Low-complexity iterative detection techniques for Slow-Frequency-Hop spread-spectrum communications with Reed-Solomon coding.

Slow-frequency-hop (SFH) spread-spectrum communications provide a high level of robustness in packet-radio networks for both military and commercial applications. The use of a Reed-Solomon (R-S) code has proven to be a good choice for use in a SFH system for countering the critical channel impairments of partial-band fading and partial-band interference. In particular, it is effective when reliability information of dwell intervals and individual code symbols can be obtained and errors-and-erasures decoding (EE) can be employed at the receiver. In this dissertation, we consider high-data-rate SFH communications for which the channel in each frequency slot is frequency selective, manifesting itself as intersymbol interference (ISI) at the receiver. The use of a packet-level iterative equalization and decoding technique is considered in conjunction with a SFH system employing R-S coding. In each packet-level iteration, MLSE equalization followed by bounded distance EE decoding is used in each dwell interval. Several per-dwell interleaver designs are considered for the SFH systems and it is shown that packet-level iterations result in a significant improvement in performance with a modest increase in detection complexity for a variety of ISI channels. The use of differential encoding in conjunction with the SFH system and packet-level iterations is also considered, and it is shown to provide further improvements in performance with only a modest additional increase in detection complexity. SFH systems employing packet-level iterations with and without differential encoding are evaluated for channels with partial-band interference. Comparisons are made between the performance of this system and the performance of SFH systems using some other codes and iterative decoding techniques

Erasure Insertion in RS-Coded SFH MFSK Subjected to Tone Jamming and Rayleigh Fading

The achievable performance of Reed Solomon (RS) coded slow frequency hopping (SFH) assisted M-ary frequency shift keying (MFSK) using various erasure insertion (EI) schemes is investigated, when communicating over uncorrelated Rayleigh fading channels in the presence of multitone jamming. Three different EI schemes are considered, which are based on the output threshold test (OTT), on the ratio threshold test (RTT) and on the joint maximum output-ratio threshold test (MORTT). The relevant statistics of these EI schemes are investigated mathematically and based on these statistics, their performance is evaluated in the context of error-and-erasure RS decoding. It is demonstrated that the system performance can be significantly improved by using error-and-erasure decoding invoking the EI schemes considered. Index Terms—Tone jamming, OTT, RTT, MO-RTT, SFH, error-and-erasure decoding (EED)

Exponential bounds on error probability with Feedback

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 95-97).Feedback is useful in memoryless channels for decreasing complexity and increasing reliability; the capacity of the memoryless channels, however, can not be increased by feedback. For fixed length block codes even the decay rate of error probability with block length does not increase with feedback for most channel models. Consequently for making the physical layer more reliable for higher layers one needs go beyond the framework of fixed length block codes and consider relaxations like variable-length coding, error- erasure decoding. We strengthen and quantify this observation by investigating three problems. 1. Error-Erasure Decoding for Fixed-Length Block Codes with Feedback: Error-erasure codes with communication and control phases, introduced by Yamamoto and Itoh, are building blocks for optimal variable-length block codes. We improve their performance by changing the decoding scheme and tuning the durations of the phases, and establish inner bounds to the tradeoff between error exponent, erasure exponent and rate. We bound the loss of performance due to the encoding scheme of Yamamoto-Itoh from above by deriving outer bounds to the tradeoff between error exponent, erasure exponent and rate both with and without feedback. We also consider the zero error codes with erasures and establish inner and outer bounds to the optimal erasure exponent of zero error codes. In addition we present a proof of the long known fact that, the error exponent tradeoff between two messages is not improved with feedback. 2. Unequal Error Protection for Variable-Length Block Codes with Feedback: We use Kudrayashov's idea of implicit confirmations and explicit rejections in the framework of unequal error protection to establish inner bounds to the achievable pairs of rate vectors and error exponent vectors. Then we derive an outer bound that matches the inner bound using a new bounding technique. As a result we characterize the region of achievable rate vector and error exponent vector pairs for bit-wise unequal error protection problem for variable-length block codes with feedback. Furthermore we consider the single message message-wise unequal error protection problem and determine an analytical expression for the missed detection exponent in terms of rate and error exponent, for variable-length block codes with feedback. 3. Feedback Encoding Schemes for Fixed-Length Block Codes: We modify the analysis technique of Gallager to bound the error probability of feedback encoding schemes. Using the encoding schemes suggested by Zigangirov, D'yachkov and Burnashev we recover or improve all previously known lower bounds on the error exponents of fixedlength block codes.by Bariş Nakiboḡlu.Ph.D

Erasure Insertion in RS-Coded SFH MFSK Subjected to Tone Jamming and Rayleigh Fading

The achievable performance of Reed Solomon (RS) coded slow frequency hopping (SFH) assisted M-ary frequency shift keying (MFSK) using various erasure insertion (EI) schemes is investigated, when communicating over uncorrelated Rayleigh fading channels in the presence of multitone jamming. Three different EI schemes are considered, which are based on the output threshold test (OTT), on the ratio threshold test (RTT) and on the joint maximum output-ratio threshold test (MO-RTT). The relevant statistics of these EI schemes are investigated mathematically and based on these statistics, their performance is evaluated in the context of error-and-erasure RS decoding. It is demonstrated that the system performance can be significantly improved by using error-and-erasure decoding invoking the EI schemes considered

Reed-Muller codes for random erasures and errors

This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels. Necessarily, the paper also studies properties of evaluations of multi-variate $GF(2)$ polynomials on random sets of inputs. For erasures, we prove that RM codes achieve capacity both for very high rate and very low rate regimes. For errors, we prove that RM codes achieve capacity for very low rate regimes, and for very high rates, we show that they can uniquely decode at about square root of the number of errors at capacity. The proofs of these four results are based on different techniques, which we find interesting in their own right. In particular, we study the following questions about $E(m,r)$, the matrix whose rows are truth tables of all monomials of degree $\leq r$ in $m$ variables. What is the most (resp. least) number of random columns in $E(m,r)$ that define a submatrix having full column rank (resp. full row rank) with high probability? We obtain tight bounds for very small (resp. very large) degrees $r$, which we use to show that RM codes achieve capacity for erasures in these regimes. Our decoding from random errors follows from the following novel reduction. For every linear code $C$ of sufficiently high rate we construct a new code $C'$, also of very high rate, such that for every subset $S$ of coordinates, if $C$ can recover from erasures in $S$, then $C'$ can recover from errors in $S$. Specializing this to RM codes and using our results for erasures imply our result on unique decoding of RM codes at high rate. Finally, two of our capacity achieving results require tight bounds on the weight distribution of RM codes. We obtain such bounds extending the recent \cite{KLP} bounds from constant degree to linear degree polynomials