Code word

About: Code word is a research topic. Over the lifetime, 8374 publications have been published within this topic receiving 98336 citations.

Sparse code multiple access

Abstract: Multicarrier CDMA is a multiplexing approach in which modulated QAM symbols are spread over multiple OFDMA tones by using a generally complex spreading sequence. Effectively, a QAM symbol is repeated over multiple tones. Low density signature (LDS) is a version of CDMA with low density spreading sequence allowing us to take advantage of a near optimal ML receiver with practically feasible complexity. In this paper, we propose a new multiple access scheme so called sparse code multiple access (SCMA) which still enjoys the low complexity reception technique but with better performance compared to LDS. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together and incoming bits are directly mapped to a multidimensional codeword of an SCMA codebook set. Each layer or user has its dedicated codebook. Shaping gain of a multidimensional constellation is the main source of the performance improvement in comparison to the simple repetition of QAM symbols in LDS. In general, SCMA codebook design is an optimization problem. A systematic sub-optimal approach is proposed here for SCMA codebook design.

Coding for Errors and Erasures in Random Network Coding

Abstract: The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modeled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U. A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum-distance decoder for this metric achieves correct decoding if the dimension of the space V capU is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.

Coded cooperation in wireless communications: space-time transmission and iterative decoding

Abstract: When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit diversity by relaying each other's messages. A particularly powerful variation of this principle is coded cooperation. Instead of a simple repetition relay, coded cooperation partitions the codewords of each mobile and transmits portions of each codeword through independent fading channels. This paper presents two extensions to the coded cooperation framework. First, we increase the diversity of coded cooperation in the fast-fading scenario via ideas borrowed from space-time codes. We calculate bounds for the bit- and block-error rates to demonstrate the resulting gains. Second, since cooperative coding contains two code components, it is natural to apply turbo codes to this framework. We investigate the application of turbo codes in coded cooperation and demonstrate the resulting gains via error bounds and simulations.

Soft decision decoding of linear block codes based on ordered statistics

Abstract: Presents a novel approach to soft decision decoding for binary linear block codes. The basic idea is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is tightly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the tradeoff between performance and decoding complexity is provided. The decoding is based on the reordering of the received symbols according to their reliability measure. The statistics of the noise after ordering are evaluated. Based on these statistics, two monotonic properties which dictate the reprocessing strategy are derived. Each codeword is decoded in two steps: (1) hard-decision decoding based on reliability information and (2) reprocessing of the hard-decision-decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test tightly related to the reprocessing strategy is introduced to reduce the number of computations at each reprocessing stage. For short codes of lengths N/spl les/32 or medium codes with 32 >

Variations on a theme by Huffman

Abstract: In honor of the twenty-fifth anniversary of Huffman coding, four new results about Huffman codes are presented. The first result shows that a binary prefix condition code is a Huffman code iff the intermediate and terminal nodes in the code tree can be listed by nonincreasing probability so that each node in the list is adjacent to its sibling. The second result upper bounds the redundancy (expected length minus entropy) of a binary Huffman code by P_{1}+ \log_{2}[2(\log_{2}e)/e]=P_{1}+0.086 , where P_{1} is the probability of the most likely source letter. The third result shows that one can always leave a codeword of length two unused and still have a redundancy of at most one. The fourth result is a simple algorithm for adapting a Huffman code to slowly varying esthnates of the source probabilities. In essence, one maintains a running count of uses of each node in the code tree and lists the nodes in order of these counts. Whenever the occurrence of a message increases a node count above the count of the next node in the list, the nodes, with their attached subtrees, are interchanged.