codes

A hybrid decoder (HD) for LDPC codes in the presence of additive white Gaussian noise is proposed. This HD employs a min-sum belief propagation (BP) decoding to correct errors, combined with erasure iterative decoding. Whenever BP decoding fails, its output is modified and artificially created erasures are introduced. The proposed HD employs an overall reduced number of iterations and achieves a similar performance to that of traditional BP decoding schemes, especially in the error-floor region, with equivalent implementation complexity. Results of HD performance obtained by computer simulation are presented.

New cyclically permutable codes

A cyclically permutable code is a binary code the codewords of which are cyclically distinct and have full cyclic order. The purpose of this paper is to construct cyclically permutable codes by means of linear p-ary constacyclic codes, where p denotes a prime number. An efficient method is used to select codewords from a constacyclic code which are constacyclically distinct and have full constacyclic order. Through a cyclic representation for the elements of GF(p) and by a correspondence of two-dimensional arrays and N-tuples, the codewords selected produce the codebook of a cyclically permutable code. The cyclically permutable codes constructed are used in the construction of protocol sequences for the M-active-out-of-T users collision channel without feedback.

Turbo decoding of simple product codes in a two user binary adder channel employing the Bahl–Cocke–Jelinek–Raviv algorithm

The main goal in this paper is an investigation of the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm applied in a turbo decoding scheme. Binary product codes are employed in a turbo coding scheme and the channel model considered is the two user binary adder channel (2-BAC) with additive white Gaussian noise. A trellis for two users is constructed for a pair of product codes tailored for use in the 2-BAC in order to employ the BCJR decoding algorithm. Computer simulation is employed to show that product codes on the 2-BAC, employing low-complexity component codes, produces considerable gain with few iterations under iterative BCJR decoding.